Matching Supply with Demand An Introduction to
Operations Management, Cachon - Exam Preparation
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Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 2 The Process View of the Organization
1) Butternut is a ski resort in Massachusetts. One of their triple chair lifts unloads 1296
skiers per hour at the top of the slope. (A triple chair lift can carry three passengers per
chair.) The ride from the bottom to the top takes 5 minutes. How many skiers are riding
on the lift at any one time? (Round the answer to the nearest whole number.)
Answer: 108 skiers
Explanation: Use Little's Law. 1296 skiers/hour * 5/60 = 108 skiers
Difficulty: 3 Hard
Topic: Littles Law
AACSB: Analytical Thinking
Blooms: Apply
2) Home Depot's annual turns are 4.7, its Cost of Goods Sold (COGS) is $44.7 billion,
and its gross margin is 33%. Recall, gross margin = (Revenue – COGS) / Revenue. What
is the average inventory it holds? (Round the answer to 2 decimal places.)
Answer: $9.51 billion
Explanation: $44.7 billion / 4.7 =$9.51 billion. Note that average inventory in dollars is
measured by the cost of goods sold, thus the gross margin does not play a role in the
calculation.
Difficulty: 3 Hard
Topic: Littles Law
AACSB: Analytical Thinking
Blooms: Apply
3) A company's holding cost is 16% per year. Its annual inventory turns are 9.5. The
company buys an item for $50. What is the average cost in dollars to hold this item in
inventory? (Round the answer to 2 decimal places.)
Answer: Average cost: $ 0.84
Explanation: The item will be turned 9.5 times a year. Thus, for each turn it stays in
inventory, the holding cost is 16%/9.5 of the cost of the item. Thus, the average cost to
hold this item in inventory is $50 * (16%/9.5) = $0.84
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Apply
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4) Trader Bob, an organic food retail chain, operates 365 days a year. In 2007, the
company turned its inventory approximately 25 times. The company's COGS were 60%
of its Sales and its annual Sales were about $7,000M that year. What was Trader Bob's
average inventory in 2007? (Round the answer to the nearest whole number.)
Answer: $168 million
Explanation: COGS = 0.6 × 7000M = 4200M. Inventory = COGS / Turns = 4200M / 25
= $168M
Difficulty: 3 Hard
Topic: Littles Law
AACSB: Analytical Thinking
Blooms: Apply
5) Assuming Trader Bob's annual inventory holding costs are 20% (an item that cost $10
to purchase would cost $2 to hold in inventory for one year), what is the inventory cost of
an item which sells for $20 and costs Trader Bob $12 to buy? Assume that this item has
inventory turns of 25 per year. (Round the answer to 3 decimal places.)
Answer: $0.096
Explanation: 20% per year with 25 turns is .20/25 = 0.008%. COGs is $12. So, inventory
cost is 0.008% × $12 = $0.096
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Apply
[The following information applies to questions 6-7.]
Joe's Beer, Bait, & Tackle Co.
Joe's Beer, Bait, & Tackle Co. is a small chain of fishing tackle stores in northern
Minnesota. In 2009, the company's revenue was $4,300,000 and its cost of sales was
$3,200,000. Assume 52 weeks and 365 days per year.
6) Joe keeps only 5.5 days-of-supply of inventory on average because much of his
inventory is live bait and micro-brew beer, both of which have a short shelf life. What is
his annual inventory turns? (Round the answer to 2 decimal places.)
Answer: 66.36
Explanation: 365/5.5 = 66.36
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Apply
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7) Given that he has 5.5-days-of-supply of inventory on average, how much inventory
does Joe have on average? (Round the answer to the nearest whole number.)
Answer: $48,219
Explanation: $3,200,000/ (365/5.5) =$48,219
Difficulty: 3 Hard
Topic: Five Reasons to Hold Inventory
AACSB: Analytical Thinking
Blooms: Apply
8) Which of the following best explains why slow turning items may not be profitable at
a brick-and-mortar retailer?
A) If turns are low, days-of-supply will also be low.
B) If turns are low, the gross margin will also be low.
C) If turns are low, the setup costs to stock the shelf will be high.
D) If turns are low, blocking and starving are more likely to occur.
E) If turns are low, units spend a long time on the retailer's shelves.
Answer: E
Explanation: a) If turns are low, days-of-supply will be high. b) it is not necessary that
the gross margin will be low, since various factors affect gross margin. c) setup costs are
not affected by turns. d) starving is less likely to occur when turns are low. e) units spend
too much time on the shelves, and this will increase the inventory holding cost.
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Analyze
9) Is it possible for two firms to have the same annual inventory turns and the same
gross-margin but different days-of-supply?
A) Yes, because days-of-supply measures how long the firm can satisfy demand with its
current inventory whereas inventory turns measures the frequency at which inventory
turns over.
B) Yes, inventory turns and gross margin are related but they are independent of days-ofsupply
C) Yes, the firm with the higher days-of-supply will have the lower return on invested
capital.
D) No, if firms have the same gross-margin then they must have the same days-of-supply.
E) No, if firms have the same inventory turns then they must have the same days-ofsupply.
F) None of the above.
Answer: E
Explanation: Knowing inventory turns uniquely specifies days of supply because
inventory turns = 365/ days of supply.
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
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AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 10-11.]
ProofSmart Inc.
ProofSmart Inc., a supplier of home insulation materials, was burned down in a recent
fire. From the remains of what used to be the accounting ledger, the following
information was recovered:
Inventory
Gross Margin
Inventory Turns
2006
$2,367,121
42%
11
2007
$2,418,257
45%
[unreadable]
Prior to the fire, ProofSmart saw a sales growth of 48% in 2007, a record performance for
the 18-year-old company. (NOTE: Gross margin is defined as 1 - (COGS/Sales).)
10) What was the sales for 2007?
Circle the answer closest to the correct answer.
A) $318,000
B) $38,000,000
C) $43,000,000
D) $66,000,000
E) $85,000,000
F) Cannot be determined from the data given
Answer: D
Explanation: 2006 COGS = 2,367,121 * 11 = $26,038,331
2006 Sales = 26,038,331 / (1-42%) = $44,893,674
2007 Sales = 44,893,674 * 148% = $66,442,638
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Apply
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11) What was the inventory turns for 2007?
Circle the answer closest to the correct answer.
A) 10
B) 11
C) 12
D) 13
E) 14
F) 15
G) Cannot be determined from the data given
H) None of these
Answer: F
Explanation: 2007 COGS = $66,442,638 * (1-45%) = $36,543,451
2007 Inventory Turns = $36,543,451/2,418,257 = 15
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Apply
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[The following information applies to questions 12-13.]
Cheap Retailers
The following table shows financial data (year 2006) for Dirt Cheap Wholesale and
Kwiki-Mart, two U.S. retailers.
Inventories ($MM)
Sales (net $MM)
COGS ($MM)
DIRT CHEAP
WHOLESALE
4754
59217
52762
KWIKI-MART
STORES
40894
397206
326606
Assume that both companies have an average annual holding cost rate of 20% (i.e. it
costs both retailers $2 to hold an item that they procured for $10 for one entire year).
12) How many days, on average, does a product stay in Dirt Cheap's inventory before it
is sold? Assume that stores operate 365 days a year. (Round the answer to 2 decimal
places.)
Answer: 32.89 days
Explanation: Dirt Cheap has a COGS=$52762M = flow rate R. Inventory I = $4754M.
Therefore, flow time T = I/R = 4754/52762 = .09 years, or 32.89 days.
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Apply
13) How much lower (expressed in dollars) is, on average, the inventory cost for Dirt
Cheap compared to Kwiki-Mart of a house hold cleaner valued at $5 COGS? Assume
that the unit cost of the house hold cleaner is the same for both companies and that the
price and the inventory turns of an item are independent. (Round the answer to 3
decimal places.)
Answer: $0.035
Explanation: Inventory turns for Dirt Cheap = 1/.09 = 11.1 turns. Flow time for KwikiMart = Inventory/COGS = 40894/326606 = 0.125. Therefore, inventory turns for KwikiMart = 7.98. Holding costs per year = 20% or $1 per unit for one year. This means
inventory costs per unit for Dirt Cheap = 1/11.1 = $0.09. For Kwiki-Mart, the inventory
costs per unit = 1/7.98 = $0.125. So, Dirt Cheap's costs are 3.5 cents or $0.035 lower.
Difficulty: 3 Hard
Topic: Inventory Turns and Inventory Costs
AACSB: Analytical Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
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Chapter 3 Understanding the Supply Process: Evaluating Process Capacity
1) The Philadelphia Airport has 5 de-icing stations. Each plane uses a single station and
each station takes 11.5 minutes to de-ice a plane. How many planes per hour can be deiced at the Philadelphia Airport? (Round the answer to 2 decimal places.)
Answer: 26.09 planes
Explanation: Each station de-ices 60 min/11.5 min planes per hour. Five stations can deice 60/11.5 * 5 = 26.09 planes.
Difficulty: 3 Hard
Topic: Process Utilization and Capacity Utilization
AACSB: Analytical Thinking
Blooms: Apply
2) Consider a process that has 3 stations, ordered in sequence: 1, 2, and 3. At each station,
two consecutive tasks are performed one after the other. The time (in seconds per unit) it
takes for a single person to perform each task is given in the table below (e.g., task A2
takes 10 seconds per unit):
Station
1
2
3
# of
Task A1 Task A2 Task B1 Task B2 Task C1 Task C2
Workers
1
20
10
2
40
40
1
1
The table also gives the number of workers at each station. What is the capacity of this
process (in units per minute)? (Round the answer to 1 decimal place.)
Answer: 1.5 units/minute
Explanation: The capacity of station 1 is 60/(20 + 10) = 2 units per minute.
Station 2 is 60/(40 + 40) = 0.75 units per worker, or 2 × 0.75 = 1.5 units in total. Station 3
is 60/(15 + 5) = 3 units per minute. The capacity of the process is the capacity of the
bottleneck, which is the slowest step. That is station 2, which produces 1.5 units/min.
Difficulty: 3 Hard
Topic: Process Utilization and Capacity Utilization
AACSB: Analytical Thinking
Blooms: Apply
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3) Consider the following four step process:
The following data are available for the four steps:
Activity time per unit (min)
Capacity per worker (units/min)
Number of workers
A
0.25
4
2
B
0.33
3
3
C
0.2
5
2
D
0.5
2
4
Suppose the steps in activity D are made easier, so the activity time per unit in step D is
reduced by 50% (to 0.25 minutes per unit). If the assignment of workers to steps remains
the same, by how much does the capacity of the entire process increase in units per
minute?
Answer: 0 units per minute
Explanation: Before the change, the process capacity is min (4 × 2, 3 × 3, 5 × 2, 2 × 4) =
8 units per min. If the activity time is cut in half for stage D, then process capacity for
step D is (1/0.25) × 4 = 16 units per min. Step A can only produce 8 units per minute, so
the total capacity of the process doesn't increase.
Difficulty: 3 Hard
Topic: How to Draw a Process Flow Diagram; Workload and Implied Utilization
AACSB: Analytical Thinking; Knowledge Application
Blooms: Analyze
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4) Panini, a popular sandwich shop, offers 3 types of sandwiches: grilled vegetables,
grilled chicken, and pastrami. The table below provides demand data:
Demand per hour
Grilled Vegetables
25
Grilled Chicken
15
Pastrami
10
There are up to five steps in the process of making sandwiches listed below with activity
times. Only 50% of customers want their sandwich toasted, no matter which sandwich is
ordered.
Step
Cut bread
Grill
Slice meat
Toast
Wrap
Grilled Vegetables
.75 minutes
1.4 minutes
2 minutes
.5 minutes
Grilled Chicken
.75 minutes
1.4 minutes
2 minutes
.5 minutes
Pastrami
.75 minutes
3 minutes
2 minutes
.5 minutes
Suppose Panini employs 1 worker at each step. What is the highest implied utilization of
this process? (Round the answer to 3 decimal places.)
Answer: 0.933
Explanation: Evaluate workload per hour on each step: Cut = 0.75 × 50 = 37.5; Grill =
1.4 × 40 = 56; Slice = 3 × 10 = 30; Toast = 2 × 0.5 × 50 = 50; Wrap = 0.5 × 50 = 25.
Implied utilizations are then 37.5/60, 56/60, 30/60, 50/60 and 25/60. The largest one is
56/60. The highest implied utilization = 0.93.
Difficulty: 3 Hard
Topic: Workload and Implied Utilization
AACSB: Analytical Thinking
Blooms: Apply
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[The following information applies to questions 5-6.]
Department of Motor Vehicles
The local Department of Motor Vehicles issues new licenses and renews licenses. (See
the diagram below.) The office receives 110 customers per hour. All customers see a
receptionist first. The receptionist directs them in one of three directions: 75% go directly
to issue license (staffed by 9 workers) where a new photo and license are done, 15% are
required to take an eye test (staffed by one worker), and 10% must first take a multiplechoice electronic written test (on one of three computers). Only 85% of people pass the
eye test and the remaining 15% exit. The customers who pass the eye test proceed to the
written test where 10% of the people fail it, while 90% pass the test and proceed to issue
license.
Data on each station are provided in the following table:
Reception
Eye Test
Written Test
Issue License
Workers
1
1
3
9
Activity time per worker (min)
0.4
5
15
6
5) What is the implied utilization of the Receptionist? (Round the answer to 2 decimal
places.)
Answer: 73.33%.
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Explanation:
Workers
Reception
1
Eye Test
1
Written Test
3
Issue License
9
Processing
Capacity per Implied
time (min)
Flow rate
hour
utilization
0.4
110
150
73%
5
110 * 0.15 = 16.5
12
138%
15
110 * 0.1 + 16.5 * 0.85 = 25.025
12
209%
6
110 * 0.75 + 25.025 * 0.9 = 105.0225
90
117%
Flow rate for receptionist = 110 customers per hour, because all customers first see the
receptionist. Hourly Capacity for receptionist = 60 minutes/0.4 minutes per customer =
150 per customer. Implied utilization of the receptionist = 73.33%.
Difficulty: 3 Hard
Topic: How to Draw a Process Flow Diagram; Workload and Implied Utilization
AACSB: Analytical Thinking
Blooms: Apply
6) What is the implied utilization of issue license? (Round the answer to 2 decimal
places.)
Answer: 116.69%
Explanation: Implied Utilization = Demand/CapacityFlow rate for issuing a license
75% of the customers go directly to issuing a new license: 0.75 × 110 = 82.5 customers
per hour
15% take the eye exam, 0.15 × 110 = 16.5, and 85% of them pass to go to the written test,
0.85 × 16.5 = 14.025 customers
10% go straight to the written test = 0.1 x 110 = 11 customers
90% of the customer pass the written test = 0.9 (11 + 14.025) = 22.5225 customers
The overall flow rate for issuing a license is = 22.5225 + 82.5 = 105.0225 customers per
hour. Hourly Capacity for receptionist = 6 minutes/9 workers = 2/3 minutes= 60
minutes / (2/3 minutes) = 90
Implied Utilization of issuing a license = 105.0225/90 = 116.69
The implied utilization of issue license is 116.69%.
Difficulty: 3 Hard
Topic: How to Draw a Process Flow Diagram; Workload and Implied Utilization
AACSB: Analytical Thinking
Blooms: Apply
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[The following information applies to questions 7-8.]
Happy Toy Company
The Happy Toy Company's R&D department is always looking for great ideas for new
toys. On average, the R&D department generates about 10 new toy ideas a week. To go
from idea to approved product, the idea must go through 5 stages:
In initial screening, a staff member spends 2 hours considering the idea. In mock-up, the
idea is sent to one of many suppliers to produce a physical mock-up of the toy. There is
essentially unlimited capacity at this stage, but it takes 4 days to get the mock-up built,
even though multiple mock-ups can be built simultaneously. In safety testing, each idea
requires 2 days from a staff member to have the idea checked for safety. In focus groups,
each idea requires 3 hours from a staff member to have the idea test marketed. Finally,
the management team meets for 4 hours per idea to decide if the toy should be added to
its line of products sold to customers.
At the end of each stage, successful ideas enter the next stage. All other ideas are
dropped. The following table summarizes the process:
Screening
Mock-up
Safety
Focus group
Final decision
Pr(Success)
60%
50%
35%
20%
Pr(Fail)
40%
Staffing
2
50%
65%
80%
7
1
1
Time per idea put
into this stage
2 hours
4 days
2 days
3 hours
4 hours
For example, there are 7 staff members that work in the safety stage. In each stage, each
idea is processed by only one staff member. For example, once one of the 7 staff
members starts working on an idea in the safety stage, the idea completes that stage in 2
days and either exits or moves to the focus group stage. Everyone works 8 hours per day,
5 days a week.
7) On average, how many ideas are in the mock-up stage? (Round the answer to 1
decimal place.)
Answer: 4.8 ideas
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Explanation: Demand for initial screening = 10 ideas per week. Output from initial
screening = 10 * 60% = 6 ideas per week. 6 ideas pass the screening stage and then enter
the mock-up stage per week. Each idea spends 4 days (5 days per week) or 0.8 weeks in
the mock-up stage. Use Little's Law, 6 * 0.8 = 4.8 ideas in the mock-up stage.
Difficulty: 3 Hard
Topic: Process Utilization and Capacity Utilization
AACSB: Analytical Thinking; Knowledge Application
Blooms: Apply
8) Among these stages, what is the highest implied utilization? (Round the answer to 2
decimal places.)
Answer: 34.29%
Explanation: The highest implied utilization is safety, 34.29%.
time per
available
Pr
idea Demand per hours per
implied
(success) Pr (Fail) Staffing (hours)
week
week
utilization
screening
60%
40%
2
2
10
80
0.2500
mock-up
100%
0
32
6
safety
50%
50%
7
16
6
280
0.3429
focus group
35%
65%
1
3
3
40
0.2250
final dicision
20%
80%
1
4
1.05
40
0.1050
Difficulty: 3 Hard
Topic: Workload and Implied Utilization
AACSB: Analytical Thinking; Knowledge Application
Blooms: Analyze
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[The following information applies to questions 9-10.]
Comfy Shoes, Inc. — Implied Utilization
Comfy Shoes, Inc. builds shoes tailored to meet each individual customer's needs.
Customers who visit the downtown offices of Comfy Shoes in Philadelphia can choose
one or more of the following four custom-tailoring services. Customers receive their
shoes in the mail within a week of their initial visit.
Service
A. Walking Basics
B. Walking Plus
C. Running Basics
D. Running Adv
Description
Take measurements for basic
walking shoes.
Choose a specific design (e.g.
material, color selection).
Take measurements for tailor-made
running shoes.
Consult physical therapist and
obtain precise needs for running
shoes and choose a specific design.
Time
Resource used
12 min.
1 attendant
12 min.
1 attendant
10 min.
1 attendant
40 min.
1 attendant
The company offers the following packages to their customers:
Package 1: Includes only Walking Basics (Service A)
Package 2: Includes Walking Basics and Walking Plus (Services A and B)
Package 3: Walking Basics, Walking Plus, and Running Basics (Services A, B, and C)
Package 4: All four services (A, B, C, and D)
Customers of Comfy Shoes visit the store at a constant rate (you can ignore any effects of
variability) of 20 customers per day. Of these customers, 45% buy Package 1, 10% buy
Package 2, 20% buy Package 3 and 25% buy Package 4. The mix does not change over
the course of the day. The store operates 12 hours a day.
9) What is the implied utilization of the attendant in service D?
Answer: Service D has an implied utilization of 28%.
Explanation: The calculations are summarized below:
Task
A. Walking Basics
B. Walking Plus
C. Running Basics
D. Running Adv
Time
#
Avail.
(min) workers Cap.
12
1
60
12
1
60
10
1
60
40
1
60
Package
1
2
3
0.45 0.10 0.20
9
2
4
2
4
3.33
Difficulty: 3 Hard
Topic: Workload and Implied Utilization
AACSB: Analytical Thinking
Blooms: Analyze
4
Total Utilization
0.25
5
20
0.33
5
11
0.183
4.166 7.5
0.125
16.66 16.66
0.278
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10) Which resource has the highest implied utilization?
A) Service A (Walking Basics)
B) Service B (Walking Plus)
C) Service C (Running Basics)
D) Service D (Running Adv)
Answer: A
Explanation: Service A (Walking Basics) has the highest implied utilization.
Difficulty: 3 Hard
Topic: Workload and Implied Utilization
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 11-12.]
Comfy Shoes, Inc. — Bottleneck
At the end of the spring season, Comfy Shoes anticipates an increase in the demand to 50
customers per day. A change in the mix of packages demanded is also expected: 30% of
the customers ask for Package 1, 10% for Package 2, 10% for Package 3 and 50% for
Package 4. The company will hire an additional attendant to help with Service A
(Walking Basics).
11) What will be the bottleneck in the process given this new demand pattern?
A) Service A (Walking Basics)
B) Service B (Walking Plus)
C) Service C (Running Basics)
D) Service D (Running Adv)
Answer: D
Explanation: Calculations are as follows:
Package
Time
#
Avail. 1
2
Task
(min) workers Cap. 0.3 0.10
A. Walking Basics 12
2
120
15 5
B. Walking Plus
12
1
60
5
C. Running Basics
10
1
60
D. Running Adv
40
1
60
3
0.10
5
5
4.166
4 Total Utilization
0.5
25
50
0.417
25
35
0.58
20.83 25
0.4166
83.33 83.33 1.388
Difficulty: 3 Hard
Topic: Bottleneck, Process Capacity, and Flow Rate (Throughput)
AACSB: Analytical Thinking
Blooms: Analyze
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12) How many customers a day will not be served?
Answer: 7 customers
Explanation: Service D receives 0.5*(50/12)*40=83.33 minutes of work every hour.
Only 60 minutes of work can be served. Thus, every hour, 23.33 minutes of work, or
23.33/40th of a customer is not served. Customers not served in a day = [(83.333 –
60)/40]*12=7 customers a day will not be served. Put another way, the worker has
60x12=720 minutes available each day. 40 min per customer means that 720/40=18
customers can be served. 50% of 50 = 25 customers arrive each day, so 25–18=7 cannot
be served.
Difficulty: 3 Hard
Topic: Bottleneck, Process Capacity, and Flow Rate (Throughput)
AACSB: Analytical Thinking; Knowledge Application
Blooms: Analyze
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[The following information applies to questions 13-15.]
Old City Photographics
Located alongside a cobblestoned street in Old City, Old City Photographics (OCP)
specializes in the processing of the traditional 35mm negative film, a once dominant
photographic medium now in decline due to the popularity of digital photography. OCP
offers three packages to their customers. With the standard package, the customer gets a
set of 6"×4" prints for $19.99. The deluxe package adds to the standard package a CDROM of high-resolution scans of the pictures for $29.99. Finally, the $39.99 pro package
is similar to the deluxe package in that it comes with a CD-ROM, although the customer
gets a contact print rather than a set of prints. (A contact print is an 8"×10" sheet of
photographic paper that has all pictures on the roll of film printed next to each other at
reduced dimensions and is used as an index.) The workflow for OCP is shown below (s =
standard, d = deluxe, p = pro):
OCP is operated by one person at every station.
13) On average, OCP receives 13 jobs per hour which consist of 44% standard, 37%
deluxe and 19% pro. Which of the following statement best describes OCP's process?
A) The process is demand-constrained.
B) The process is capacity-constrained and "process film" is the bottleneck
C) The process is capacity-constrained and "scan film" is the bottleneck.
D) The process is capacity-constrained and "make 6"×4" prints" is the bottleneck.
E) The process is capacity-constrained and "make contact print" is the bottleneck.
Answer: A
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Explanation: Implied utilization is:
(100% * 13 jobs/hr * 2min/job ) / (60 min/hr) = 0.43 at "process film"
((37% + 19%) * 13 jobs/hr * 5 min/job ) / (60 min/hr) = 0.61 at "scan film"
((44% + 37%) * 13 jobs/hr * 4 min/job) / (60 min/hr) = 0.70 at "make 6"×4" prints"
(19% * 13 jobs/hr * 10 min/job) / (60 min/hr) = 0.41 at "make contact print"
As implied utilization is less than 1.0 at all steps, the process is demand-constrained.
Difficulty: 3 Hard
Topic: Bottleneck, Process Capacity, and Flow Rate (Throughput)
AACSB: Analytical Thinking; Knowledge Application
Blooms: Analyze
14) What is the implied utilization (ratio of workload relative to capacity) at "Scan
Film"?
A) less than 50%
B) 50% to 60%
C) 60% to 70%
D) 80% to 90%
E) 90% to 100%
F) more than 100%
Answer: C
Explanation: ((37% + 19%) * 13 jobs/hr * 5 min/job ) / (60 min/hr) = 0.61
Difficulty: 3 Hard
Topic: Workload and Implied Utilization
AACSB: Analytical Thinking
Blooms: Apply
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15) Fixing the relative proportions of job types, what is the largest number of jobs per
hour that OCP can handle? Choose the answer from the list below that is closest to the
correct answer.
A) 10
B) 11
C) 12
D) 13
E) 14
F) 15
G) 16
H) 17
J) 18
Answer: J
Explanation: From the calculations for OCP1, we know that "make 6"×4" prints" will
become the bottleneck once the process is capacity-constrained (if the mix of jobs does
not change). The answer to our present question is given by the solution X to the equation
((44% + 37%) * X jobs/hr * 4 min/job) / (60 min/hr) = 1.00.
Re-arranging the equation yields X = (60 min/hr) / (81% * 4 min/job) = 18.5 jobs/hr.
Difficulty: 3 Hard
Topic: Multiple Types of Flow Units
AACSB: Analytical Thinking; Knowledge Application
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 4 Estimating and Reducing Labor Costs
[The following information applies to questions 1-3.]
Furniture Face Lift refinishes old wood furniture. Their process for refinishing chairs has
8 workers and 4 stations. Each chair starts at the Stripping station, then goes to Priming,
then to Painting and finally to Inspection. Where there are multiple workers within a
station, each worker works independently on his/her own chair. Assume inventory
buffers are allowed between each station.
Station
Stripping
Priming
Painting
Inspection
Staffing
3
2
2
1
Processing time (hours
per chair per worker)
2.5
1.5
1.75
0.8
1) What is the maximum number of chairs per hour that can be produced? Assume they
start the day with inventory at each station to work on.
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Answer: 1.14 chairs per hour.
Explanation: The average time needed to finish one chair at each station are as follows.
Capacity = staffing/activity time
Station
Stripping
Priming
Painting
Inspection
Staffing
3
2
2
1
Activity time (hours) Capacity = staffing/activity time
2.5
1.2
1.5
1.333333333
1.75
1.142857143
0.8
1.25
Painting is the bottleneck since it has the lowest capacity. The process capacity is the
capacity of the bottleneck. Thus, the process capacity is 1.14 chairs per hour.
Difficulty: 3 Hard
Topic: Analyzing an Assembly Operation
AACSB: Analytical Thinking
Blooms: Apply
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2) Suppose at the start of the day there is no inventory of chairs in the shop. That is, there
are no chairs within any of the stations nor between them in any buffer. A truck loaded
with 15 chairs arrives. How many hours will it take them to complete these 15 chairs?
Answer: 18.8 hours
Explanation: It takes 2.5 + 1.5 + 1.75 + 0.8 = 6.55 hours for the first chair to be
produced. It takes 1/1.14 hours for each of the subsequent chairs. In total, it takes 6.55 +
1/1.14 * 14 = 18.8 hours to complete 15 chairs.
Difficulty: 3 Hard
Topic: Analyzing an Assembly Operation
AACSB: Analytical Thinking
Blooms: Analyze
3) Suppose now that each worker is trained to do all tasks and each worker works on a
chair from start to finish, i.e., each worker does Stripping, Priming, Painting, and
Inspection. What is the maximum capacity of the process in chairs per hour?
Answer: 1.22 chairs per hour
Explanation: In this system, there will be no bottleneck, i.e., every worker is working at
their full capacity. It takes each worker 2.5 + 1.5 + 1.75 + 0.8 = 6.55 hours to finish one
chair. 3 + 2 + 2 + 1 = 8 workers can complete 8/6.55 = . The maximum capacity is 1.22
chairs per hour.
Difficulty: 3 Hard
Topic: Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 4-6.]
The White Tooth Device Company is a manufacturer of high-end electric toothbrushes.
For each toothbrush, there is a sequence of assembly steps performed by five workers.
Each worker does two tasks. Inventory buffers are allowed between workers.
Worker
A
A
B
B
C
C
D
D
E
E
Task
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
Time (seconds)
40
25
20
15
10
15
10
20
25
35
4) What is the capacity of this process (toothbrushes per minute)?
Answer: 0.92 toothbrushes per minute.
Explanation: The process time for each worker is: A: 65 sec, B: 35 sec, C: 25 sec, D: 30
sec, E: 60 sec. Worker A is the bottleneck. The process capacity is 60sec/65sec = 0.92
toothbrushes per minute
Difficulty: 3 Hard
Topic: Analyzing an Assembly Operation
AACSB: Analytical Thinking
Blooms: Apply
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5) Suppose two workers could be hired, F and G, and they take the same time to complete
tasks as the current five workers. F and G can be assigned to work on the same pair of
tasks as one of the current workers. For example, F could be assigned tasks T1 and T2
(just like worker A) while G is assigned T5 and T6 (just like worker C). They cannot be
assigned tasks that are currently assigned to two workers. For example, F cannot be
assigned to tasks T2 and T3 (because they are currently being done by workers A and B).
What is the capacity of this process with workers F and G included (toothbrushes per
minute)?
Answer: 1.71 toothbrushes per minute
Explanation: Assign one new worker, F, along the bottleneck worker A. Thus, the time
to complete T1 and T2 for one toothbrush, for workers A and F, is 65 sec/2 = 32.5 sec.
Now the bottleneck is worker E. Assign the other worker, G, to tasks T9 and T10. The
time to complete T9 and T10 for one toothbrush is 60 sec/2 = 30sec. The new bottleneck
is B, with 35 sec activity time. Thus, the new process capacity with workers F and G is
60 sec/35 sec = 1.71 toothbrushes per minute.
Difficulty: 3 Hard
Topic: Scale Up to Higher Volume
AACSB: Analytical Thinking
Blooms: Analyze
6) Return to the case of 5 workers. Suppose the assignment of tasks to workers can
change, but the sequence of tasks must remain the same. Workers must be assigned to
consecutive tasks and each task can be assigned to only one worker. For example, worker
A could do tasks T1-T3 (because they are consecutive) but cannot be assign T1, T2, and
T4. If worker A is assigned to tasks T1-T3, then worker B's first task must be T4 (worker
B cannot also be assigned to task T3). Because a U-shaped line is used, tasks T1 and T10
can actually be considered consecutive tasks — worker A could be assigned tasks T10,
T1, and T2. What would the maximum capacity be after possibly reassigning tasks
(toothbrushes per minute)?
Answer: 1.2 toothbrushes per hour
Explanation: The total process time for one toothbrush is (40 + 25 + 20 + 15 + 10 + 15 +
10 + 20 + 25 + 25 + 35) = 215 sec. If we have 5 workers, the system can do no better
than 215/5 = 43sec/worker. We try to assign tasks in which the process time at the
slowest worker is as close as to 43sec/worker. The best we can do is the following: A:
T1(40 sec), B: T2 and T3(45 sec), C: T4-T7(50 sec), D: T8-T9 (45 sec), T10(35 sec). The
bottleneck is worker C. The process capacity is 60 sec/50sec = 1.2 toothbrushes per hour.
Difficulty: 3 Hard
Topic: Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 7-10.]
Imagine US is a startup that offers high definition 3D prenatal ultrasounds for high-end
customers. The service process includes five activities that are conducted in the sequence
described below. (The time required for each activity is shown in parentheses):
Activity 1: Welcome a patient and explain the procedure. (8 minutes)
Activity 2: Prep the patient (e.g., show them to the room, apply ultrasound gel). (5
minutes)
Activity 3: Take images. (14 minutes)
Activity 4: Analyze images. (12 minutes)
Activity 5: Discuss diagnostic with the patient. (16 minutes)
At each location, there are employees (servers) S1, S2, and S3. The assignment of tasks
to servers is the following:
S1 does Activity 1.
S2 does Activities 2 and 3.
S3 does Activities 4 and 5.
7) What is the capacity of this process (in customers per hour)?
Answer: 2.14 customers per hour
Explanation: The activity time at S1, S2, and S3 is 8 minutes, 19 minutes, and 28
minutes, respectively. S3 is the bottleneck. The capacity of the process is the capacity of
the bottleneck. 60 min/28 min = 2.14 customers per hour.
Difficulty: 3 Hard
Topic: Analyzing an Assembly Operation
AACSB: Analytical Thinking
Blooms: Apply
8) Suppose that 2 patients arrive every hour on average. Ignoring any "start of day" or
"end of day" effects, what is the utilization of Server 1 (as a %)?
Answer: 26.67%
Explanation: S1's capacity is 60min/8min=7.5 customers/hour, and the demand rate is 2
customers/hour, which is smaller than the process capacity 2.14 customers/hour. Thus,
the system is demand-constrained. The utilization of S1 is: 2/7.5 = 26.67%.
Difficulty: 3 Hard
Topic: Labor Content and Idle Time; Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Analyze
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9) Suppose each activity can be done by any server and any server can do any set of
activities. However, each activity is done by only one server. For example, a feasible
assignment includes: S1 does activities 1 and 5, S2 does activities 2 and 4, and S3 does
activity 3. Of course, the original assignment of servers to activities is also feasible. What
is the maximum capacity of the process (in customers per hour)?
Answer: 3 customers per hour
Explanation: The total activity time = 8 + 5 + 14 + 12 + 16 = 55 min. A perfectly
balanced line will have each server working 55/3=18.3min. The best we can do is to
combine the 8min task with the 12 min task, and the 5 min task with the 14 min task.
Thus, the capacity of the process will be 60 min/20 min = 3 customers per hour.
Difficulty: 3 Hard
Topic: Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Analyze
10) Now suppose each activity can be assigned to more than one server, each activity can
be done by any server and any server can do any set of activities. What is the maximum
capacity of the process (in customers per hour)?
Answer: 3.27 customers per hour
Explanation: We assign all the tasks to each server. There will be no idle time in this
case. The process capacity is 60min/55min * 3 = 3.27 customers per hour.
Difficulty: 3 Hard
Topic: Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Apply
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[The following information applies to questions 11-12.]
A process requires six tasks, A, B, C, D, E, and F, that must be performed in that order.
Currently, there are 3 employees that are equally skilled at each task. Employee 1 is
assigned tasks A and B, employee 2 is assigned tasks C and D, and employee 3 is
assigned tasks E and F. The task times (all in seconds) are given in the process diagram
below. For example, task A requires 90 seconds.
11) Suppose the system started without any work in process inventory (i.e., an empty
system). How long would this process take to produce 10 units (in seconds)?
Answer: 1,440 seconds
Explanation: The first unit takes 270 seconds. The next 9 units take 9 × 130 seconds =
1,170. The total time is 270 + 1,170 = 1,440.
Difficulty: 3 Hard
Topic: Time to Process a Quantity X Starting with an Empty Process
AACSB: Analytical Thinking
Blooms: Apply
12) Suppose now the 3 employees can be assigned to any task, but employees must be
assigned to consecutive tasks (e.g., an employee cannot be assigned tasks B and D). What
would be the processes' maximum capacity (units per hour)?
Answer: 40 units per hour
Explanation: If you assign task A to employee 1, tasks B and C to employee 2, and tasks
D, E and F to employee 3, then employee 2 is the bottleneck with a capacity of 1/(40 +
60) = 1/100 units per second. There are 3600 seconds in an hour so the process can
produce 1/100 × 3600 = 36 units. However, if you assign every task to each employee,
then each employee takes 270 seconds per unit, or one unit produced every 90 seconds,
which yields 3600 / 90 = 40 units per hour.
Difficulty: 3 Hard
Topic: Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 13-17.]
Mr. K's Hair Salon
Mr. K's is a very popular hair salon. It offers high-quality hair-styling and physical
relaxation services at a reasonable price, so it always has unlimited demand. The service
process includes five activities that are conducted in the sequence described below. (The
time required for each activity is shown in parenthesis):
Activity 1: Welcome a guest and offer homemade herb tea. (10 minutes)
Activity 2: Wash and condition hair. (10 minutes)
Activity 3: Neck, shoulder, and back stress release massage. (10 minutes)
Activity 4: Design the hairstyle and do the hair. (25 minutes)
Activity 5: Check out the guest. (5 minutes)
Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment
of tasks to servers is the following:
S1 does Activity 1.
S2 does Activities 2 and Activity 3.
S3 does Activities 4 and Activity 5.
13) Which server is the bottleneck of the process?
A) S1
B) S2
C) S3
Answer: C
Explanation: S1 can process 1/10 customers per minute. S2 can process 1/20 customers
per minute. S3 can process 1/30 customers per minute. S3 has the lowest capacity and is
hence the bottleneck.
Difficulty: 3 Hard
Topic: Time to Process a Quantity X Starting with an Empty Process
AACSB: Analytical Thinking
Blooms: Apply
14) What is the utilization of server 2?
Answer: 66.7%
Explanation: Since we assume that there is unlimited demand, the flow rate is equal to
the capacity of the process, i.e., 2 customers per hour. The capacity of S2 is 3 customers
per hour. The utilization at S2 is 2/3 = 66.7%.
Difficulty: 3 Hard
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Apply
15) What is the average labor utilization of the servers? Assume the process operates at
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its capacity.
Answer: 66.7%
Explanation: The labor content = 10 + 20 + 30 = 60 min. and total idle time = 20 + 10 =
30 min. The Average labor utilization = 60/(60 + 30) = 2/3 = 66.7%.
Difficulty: 3 Hard
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Apply
16) Assume a wage rate of $18 per hour. What are the direct labor costs for one guest?
Answer: $27
Explanation: Direct labor costs = (Total wages) / (flow rate). There are three employees
with a wage of $18/hr implying that the total wages per hour. are given by 18 × 3 =
$54/hr. We deduce that direct labor costs = 54/2 = $27.
Difficulty: 3 Hard
Topic: Labor Content and Idle Time; Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Apply
17) To increase the service rate, Mr. K's is considering two alternatives:
Alternative I: To hire a new employee to help any one (and only one) of the servers
without changing the tasks performed by each server.
Alternative II: To redesign the assignment of tasks to servers. For this, Mr. K's is
evaluating to reassign Activity 5 from S3 to S1.
What would be the costs of direct labor of serving one guest under each of the two
alternatives? Assume that the system operates at its capacity.
Answer: Alternative I: $24; Alternative II: $22.50
Explanation: Under Alternative I, the additional worker would help S3 and under this
case the bottleneck would become S2 with a capacity of 3 customers/hr.
Direct labor costs = (18 * 4)/3 = $24
Under Alternative II, S3 would still be the bottleneck but the new capacity of S3 will be
of 60/25 = 2.4 customers/hr.
Direct labor costs = (18 * 3)/2.4 = $22.50
Difficulty: 3 Hard
Topic: Scale Up to Higher Volume; Increasing Capacity by Line Balancing
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 18-25.]
ONE HOUR LOAN
One Hour Loan offers customized loans. Customers call a toll-free number with a
specific loan request and obtain a response within an hour. One Hour Loan's business
process includes five activities which must be conducted in the sequence described
below. (The time required for each activity is shown in parenthesis):
Activity 1: Answer customer call and record key information. (4 minutes)
Activity 2: Gather and format the data (obtain credit scores, organize customer specific
needs) for analysis (5 minutes)
Activity 3: Analyze the information: Check the creditworthiness and decide loan amount
and APR to offer. (7 minutes)
Activity 4: Perform final checks on loan offer (2 minutes)
Activity 5: Call the customer back with the new loan offer and close. (4 minutes)
Three workers conduct the whole process in a worker paced line. The assignment of tasks
to workers is the following:
W1 does Activity 1.
W2 does Activities 2 and 3.
W3 does Activities 4 and 5.
18) What is the bottleneck of the process?
A) W1
B) W2
C) W3
Answer: B
Explanation: W2 is the bottleneck.
Difficulty: 2 Medium
Topic: Analyzing an Assembly Operation
AACSB: Analytical Thinking
Blooms: Apply
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19) How much time will it take to process 100 loans? (Assume that the process starts
with an empty production line.)
Answer: 1,210 minutes
Explanation: Time through an empty process +
=4+5+7+2+4+
= 1210 minutes
Difficulty: 2 Medium
Topic: Time to Process a Quantity X Starting with an Empty Process
AACSB: Analytical Thinking
Blooms: Apply
20) What is the utilization of worker 3? (You can assume that the process operates at
capacity and you do not have to consider any empty system effects).
Answer: 0.5
Explanation:
utilization =
utilizationw3 =
= 0.5
Difficulty: 2 Medium
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Apply
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21) What is the average labor utilization of the workers? Assume the process operates at
its capacity and there are no empty system effects.
Answer: 11/18
Explanation:
uworker1 =
uworker2 = 1
=
uworker3 =
∴ average utilization =
Difficulty: 2 Medium
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Analyze
22) What are the direct labor costs for one loan application? Assume a wage rate of $20
per hour.
Answer: $12 per loan
Explanation:
Cost of direct labor =
=
= $12 per loan
Difficulty: 2 Medium
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Apply
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23) To increase the production rate, One Hour Loan is considering two alternatives:
Alternative I: To hire a new worker to help any one (and only one) of the workers
without changing the tasks performed by each worker.
Alternative II: To redesign the assignment of tasks to workers. For this, the company is
evaluating to re-assign Step 2 from W2 to W1.
Suppose that Alternative I is chosen. Which worker should the new employee assist?
A) W1
B) W2
C) W3
Answer: B
Explanation: The new employee should assist W2 because he is the bottleneck.
Difficulty: 2 Medium
Topic: Increasing Capacity by Line Balancing; Scale Up to Higher Volume
AACSB: Analytical Thinking
Blooms: Apply
24) What would be the costs of direct labor of one loan application under the solution
depicted above? Assume there is sufficient demand (system operates at its capacity) and
there are no empty system effects.
Answer: $8
Explanation: To compute the cost, we calculate:
Difficulty: 2 Medium
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Apply
= $8
25) What would be the direct labor costs for Alternative II?
Answer: $9
Explanation:
To compute the cost, we calculate:
Difficulty: 2 Medium
Topic: Labor Content and Idle Time
AACSB: Analytical Thinking
Blooms: Apply
= $9
Matching Supply with Demand: An Introduction to Operations Management, 4e
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(Cachon)
Chapter 5 Batching and Other Flow Interruptions: Setup Times
and the Economic Order Quantity Model
[The following information applies to questions 1-2.]
The Yum and Yee food truck near the business school serves customers during the lunch
hour by taking orders and making fresh batches of stir-fry. Customers have only one
choice during the lunch hour since the objective is to maximize the number of customers
served. Assume that each customer places just one lunch order, and all lunch orders are
the same size—one unit of stir-fry.
The stir-fry cooking works in this manner. First, a batch of orders is cooked in a wok by
one person. The cooking depends upon the number of orders in the batch. The time to
cook just one order is 3 minutes. For each additional order in the batch, it takes 0.5
minutes more to cook. Thus, cooking two orders in a batch takes 3.5 minutes, cooking
three orders takes 4 minutes, and so on.
The other process is bagging and accepting payments (done by a separate person), which
takes 0.80 minutes per order.
1) If Yum and Yee operates with batch sizes of 8 units, what is their process capacity (in
orders per minute)?
Answer: 1.23 units per minute
Explanation: The capacity for cooking setup time is 2.5 min. and processing time per
order is 0.5min. The food truck produces 8 units with 2.5min + 0.5min * 8 = 6.5 min. The
capacity is 8/6.5 min = 1.23 units/min.
The capacity for bagging and accepting payments: 1min/0.8min = 1.25units/min.
The process capacity is the capacity of cooking(bottleneck) = 1.23unit/min.
Difficulty: 3 Hard
Topic: The Impact of Setups on Capacity
AACSB: Analytical Thinking
Blooms: Analyze
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2) Calculate the batch size (in orders) that will maximize the overall flow rate (assume
there is ample demand)? Do NOT round the batch size (i.e., assume for this calculation
that a non-integer batch size is possible).
Answer: 8.33 units per batch
Explanation: Optimal order size should equalize the capacity of the cooking step and the
bagging step. That is, suppose the batch size is denoted by x, then we have (2.5 + 0.5 * x)
/x = 0.8 min. Solve for x; x = 8.33 units/batch.
Or use the formula:
Capacity = 1/0.8 min = 1.25 orders/min
Batch size = Capacity * setup time /(1- capacity * processing time)
= 1.25 * 2.5 / (1- 1.25 * 0.5) = 8.33 units/batch.
Difficulty: 3 Hard
Topic: Interaction between Batching and Inventory
AACSB: Analytical Thinking
Blooms: Analyze
3) Recall the salt production process. At a facility on the island of Vanuatu, they have 7
salt pans, each covering 6 acres. The pans are flooded with sea water, and evaporation
leaves the pan dry, covered with sea salt. From the time the pan is flooded, it takes 10
weeks on average for a salt pan to be ready for harvesting. Harvesting the salt involves
using bulldozers to scoop up the salt, which is then carted off to a terminal to be loaded
on a ship. A single bulldozer requires 3 days to harvest each acre of salt, and this facility
has 2 of them. There is ample capacity of trucks to transport salt from the pans to the
terminal. Harvesting can occur any day during the week, and clearly, the pan cannot be
flooded during harvesting. Each acre yields 1000 cubic meters (m3) of salt. After the salt
is harvested from a pan, it is flooded with sea water to begin the process again. Assume
(i) there is ample demand for salt, and (ii) ship capacity and the loading process is
sufficiently fast so that they do not constrain the process. How much salt can this facility
produce per day on average (in m3)?
Answer: 532 m3
Explanation: Every 6 acres require 10 weeks for evaporation. With one bulldozer, 18
days are required for harvesting, but they have 2, so the harvesting of the pan can be done
in 9 days. So, 6 acres can be produced in 10 × 7 + 9 = 79 days. Six acres yield 1,000 m3,
and 6,000 / 79 = 75.9 m3 is produced per pan per day. There are 7 pans, so the total
production is 7 × 75.9 = 532 m3
Difficulty: 3 Hard
Topic: Interaction between Batching and Inventory
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 4-6.]
Sarah's Organic Soap Company makes four kinds of organic liquid soap: regular,
lavender, citrus, and tea tree. The demand for the four scents are 150, 120, 75, and 50 kg
per hour respectively. Sarah's production process can produce any soap at the rate of 450
kg per hour, but 1.5 hours are needed to switch between scents. During those switchover
times, the process doesn't produce any soap. Sarah wants to choose a production schedule
that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii)
minimizes the amount of inventory held.
4) How many kg of regular soap should Sarah produce before switching over to another
scent?
Answer: 7,363.636 kg
Explanation: The total setup time is 1.5 * 4 = 6 hours. The total demand for all four
scents per hour is 150 + 120 + 75 + 50 = 395 kg/hour. The process capacity equals the
demand, which is 395 kg/hr. The processing time = 1/450 hr. The batch size = capacity *
setup time / (1- capacity * processing time) = 395 * 6 / (1- 395/450) = 19,390.91 kg.
In each batch, 150/395 * 19,390.91 = 7,363.636 kg of regular soap should be produced.
Difficulty: 3 Hard
Topic: Setup Times and Product Variety
AACSB: Knowledge Application
Blooms: Apply
5) Sarah needs to purchase organic palm oil to make her soaps. She needs 1,000 kg of
palm oil per day on average. The supplier charges a $60 delivery fee per order (which is
independent of the order size) and $4.75 per kg. Sarah's annual holding cost is 25%.
Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory
holding and ordering costs, how much palm oil should she purchase with each order (in
kg)?
Answer: 5,125.786 kg
Explanation: Use EOQ formula, Q = sqrt (2 * fixed cost * flow rate/holding cost)
= sqrt (2 * $60 * 1,000/ ($4.75 * 0.25/(52 * 5))) = 5,125.786 kg.
Difficulty: 3 Hard
Topic: Balancing Setup Costs with Inventory Costs: The EOQ Model
AACSB: Analytical Thinking
Blooms: Analyze
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6) Sarah's supplier is willing to sell her palm oil at a 5% discount if she purchases 10,000
kg at a time. If she were to purchase 10,000 kg per order, what would be her average
inventory holding and delivery fees per day (in $)? (Note: Do not include her purchasing
costs per day, which would be 1,000 × 4.75 × 95%.)
Answer: Inventory cost per day: $21.6947; Delivery fees per day: $6
Explanation: Delivery cost per day will be $60/(10,000kg/1,000kg/day) = $6/day.
The average inventory level is 10,000/2 = 5,000kg. Inventory cost per day will be $4.75 *
(1-5%) * (25%/52/5) * 5,000kg = $21.6947. The sum of the two is $27.6947.
Difficulty: 3 Hard
Topic: Balancing Setup Costs with Inventory Costs: The EOQ Model
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 7-9.]
Joe needs to purchase malt for his micro-brew production. His supplier charges $35 per
delivery (no matter how much is delivered) and $1.20 per gallon. Joe's annual holding
cost per unit is 35% of the dollar value of the unit. Joe uses 5,000 gallons of malt per
week.
7) How many gallons should Joe order from his supplier with each order?
Answer: 6,583 gallons
Explanation: Suppose Joe orders x gallons per order. The fixed portion of the delivery
cost is $35 * 5,000 * 52/x per year. The average annual inventory holding cost is x/2 *
1.2 * 35%. Then, the total weekly cost is $35 * 5,000 * 52/x + x/2 * 1.2 * 35%. The cost
is minimized at x = sqrt (35 * 5,000 * 52/ (0.6 * 35%)) = 6,583 gallons.
Difficulty: 3 Hard
Topic: Balancing Setup Costs with Inventory Costs: The EOQ Model
AACSB: Analytical Thinking
Blooms: Analyze
8) Suppose Joe were to order 3,800 gallons each time he orders. How many orders per
year would he place on average?
Answer: 68.42 orders per year
Explanation: 5,000 * 52 /3800 = 68.42
Difficulty: 3 Hard
Topic: Balancing Setup Costs with Inventory Costs: The EOQ Model
AACSB: Knowledge Application
Blooms: Apply
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9) If Joe places an order for 15,000 gallons, then he will receive a 4% discount off the
regular price of $1.20. If Joe were to do this with each order, what would be his average
weekly total cost (in $)? Note: Include the cost to purchase the units, the delivery
charges, and inventory holding costs.
Answer: $5,830 is the average weekly total cost
Explanation: With a 4% discount, the malt is 1.2 * (1 - 0.04) = $1.152 per gallon. The
weekly purchase cost is $1.152 * 5,000 = $5,760. Weekly delivery charges equal
5,000/15,000 * $35 = $11.67. The weekly inventory holding cost is 15,000/2 * $1.152 *
(35%/52) = $58.15. The total cost is $5,760 + $11.67 + $58.15 = $5,830.
Difficulty: 3 Hard
Topic: Balancing Setup Costs with Inventory Costs: The EOQ Model
AACSB: Analytical Thinking
Blooms: Analyze
10) It is costly to hold inventory (e.g., storage costs, obsolescence costs, etc.) but
inventory can also be useful in a process because… (choose the best answer)
A) Adding inventory to a process will shorten the average time a unit spends in a process.
B) Adding inventory to a process can increase the capacity of the process.
C) Adding inventory to a process is likely to increase quality.
D) None of the above.
E) All of the above.
Answer: B
Explanation: Adding inventory (or adding buffer) reduces the chance that the process is
starving for items to work on, thus improves the processes capacity. The average time
that a unit spends in a process is the sum of processing time at each step and the time
spent waiting for servers to be available. Adding inventory will not affect the processing
time nor the waiting time, as waiting time is determined by the processing time of each
step. Thus, A is not correct. Inventory does not influence quality either.
Difficulty: 3 Hard
Topic: Choosing a Batch Size in the Presence of Setup Times
AACSB: Reflective Thinking
Blooms: Analyze
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11) Which of the following most directly expresses the motivation behind the expression
"Do not block the bottleneck!"?
A) If the bottleneck has nothing to work on, the overall capacity of the process will be
lower than it could be.
B) If the bottleneck is prevented from working (e.g., it has nowhere to put its output,) the
overall capacity will be reduced.
C) Blocking the bottleneck will increase the coefficient of variations of the arrival
process, which decreases capacity.
D) Blocking the bottleneck increases inventory turns, which increases the annual holding
costs.
E) It is not good to block the bottleneck because there are economies of scale in inventory
management.
Answer: B
Explanation: To prevent a reduction in capacity, processing at the bottleneck must
remain constant. If work at the bottleneck location is blocked, then overall production is
affected.
Difficulty: 3 Hard
Topic: Choosing a Batch Size in the Presence of Setup Times
AACSB: Reflective Thinking
Blooms: Analyze
12) Which of the following most directly expresses the motivation behind the expression
"Buffer or Suffer"?
A) Adding product variety to a process with setup times is likely to increase the average
amount of inventory needed.
B) To increase capacity, it is important to reduce setup times in a process.
C) If you want to increase the capacity of a process, add capacity first to the bottleneck.
D) If there is variability in the arrival process, or during activity times, make sure there is
sufficient inventory between stages, otherwise capacity will be reduced.
E) When there are setup costs, producing in large enough batches is important to avoid
reducing capacity.
Answer: D
Explanation: The addition of extra inventory, or buffer, helps prevent a loss in
production time during periods of inactivity. Production capacity is maximized when
there is a safety stock of supplies between production stages.
Difficulty: 3 Hard
Topic: Interaction between Batching and Inventory
AACSB: Reflective Thinking
Blooms: Analyze
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13) Henry Ford famously proclaimed, "You can have any color you want, as long as it is
black." Which of the following best reflects his motivation for this position?
A) He believed that customers didn't like other colors, so why go through the hassle of
making different color cars.
B) With more than one color, the process would have switch over time, and that could
reduce the overall utilization of the process.
C) He wanted to establish "black" cars as part of his company's brand image at that time.
D) Assembling non-black cars takes longer than black cars.
E) He understood that increasing inventory in a process could lead to a longer flow time
through the process.
Answer: B
Explanation: With more than one color, the process would have to switch from one color
to another, which would incur idle time on switchovers and utilization would decrease.
Difficulty: 3 Hard
Topic: Interaction between Batching and Inventory
AACSB: Reflective Thinking
Blooms: Analyze
14) A high-volume paper manufacturer borrows $1M to purchase a new printing
machine. The annual debt payment is $150,000. The machine can make different types of
paper, but the machine must be shut down for one day each time it switches production to
a different kind of paper. The manufacturer spends about 24 days per year due to produce
changeovers. Dividing the annual debt payment over those 24 days yields $6,250 per day.
Should this cost, $6,250, be used as an input to the EOQ model to determine optimal
batch sizes for each type of paper? Choose the best answer/explanation.
A) Yes, $6,250 is incurred per day independent of the subsequent production volume, so
it is the setup cost in the EOQ model.
B) Yes, $6,250 is incurred per day independent of the subsequent production volume, so
it is the holding cost in the EOQ model.
C) No, the square root of $6,250 should be input into the EOQ model as the setup cost.
D) No, $150,000 should be input into the EOQ model as the holding cost because it is the
opportunity cost of capital.
E) None of the above
Answer: E
Explanation: The annual debt payment is a sunk cost and should not be used in the
calculations of the batch sizes.
Difficulty: 3 Hard
Topic: The Impacts of Setup on Capacity
AACSB: Reflective Thinking
Blooms: Analyze
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[The following information applies to questions 15-18.]
Kick Scooters
Metal frames for kick scooters are manufactured in two steps: stamping and assembly.
Each frame is made up of three pieces: one unit of part A and two units of part B.
The parts are fabricated by a single stamping machine that requires a setup time of 90
minutes switching between the two part types. Once the machine is set up, the activity
time for parts, regardless of type, is 30 seconds each piece. Currently, the stamping
machine rotates its production between one batch of 120 part A's and 240 part B's.
Completed parts move only when the entire batch is produced.
During assembly, parts are assembled manually to form the finished products. The three
parts and a number of small purchased components are required for each unit of final
product. Each product requires 30 minutes of labor time to assemble. There are 12
workers in assembly. There is sufficient demand to sell every scooter the system can
make.
15) At the current batch sizes, the bottleneck of the system is
A) stamping
B) assembly
C) they both have the same capacity
D) cannot be determined
Answer: A
Explanation: The capacity at stamping is 120/(90 + 120 * 0.5 + 9 + 240 * 0.5) * 60 = 20
units per hour. The capacity at assembly is 1/30 * 12 * 60 = 24 units per hour. Therefore,
stamping is the bottleneck.
Difficulty: 3 Hard
Topic: Choosing a Batch Size in the Presence of Setup Times
AACSB: Analytical Thinking
Blooms: Analyze
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16) At the current batch sizes, what is the process capacity in units per hour? Choose the
answer below that is closest to the correct answer. A unit refers to a complete scooter
frame (i.e. one part A and two parts B).
A) 1 unit/hour
B) 5 units/hour
C) 10 units/hour
D) 20 units/hour
E) 30 units/hour
F) 40 units/hour
Answer: D
Explanation: Since stamping is the bottleneck, its capacity is also the process capacity.
Difficulty: 3 Hard
Topic: Choosing a Batch Size in the Presence of Setup Times
AACSB: Knowledge Application
Blooms: Analyze
17) One way to increase process capacity is to
A) increase the batch size at the stamping step
B) decrease the batch size at the stamping step
C) add more workers at assembly
D) none of the above
Answer: A
Explanation: At a batch-producing step, increasing the batch size increases the capacity
at the step.
Difficulty: 3 Hard
Topic: Choosing a Batch Size in the Presence of Setup Times
AACSB: Reflective Thinking
Blooms: Analyze
18) Which batch size for the stamping machine would minimize inventory without
decreasing the current flow rate? Choose the answer below that is closest to the correct
answer.
A) 60 sets
B) 120 sets
C) 180 sets
D) 240 sets
E) 300 sets
Answer: C
Explanation: At a batch size of 180, the capacity at stamping is 180/(90 +180 * 0.5 + 90
+ 360 * 0.5) * 60 = 24 units per hour.
Difficulty: 3 Hard
Topic: Choosing a Batch Size in the Presence of Setup Times
AACSB: Knowledge Application
Blooms: Apply
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Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 6 The Link between Operations and Finance
[The following information applies to questions 1-3.]
Full Limo Inc
Full Limo Inc. offers high-end transportation services between the King of Prussia Mall
(KPM) and Center City Philadelphia (22.5 miles). The invested capital is $800,000,
corresponding to the investment in the 4 luxury vans it owns (you can ignore all other
invested capital). Each van can carry 10 passengers. Each van makes 12 daily trips from
Philadelphia to KPM and 12 daily trips from KPM to Philadelphia. The company charges
$10 for each one-way ride. The current load factor is 40% (that is, each ride has 4
passengers on average). A significant source of operating costs is the fuel cost. The
company vans have a fuel economy each of 20 mpg (miles/gallon). Current fuel prices
are $2.629/gallon. The staff costs and other costs of operating the service and running the
business are $1M per year. The company operates 365 days a year.
1) Draw an ROIC (return on invested capital) tree for the company.
Answer:
Explanation: ROIC = Profit / IC = (Revenue – Costs)/ IC
Difficulty: 3 Hard
Topic: Building an ROIC Tree
AACSB: Knowledge Application
Blooms: Apply
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2) What is the ROIC?
Answer: 37.25%
Explanation: Revenues = 24 * 4 * 4 * 10 * 365 = 1,401,600
Costs = 1,000,000 + 24 * 4 * 22.5 * 365 * 2.629/20 = 1,103,635
Profits = 1,401,600 - 1,103,635 = 297,965
ROIC = 297,965/800,000 = 37.25%
Difficulty: 3 Hard
Topic: Building an ROIC Tree
AACSB: Analytical Thinking
Blooms: Analyze
3) Assume that the company can increase the fuel efficiency of the vans to 25mpg. What
would be the new ROIC?
Answer: 39.84%
Explanation: Revenues = 24 * 4 * 4 * 10 * 365 = 1,401,600
Costs = 1,000,000 + 24 * 4 * 22.5 * 365 * 2.629/25 = 1,082,908
Profits = 1,401,600 - 1,082,908 = 318,692
ROIC = 318,692/800,000 = 39.84%
Difficulty: 3 Hard
Topic: Valuing Operational Improvements
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 4-5]
Five Seasons Hotel
Five Seasons Hotel is a chain with 10 hotels. Strategically, the chain implements a
cookie-cutter approach to building and running its hotels, in that all hotels are practically
identical. Five Seasons invested $150 million in acquiring the land for all hotels and $500
million in building and furnishing the 10 hotels to a guest-ready stage. Each hotel has 150
rooms. Each room has a rack rate of $200 per night, but the hotel gives an average
discount of $30 per night off this base price. Each hotel costs $1 million in materials to
run and is staffed by 58 employees, each paid an average compensation of $50,000 a
year. This staffing level implies a certain service level, which together with the rack rate
and discount, determines the chain’s average occupancy rate—the percent of available
rooms sold—in this approximate way:
Chain-wide average occupancy rate = 0.01 × number of employees per hotel - (0.0015 ×
base Price) + (0.01 × discount), subject to a maximum of 100% and a minimum of 0%
(base Price and discount are expressed in [$]). The company operates 365 nights a year.
4) What is the ROIC?
Answer:
Difficulty: 3 Hard
Topic: Building an ROIC Tree
AACSB: Knowledge Application
Blooms: Apply
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5) Reducing the number of employees reduces staffing costs, but it also reduces the
occupancy rate when service level drops. What is the ROIC if Five Seasons reduces the
number of employees to 50 per hotel?
Answer: 1.78%
Explanation: Revenues = 10 * 150 * .5 * (200-30) = 46,537,500
Labor Costs = 10 * 50 * 50,000 = 25,000,000
Expenses = 10,000,000 + 25,000,000 = 35,000,000
Profits = 46,537,500 – 35,000,000 = 11,537,500
ROIC = 11,537,500 / 650,000,000 = 1.78%
Difficulty: 3 Hard
Topic: Valuing Operational Improvements
AACSB: Analytical Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 07 Quality and Statistical Process Control
1) Which of the following identifies the process where a chemist accidentally creates a
potentially explosive solution due to miscalculation?
A) Natural Variation
B) Common Cause Variation
C) Assignable Cause Variation
D) Environmental Variable
E) Outcome Variable
Answer: C
Explanation: An assignable cause variation attributes the miscalculation of the solvents
that led to this potentially explosive solution. Natural variation and common cause
variation are the same and include naturally occurring differences. Environmental
variables also happen as a result of the environment such as weather. Outcome variables
are the products that result from the process. In this case, the potentially explosive
solution that resulted would be an example of an outcome variable.
Difficulty: 3 Hard
Topic: The Statistical Process Control Framework
AACSB: Analytical Thinking
Blooms: Analyze
2) Sarita works for a busy bakery in downtown Manhattan. She noticed this morning that
her large batch of bagels did not rise properly during the time that they were in the oven
the way they usually do. With very little time before the shop opens for the morning rush,
she decides to study this situation with the statistical process control, or SPC, approach.
Which of the following should she do in this particular situation?
A) She should measure the capability of the process in making defects.
B) She should monitor her process to see whether this variation is aligned to the usual
pattern or if an assignable cause occurred.
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C) If she determines that this is a result of an assignable cause, she should investigate the
root cause of the variation.
D) She should try to avoid this from recurring if it was from an assignable cause and
possibly utilize a different recipe that is more robust.
E) Based on the information we have so far, Sarita should do all of the above.
Answer: E
Explanation: At this point, we do not know what caused Sarita's morning batch of bagels
not to rise properly. She should follow the four steps of the statistical process control
(SPC) approach to determine what variations within the process may have caused this
and what actions to take to reduce the possibility of this occurring again.
Difficulty: 3 Hard
Topic: The Statistical Process Control Framework
AACSB: Reflective Thinking
Blooms: Analyze
3) Which of the following is an outcome variable when studying a set of adult twins?
A) The heights of the adult twins.
B) The average amount of calories that the adult twins consumed as children.
C) The environment that adult twins grew up in.
D) The height of the twins' parents.
E) None of the above.
Answer: A
Explanation: The average amount of calories the twins consumed as children is
considered an input variable, while the environment they grew up in is an environmental
variation. The height of their parents is considered an input variable because of their
genetic contributions. Hence, the twins' heights are outcome variables that result from the
input and environmental variables.
Difficulty: 3 Hard
Topic: The Statistical Process Control Framework
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 4-6.]
Comfort Living Appliances has just released plans for a new flexible, yet light-weight
vacuum cleaner. The proprietary component of this device is the pivot function of the
handle. The plans have indicated that there remains the possibility of variation within this
pivot function. The designers have specified that the height of this section should
measure 44.550 mm in height but concede that anywhere between 44.500 and 44.645 is
acceptable before the function interferes with the hose extender.
4) What is the lower specification limit (LSL) of this vacuum cleaner's pivot function?
Answer: 44.500
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Explanation: The designers stated that the height of the pivot function is ideally at a
height of 44.550, but that anywhere between 44.500 and 44.645 is acceptable; hence, the
LSL is 44.500.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Knowledge Application
Blooms: Apply
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5) What is the tightness of the design specification for the height of the pivot function?
A) 44.645
B) 44.550
C) 0.140
D) 0.145
E) 44.500
Answer: D
Explanation: The tightness is defined by the difference between the upper specification
limit (USL) and the lower specification limit (LSL).
Hence, 44.645 - 44.500 = 0.145.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Knowledge Application
Blooms: Apply
6) Let's assume the designers have estimated a standard deviation for the pivot function
of 0.019321 and assigned this a six-sigma process. What is the process capability?
Answer: 1.25.
Explanation: To calculate process capability we use the following equation:
Cp = (USL - LSL)/6 σ-hat. So, Cp = (44.645-44.500)/(6 * 0.019321) = 1.25.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Analytical Thinking
Blooms: Analyze
7) Many organizations aim for alignment within six-sigma program requirements. Which
of the following does that include?
A) A minimum process capability index of 1.33.
B) A process capability of 2.0 at every step.
C) A USL that is six standard deviations above the mean.
D) An LSL that is 3 standard deviations below the mean.
E) A process capability of 2.0 at every step and a USL that is six standard deviations
above the mean.
Answer: E
Explanation: Although requiring a minimum process capability index of 1.33 is a
common recommendation, six-sigma program requirements actually call for 2.0 at every
step of the process. Six-sigma also requires that both the USL and LSL are six standard
deviations away from the mean. The correct choice is a process capability of 2.0 at every
step and a USL that is six standard deviations above the mean.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Analytical Thinking
Blooms: Analyze
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8) What is the maximum standard deviation allowed for a process to meet the rigorous
six-sigma standards?
Answer: 6.
Explanation: The rigorous six-sigma program views every defect as an occurrence that
should not have happened. Hence, the objective is to keep the probability of a defect as
low as possible. Six-sigma allows for the upper specification limit to be no more than six
standard deviations above the mean, and the lower specification limit should not be any
more than six standard deviations below the mean.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Reflective Thinking
Blooms: Analyze
9) A company has an assigned LSL of 39.255mm and a USL of 39.195mm for one of its
critical components. The standard deviation of the sample it checks daily is 0.012875
with a sigma of 4.5. What is the process capability index for this component?
Answer: 1.0356.
Explanation: Utilize the following equation to determine the process capability index:
Cp = (USL - LSL)/4.5 σ-hat.
For this component, we would calculate (39.225 - 39.195)/4.5 * .012875 = 1.0356.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 10-13.]
An integral component for a large tractor model has a USL of 950 mm and an LSL of
949.90 mm. Assuming this follows a six-sigma process and the standard deviation is
0.0128.
10) What is the process capability score?
A) 1.3881
B) 1.3021
C) 1.3939
D) 1.3722
E) 2.0021
Answer: B
Explanation: We will use the following equation to solve for the process capability
index: Cp = (USL - LSL)/6 σ-hat or (950 - 949.90)/6 * 0.0128 which equals 1.302.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Analytical Thinking
Blooms: Analyze
11) Based on the capability score for the tractor component above, what is the present
defect frequency in ppm?
A) 63.3
B) 26.7
C) 10.8
D) 4.2
E) 1.59
Answer: A
Explanation: Since the capability index above is 1.3021, we can refer to Table 7.1 which
depicts defect probability.
A capability index would correlate to 63.34248 ppm.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Knowledge Application
Blooms: Apply
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12) Let's say the tractor company who makes the component above would like to reduce
their ppm to 26. To what level would they have to reduce the standard deviation to
achieve this objective?
Answer: 0.0119
Explanation: To obtain 26 ppm, the capability score would have to be 1.4 according to
Table 7.1. We then use the following equation to identify the target variation but will use
the preferred capability score:
sigma-hat = (USL - LSL)/6 * Cp, or (950 - 949.9)/(6 * 1.4) = 0.0119.
The tractor company will be able to reduce their ppm to 26 if they can lower the standard
deviation from 1.3021 to 0.0119.
Difficulty: 3 Hard
Topic: Capability Analysis
AACSB: Analytical Thinking
Blooms: Analyze
13) When variation in the process is observed to be abnormal, what would this indicate?
Answer: Assignable cause variation
Explanation: When process variation is deemed to be normal, we can attribute this to
common cause variation. However, when the variation is abnormal, this indicates that
there must be some culpable assignable cause variation.
Difficulty: 3 Hard
Topic: Conformance Analysis
AACSB: Knowledge Application
Blooms: Apply
[The following information applies to questions 14-17.]
Let's say an operations specialist has measured the estimated standard deviation of all
parts for a process to be 0.002921374 for five observation periods. The X-double-bar, or
average across averages, is 57.258.
14) What is the estimated standard deviation for this sample of measurements?
Answer: 0.001306478
Explanation: To calculate the estimated standard deviation, divide the standard deviation
of all parts by the square root of the number of observation periods. For this sample of
measurements, calculate 0.002921374/
Difficulty: 3 Hard
Topic: Conformance Analysis
AACSB: Knowledge Application
Blooms: Apply
= 0.001306478.
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15) What is the upper control limit (UCL) for this sample that will keep this process
within control?
Answer: 57.26191943
Explanation: A process must remain within three standard deviations from the average
across averages, or long-term mean. To calculate this, use the formula:
UCL = X-bar-bar + [3 * ESD(X-bar)].
For this case, we plug in 57.258 + (3 * 0.001306478) = 57.26191943.
Difficulty: 3 Hard
Topic: Conformance Analysis
AACSB: Knowledge Application
Blooms: Apply
16) What is the lower control limit (LCL) for this sample that will prevent the sample
mean from becoming out of control?
Answer: 57.254080567
Explanation: Utilize the following equation to identify the LCL that is within three
standard deviations: LCL = X-bar-bar - [3 * ESD(X-bar)].
For the LCL we compute 57.258 - (3 * 0.001306478) = 57.254080567.
Difficulty: 3 Hard
Topic: Conformance Analysis
AACSB: Knowledge Application
Blooms: Apply
17) A few weeks later, this operations specialist begins to notice a trend in which the
daily sample averages are falling just outside the upper and lower control limits. What
would this be an indication of?
A) The process is out of control.
B) The process is beyond three standard deviations of the mean.
C) This indicates that an assignable cause has occurred.
D) This pattern justifies the need to investigate further.
E) All of the above statements are correct.
Answer: E
Explanation: If there is a trend of averages outside the control limits, this indicates that
the process is out of control. In other words, something is occurring that is causing the
measurements to reach beyond three standard deviations and an assignable cause is more
than likely the culprit. A trend such as this would qualify the operations specialist to
investigate and make the necessary steps to bring these measurements back into control
within the specification limits.
Difficulty: 3 Hard
Topic: Conformance Analysis
AACSB: Reflective Thinking
Blooms: Analyze
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18) Ironworks Fence Company picked up on a defect in the way its rails line up on its
latest batch of residential fencing. The control chart that it updates periodically has
indicated that this is because of an assignable cause variation. What is the first thing that
should occur after this observation?
A) Calculate the control limits.
B) Calculate the specification limits.
C) Calculate the defects with binary outcomes.
D) Construct a diagram that analyzes the potential root causes.
E) All of the above.
Answer: D
Explanation: Ironworks Fence Company should investigate the root cause of this defect
by constructing a diagram that shows the input and environmental variables and their
relationship with the outcome variable. Some examples of diagrams that can be used as
tools to analyze this include fishbone diagrams, cause-effect diagrams, Ishikawa
diagrams, or the "Five Whys" model.
Difficulty: 3 Hard
Topic: Investigating Assignable Causes
AACSB: Reflective Thinking
Blooms: Analyze
19) Ironworks Fence Company decided to create a p-chart with a large sample size of 200
fence sections to identify the number of defective parts. They find that the average across
averages is a defect of 8%. What is the estimated standard deviation of effects for this
sample size?
A) 0.0192
B) 0.0183
C) 0.0191
D) 0.0182
E) 0.0121
Answer: A
Explanation: To find the estimated standard deviation, we use the equation:
estimated standard deviation =
. So for this case, we
calculate
= 0.0192.
Difficulty: 3 Hard
Topic: Defects with Binary Outcomes: p-Charts
AACSB: Knowledge Application
Blooms: Apply
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20) What is the upper control limit for the percentage of defective parts based on the
estimated standard deviation above?
A) 0.1379
B) 0.1372
C) 0.1376
D) 0.1299
E) 0.1400
Answer: C
Explanation: To determine the UCL for this sample size, we calculate
UCL = p-bar + (3 * estimated standard deviation).
So, we plug in .08 + (3 * 0.0192) to get 0.1376 for the upper control limit of defective
parts.
Difficulty: 3 Hard
Topic: Defects with Binary Outcomes: p-Charts
AACSB: Knowledge Application
Blooms: Apply
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 08 Lean Operations and the Toyota Production System
1) Which of the following statements about the Kanban system is/are accurate?
I. Deploying the Kanban system leads to pulling work through the system instead of
pushing work.
II. Deploying the Kanban system leads to pushing work through the system instead of
pulling work.
III. The Kanban system controls the work in process inventory.
IV. The Kanban system is a quality method that reduces defects.
V. Kanban requires cross-training all workers.
A) I only
B) II only
C) III and IV only
D) I, II, and III only
E) I, II, and IV
F) I and IV only
G) I and III only
Answer: G
Explanation: The Kanban system is a production flow system that involves the pulling of
work rather than pushing within the TPS framework. This system is related to the process
of work, not reducing defects.
Difficulty: 3 Hard
Topic: TPS Framework
AACSB: Reflective Thinking
Blooms: Analyze
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2) Please write the letter corresponding to the most appropriate example or definition
from choices (a) through (g) below on the blank line next to each word.
a) Examples of these include workers having to make unnecessary movements (i.e.,
excessive reaching or walking to get tools or parts), working on parts that are defective,
and idle time.
b) This is a system that enables a line worker to signal that he or she needs assistance
from his or her supervisor, for example in the case of a defect. It is used to implement the
Jidoka principle.
c) This is a brainstorming technique that helps structure the process of identifying the
underlying causes of an outcome that is usually undesirable.
d) As an example of this philosophy, workers in the Toshiba case had notebooks at their
workstations that they used to jot down improvement ideas.
e) This is a method that controls the amount of work-in-process inventory.
f) If an automotive assembly plant used this technique, the adjacent cars on an assembly
line would be mixed models (e.g., Model A with a sunroof, Model A without a sunroof,
Model B, Model B with a sunroof), in proportions equal to customer demand.
g) This makes production problems visible and stops production upon detection of
defects.
Please assign ONE LETTER to each of the following terms:
Kanban
Muda
Heijunka
Andon cord
Kaizen
Ishikawa
Jidoka
____
____
____
____
____
____
____
Answer:
Kanban
__e__
Muda
__a__
Heijunka
__f__
Andon cord __b__
Kaizen
__d__
Ishikawa
__c__
Jidoka
__g__
Difficulty: 3 Hard
Topic: The Seven Sources of Waste
AACSB: Reflective Thinking
Blooms: Analyze
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3) In the Toyota Production System, Jidoka refers to
A) the level of production where different models are produced alongside each other on
the assembly line.
B) continuous improvement where workers organize meetings to discuss ways of
improving the production process.
C) the inventory retrieval system where parts are replenished only when they are needed.
D) the aggressive reduction of changeover and setup times.
E) continuous line-balancing to maximize utilization.
F) the cross-training of workers for a wide range of skills.
G) none of the above
Answer: G
Explanation: Jidoka is a system for quality improvement where work is stopped as soon
as a defect is detected.
Difficulty: 3 Hard
Topic: TPS Framework
AACSB: Reflective Thinking
Blooms: Analyze
4) Which of the following statements accurately describe the Toyota Production System?
I. The entire production is shut down every time the Andon cord is pulled.
II. There is zero idle time at each production step.
III. The TPS uses no buffers.
IV. TPS uses buffer inventories between line segments to avoid blocking and starving of
the production line.
A) I only
B) II only
C) III only
D) IV only
E) I, II, III, and IV
F) II and IV
G) II, III, and IV
H) I and IV
Answer: C
Explanation: The need to buffer, or hold inventory, is not necessary with the Toyota
Production System because of the focus on quality work.
Difficulty: 3 Hard
Topic: TPS Framework
AACSB: Analytical Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 09 Variability and Its Impact on Process Performance: Waiting Time Problems
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[The following information applies to questions 1-2.]
UP Fitness will install 3 new trapezoidal gel-resistance toners, or "trappies," which are
the latest exercise gadget specifically designed to contour upper back muscles. Clients
who want to use these machines arrive at the rate of 85 per hour. The coefficient of
variation of the interarrival times is 3. If all three machines are busy, UP Fitness clients
use other pieces of equipment, waiting for one of the "trappies" to become available. The
trappy experience is intense—120 seconds of explosive exercise intensity. The standard
deviation of the usage times (measured in seconds) is quite small—only 30.
1) On average, how many UP Fitness clients are using a trappy?
Answer: 2.83 clients
Explanation: The capacity of UP Fitness is 3600 sec/120 sec * 3 = 90 clients per hour.
The utilization of the UP Fitness is 85/90 = 0.944. That is, on average 3 * 0.944 = 2.83
machines are in use. In other words, 2.83 clients are using a trappy on average.
Difficulty: 3 Hard
Topic: Motivating Example: A Somewhat Unrealistic Call Center
AACSB: Knowledge Application
Blooms: Apply
2) On average, how many UP Fitness clients are waiting to use a trappy?
Answer: 69.39 clients
Explanation: The processing time is 120 sec, or 2 min. Utilization is 0.994. The time
queue is (2/3) * ((0.944^sqrt(2(3 + 1)) - 1)/(10.944)) * (3^2 + (30/120)^2)/2 = 48.98 min.
From Little's Law, 48.98 * (85/60) = 69.39 clients
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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3) Max Stamp approves study abroad documents for Penn. Students must wait in line
with their forms outside Max's office. One student at a time is allowed in his office, and
Max takes precisely 25 minutes to evaluate each student's set of documents. On average,
2.2 students per hour go to his office, and they spend on average 160 minutes trying to
get their forms approved (time waiting in queue plus time in Max's office for him to
evaluate their documents). On average, how many students are waiting outside of Max's
office? (Note: Ignore start-of-the-day and end-of-the-day effects.)
Answer: 4.95 students
Explanation:
p = 25
a = 60/2.2 = 27.27
Tq = T - Tp = 160 - 25 = 135
Iq = (1/a) * Tq = (1/27.27) * 135 = 4.95.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
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4) Larry Ellison starts a company that manufactures high-end custom leather bags. He
hires two employees. Each employee only begins working on a bag when a customer
order has been received and then she makes the bag from beginning to end. The average
production time of a bag is 1.8 days with a standard deviation of 2.7 days. Larry expects
to receive one customer order, per day on average. The interarrival times of orders have a
coefficient of variation of 1. What is the expected duration, in days, between when an
order is received and when production begins on the bag? (Note: Include the time waiting
to start production, but do not include the time in production.)
Answer: 12.55 days
Explanation:
Expected duration between when an order is received and when production starts = 12.55
Parameters are
Number of staff members (m)
2
Interarrival time (a)
1 day
Std dev of interarrival time (σa)
1 day
Activity or processing time (p)
1.8 day
Std dev of processing time (σp)
2.7 day
Coefficient of Variation of Interarrival CVa = σa/a = 1
Coefficient of Variation of Processing CVp = σp/p = 1.5
Utilization (u) = p/(a * m) = 1.8/(1 * 2) = 0.9
Expected waiting time Tq = (p/m) * ((u^sqrt(2(m + 1)) - 1/(1 - u)) * (CVa2 + CVp2)/2
We need to evaluate Tq. The capacity factor is (p/m) = 1.8/2 = 0.9. The utilization factor
is 9 and the variability factor is 1.63. Multiply the three terms and you get 13.16.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 5-6.]
Find a Doctor, or FaD, is a small startup that helps people find a physician that best meets
their needs (location, insurance accepted, etc.). During a "slow" time for them, they have
7 staff members taking calls from customers. On average, one call arrives every 6
minutes (with a standard deviation of 6). Each staff member spends 20 minutes with each
customer (on average, with a standard deviation of 30).
5) What is the probability that one of their staff members is busy (as a %)?
Answer: 47.62%
Explanation: Utilization of each staff member is p/(a * m) = 20/(6 * 7) = 47.62%.
Difficulty: 3 Hard
Topic: Processing Time Variability
AACSB: Knowledge Application
Blooms: Apply
6) How long (in minutes) does a customer spend on average waiting on hold before they
can start speaking to a representative from FaD?
Answer: 0.96 minutes
Explanation: Processing time = 20 minutes utilization = 47.62%
Time in queue =
×
Difficulty: 3 Hard
Topic: Processing Time Variability
AACSB: Knowledge Application
Blooms: Apply
×
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7) The organizers of a conference in the Philadelphia Convention Center are evaluating
the possibility of setting up a computer area where attendees can check their e-mail on
computers provided by the organization. There will be one common queue for all
computers, and only one person uses a computer at a time. On average, there are 15
attendee arrivals per hour, the standard deviation of the time between arrivals is 4, and
the average time a person spends on the computer is 10 minutes (with standard deviation
3). To ensure that waiting times are not too long, the organizers want to ensure that the
utilization of the computers doesn't exceed 90%. At least how many computers do they
need to have?
Answer: 3 computers
Explanation: The activity time is 10 min. with the interarrival time of 60/15 = 4 min. To
ensure at most 90% utilization, i.e., 10/(m * 4) <= 0.9, we need m >= 10/4/0.9 = 2.78.
That is, they need at least 3 computers.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
8) A small call center normally has 5 employees answering calls while open. On average,
5 calls arrive every 4 minutes with a CVa = 1. Under normal operating conditions each
employee on average handles each call in 3.5 minutes with a standard deviation of 3.
Today, however, one employee has the flu, and they need to operate with 4 employees
during this time. The manager is nervous that they may be supply constrained and so she
directs her employees to hurry their processing of calls today. What is the maximum
average processing time for each call that they need to achieve today so that they have a
stable queue? (Note: there will be supply constrained if their processing time is higher
than this target and there will be demand constrained if it is lower than this target. Choose
the closest answer. Assume CVa and CVp don't change even after the potential change in
processing times).
Answer: 3.2 minutes
Explanation: Utilization is p/(a * m) and this equals 100% at the target processing rate.
Hence 1.0 = p/(4/5 * 4). Solve for p = 16/5 = 3.2.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 9-10]
CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD
owns 5 supercomputers that can be accessed through the Internet. Their customers send
jobs that arrive on average every 4 minutes. The standard deviation of the interarrival
times is 4 minutes. Executing each job takes on average 16 minutes on one of the
supercomputers (during this time, the computer cannot perform any other work). The
standard deviation of this processing time is 24 minutes.
9) What is the utilization (as a %) of each supercomputer?
Answer: 80%
Explanation: The utilization is p/(a * m) = 16 min/(4 min * 5) = 0.8
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
10) On average, how many jobs are waiting to start processing?
Answer: 3.75 jobs
Explanation: Tq = (16/5) * ((0.8^
- 1)/(1 - 0.8)) = 3.75
Iq = (1/4)jobs/min * 15.003 min = 3.75 jobs
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 11-12.]
FestEvents is a concert organizer that is evaluating the installation of portable toilets at an
outdoor venue where a concert is going to take place. In particular, it is considering an
area of the venue that is far away from the existing restrooms. Assume there will be one
single queue to access all the portable toilets in this area and that only one person uses a
toilet at a time. FestEvents is concerned that if the line is too long, people will find other
ways and places to answer nature's call.
FestEvents estimates that there will be 4 arrivals per minute on average to the toilets, with
a standard deviation of the time between arrivals of 15 seconds. The average time a
person spends using the toilet is 3.12 minutes with a standard deviation of 2 minutes.
11) Suppose FestEvents installs 20 portable toilets. On average, what fraction of the
toilets will be occupied during the event?
Answer: 0.624 toilets
Explanation: (1/4) = 0.25 min
utilization = p/(a * m) = 3.12 min/(0.25 min * 20) = 0.624
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of Multiple Resources
AACSB: Knowledge Application
Blooms: Apply
12) What is the minimum number of portable toilets that FestEvents must install to
ensure that the queue length will not continue to grow without limit (i.e., so that the
queue will be stable)? (Note: Your answer should be an integer—they can install 2 toilets
or 3 toilets, but they cannot install 2.6 toilets.)
Answer: 13 toilets
Explanation: To ensure that the queue length will not continue to grow without limit, the
capacity should be greater than demand, or implied utilization should be smaller than 1.
That is, p/(a * m) <1, or m > p/a = 3.12 min/(1/4 min) = 12.48. Round the result up, so 13
toilets are needed.
Difficulty: 3 Hard
Topic: Impact of Pooling: Economies of Scale
AACSB: Knowledge Application
Blooms: Apply
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13) The Journal of Cryptic Psychology follows the following process to decide what to
print. First, authors submit their papers to one of the 40 Associate Editors who either
"reject" the papers or allow the authors to "revise" their papers. If the decision is "revise,"
then an author revises his/her paper based on the Associate Editor's comments, and when
finished, submits the revision to the Editor.
The Editor decides to "reject" or "accept" the paper, and only accepted papers are printed
in the journal. Associate Editors choose "revise" with only 20% of papers they see, and
the Editor accepts only 75% of the papers she sees. The average and standard deviation of
processing times are given in the table below:
The journal prints, on average, 30 papers per year. On average, how many manuscripts
are currently being revised by authors?
Answer: 40 papers per year
Explanation: The journal prints 30 papers per year, but the Editor accepts only 3/4 of
them. So, the Editor must read 30 × 4/3 = 40 papers per year. Hence, the authors must be
revising 40 papers per year. Use Little's Law, I = R * T, where R is 40 and T is 1/2, so I =
20 papers.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
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14) You currently have 7 items on your "to-do" list. Below are the items, and the
estimated times to complete them.
Restring your snowshoes so you can get to class
Take a nap
Work on a homework assignment
Update your Facebook account
Call your mother
Eat some food
Call a friend to discuss weekend plans
- 120 minutes
- 100 minutes
- 80 minutes
- 60 minutes
- 30 minutes
- 20 minutes
- 10 minutes
Suppose you immediately start with your tasks, no other tasks get added to your to-do list
today, and you sequence them to minimize the average time the tasks wait before you
start them. What will you be doing in 190 minutes from the time you start? (Note: Record
the underlined task name above for your answer.)
Answer: You will be doing homework from the time you start.
Explanation: Do the shorter tasks first. The sequence is as follows: friend (finishes after
10 min), food (30 min), mother (60 min), Facebook (120 min), homework (200 min),
nap, snowshoes. Since 60 min < 190 min < 120min, you will be doing homework in 190
minutes from the time you start.
Difficulty: 3 Hard
Topic: Reducing Variability
AACSB: Knowledge Application
Blooms: Apply
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15) A computer server currently has a queue of 5 jobs, sequenced from A to E. A is the
one that has been waiting the longest and E is the one that was most recently received.
The following table provides their processing times in milliseconds.
Time (milliseconds)
A
5
B
78
C
50
D
2
E
15
Suppose the server is designed to minimize the average waiting time across jobs (i.e.,
time in the queue waiting to start processing). Ignore the amount of time these jobs have
already been waiting. Suppose the server is immediately available to start working on one
of the jobs and the server is aware of each job's processing time. What is the minimum
total time these five jobs will wait before beginning processing? (Note: Additional jobs
may or may not arrive before the processing of these jobs is completed. For example, if A
is processed first and B next, then A's wait will be 0 and B's wait will be 5 (the time to
complete A) so the total time for these two jobs alone is 0+5=5.)
Answer: 103 minimum total time
Explanation: Use the shortest processing time to evaluate. Hence, the jobs will be
sequenced D, A, E, C, B. Wait times are D = 0, A = 2, E = 2 + 5, C = 2 + 5 + 15, B = 2 +
5 + 15 + 50. Total time is 2 + 7 + 22 + 72 = 103. This is the minimum, and it will only be
longer if additional jobs arrive.
Difficulty: 3 Hard
Topic: Economic Implications: Generating a Staffing Plan
AACSB: Knowledge Application
Blooms: Apply
16) Which of the following best reflects pooling capacity to reduce restroom queue
lengths?
A) Add more toilets to increase capacity.
B) Install a flexible partition that can alter the size of the women's and the men's
restrooms.
C) Convert the separate men's and women's rooms into a single unisex restroom (that
both men and women can use).
D) Remove mirrors in the restroom to decrease the time users spend in the restroom.
E) Add automatic flush capability to each toilet to decrease processing times.
Answer: C
Explanation: By allowing anyone to use any of the restrooms whether male or female,
there is a continuous flow within the queue. Increasing the number of toilets may not help
with an extremely large crowd that would still cause pooling. Stall sizes and the removal
of mirrors will not affect the speed of restroom use. The automatic flush may decrease
processing time but narrowing the resource to one unisex restroom-type is more effective.
Difficulty: 2 Medium
Topic: Impact of Pooling: Economies of Scale
AACSB: Reflective Thinking
Blooms: Evaluate
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17) The following four graphs (labeled A, B, C, and D in the upper right corner) display
the number of customers in a queuing system (y-axis) over a long period of time (x-axis).
Which of the following is most likely a stable system?
A) Only A
B) Only B
C) Only C
D) Only D
E) Only B and C
F) None of them
G) All of them
Answer: D
Explanation: Graph D is representative of a stable system because the number of
customers remains near or below 30 with a rapid decline of customers along a decreasing
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trend in seconds.
Difficulty: 2 Medium
Topic: Variability: Where It Comes from and How It Can Be Measured
AACSB: Analytical Thinking
Blooms: Analyze
18) A pediatric practice has 5 physicians. Historically, patients were assigned to one
physician, and the same physician always treated these patients. For example, Alice's
patients always visited her (for "well visits" and "sick visits") and never interacted with
the other physicians. However, they have decided to change how they see patients. Now
patients will be seen by whoever is available (i.e., not treating patients). Based on our
discussion of queuing theory, which of the three outcomes below are likely to occur due
to this change?
i) The coefficient of variation of patient interarrival times will increase.
ii) The utilization of each physician will increase.
iii) The average number of patients actually with a physician (that is, "inventory in
process") will increase.
A) i only
B) ii only
C) iii only
D) i and ii only
E) i and iii only
F) ii and iii only
G) all of them (i, ii, and iii)
H) none of them (neither i, ii, nor iii)
Answer: A
Explanation: The interarrival time is not affected by the change in the process. ii) Some
physicians might see an increase in the utilization, while others might not. It is not
certain. iii) Inventory in process will not change because of the flow rate (i.e., arrival
rate) does not change and the activity time does not change.
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Reflective Thinking
Blooms: Analyze
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19) YourNurse (YN) Inc. uses certified nurses to answer medical queries from customers
over the phone. When patients call into YN, they are first asked to provide their zip code
which then allows YN to route their call to the call center nearest to the patient (they
operate 10 across the country). Which single suggestion in the following list (and
explanation) is most likely to reduce the average time callers wait before speaking with a
nurse?
A) Run an advertising campaign to increase demand and to utilize their nurses better.
B) Train their nurses so that they spend more time answering the patients' questions.
C) Instead of using callers' zip codes, route calls to the call center with the fewest callers
to help prevent situations in which there are idle nurses at the same time that there are
callers on hold.
D) Play a recording of useful medical information while callers are on hold to decrease
their perception of how long they are waiting.
E) None of the above
Answer: C
Explanation: Callers will be able to speak with a nurse in shorter amounts of time if all
10 call centers across the country are speaking with patients regardless of their zip code
location.
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 20-22.]
The Right to Vote (and not to wait)
In the previous two presidential elections in the United States, very long wait times have
been witnessed at precincts (voting stations) in states that ultimately decided the election
(Florida in 2000 and Ohio in 2004). In Philadelphia as well, some voters complained
about the long lines in some precincts, with most of the complaints coming from precinct
A. In 2004, the average number of voters arriving at Precinct A was 35 per hour and the
arrivals of voters was random with interarrival times that had a coefficient of variation of
1 (CVa=1). Philadelphia deployed 1 voting machine in Precinct A. Suppose that each
voter spent, on average, 100 seconds in the voting booth (this is the time needed to cast
his/her vote using a voting machine), with a standard deviation of 120 seconds.
20) How long, on average, did a voter have to wait in line at precinct A in 2004 before
entering a booth to cast his/her vote? Circle the closest answer.
A) 56 minutes
B) 58 minutes
C) 60 minutes
D) 62 minutes
E) 71 minutes
F) 75 minutes
G) There is not sufficient information to answer the question.
Answer: E
Explanation: m = 1
average activity time: p = 1.71 min.
average interarrival time: a = 60/35 = 1.67 min.
utilization = p/(a * m) = 0.97
CVa = 1
CVp = 1.2
Tq = 71.7 minutes
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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21) Given the long wait times for Precinct A, the city of Philadelphia is thinking of
alternative solutions to improve voting conditions. One of the proposed solutions is as
follows.
Proposal 1: Deploy an additional voting machine in precinct A. Assume that the voter
turnout is expected to have similar characteristics in 2008 as in the previous election.
Under Proposal 1, how long, on average, would a voter have to wait in line in precinct A
in 2008 before casting his/her vote? Circle the closest answer.
A) 1 minute
B) 5 minutes
C) 6 minutes
D) 10 minutes
E) 11 minutes
F) There is not sufficient information to answer the question.
Answer: A
Explanation: m = 2
average activity time: p = 1.71 min.
average inter-arrival time: a = 60/35 = 1.67 min.
utilization = p/(a * m) = 0.49
CVa = 1
CVp = 1.2
Tq = 0.7 minutes
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
22) Under Proposal 1, on average, at precinct A, what would be the ratio of the average
number of people voting at a booth over the average number of people waiting in line.
Circle the closest answer.
A) 0.4
B) 1.4
C) 2.4
D) 3.4
E) 4.4
F) 5.4
G) There is not sufficient information to answer the question.
Answer: C
Explanation: Ip = m * u = 0.97
Iq = Tq /a = 0.41
Ip /Iq = 0.97/0.41 = 2.37
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
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Blooms: Apply
[The following information applies to questions 23-27]
Philly Barber Shops
Newt Philly needs to decide where to get a haircut. He has narrowed the choice down to
two local hair salons—Large Hair Salon (LHS) and Small Hair Cutters (SHC).
During busy periods, a new customer walks into LHS every 15 minutes (with a standard
deviation of 15 minutes). At SHC, a customer walks in every hour (with a standard
deviation of 1 hour). LHS has a staff of 4 barbers, while SHC has 1 barber. Typical
service time at either salon lasts 30 minutes (with a standard deviation of 30 minutes).
23) If Newt walks into LHS during a busy period, how long must he wait in line before
he can see a barber? (Note: Only include the waiting time, not any service time.)
Answer: 3.35 minutes
Explanation:
utilization =
=
= 0.5
Tq =
=
×
×
×
×
= 3.35 minutes
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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24) If Newt goes to SHC, how long must he wait in line before his haircut starts?
Answer: 30 minutes
Explanation:
utilization =
Tq =
= 0.5
×
×1
= 30 minutes
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
25) Assume that it takes Newt 10 minutes to leave work and walk to LHS and 10 minutes
to walk back (i.e., each way of the walk takes 10 minutes). How long will he need to
leave work for to get a haircut at LHS?
Answer: 53.35 minutes
Explanation: Tq + Activity time + travel time
= 3.35 + 30 + 20
= 53.35 minutes
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
26) LHS will buy out SHC. LHS will then close SHC's operations and serve all
customers, including existing SHC customers, at the LHS location only. Assuming that
the previous traffic of SHC customers now flows to the LHS location, what is the new
interarrival time at LHS?
Answer: 12 minutes
Explanation:
= 12 minutes
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
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27) To accommodate the new flow rate, LHS now staffs one additional barber (to
increase the headcount to 5). Is the new waiting time at LHS less than or greater than the
waiting time of LHS before the merger? (Note: Assume that the coefficient of variation
of customer interarrival times is 1).
A) The new waiting time at LHS is less than the waiting time before the merger.
B) The new waiting time at LHS is greater than the waiting time before the merger.
Answer: A
Explanation:
utilization =
Tq =
×
= 0.5
×1
= 2.17 minutes
∴ The new waiting time at LHS is shorter now than before.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 28-33.]
Pharma Dev
Pharma Dev develops and markets new technological products to be used in health care.
The development of a new product operates as follows.
When a new technology meets the requisite market potential, a new patent is filed.
Patents are granted for 12 years starting from the date of issue. Once the patent is filed,
the new technology is developed at one of its three independent development centers and
is then launched to the market. Each product is developed at only one center, and each
center can only develop a single patented technology at a time.
On average, Pharma Dev files a new patent every 5 months (with a standard deviation of
5 months). The average development process lasts 12 months (with a standard deviation
of 24 months).
28) What is the utilization of Pharma Dev's development facilities?
Answer: The utilization is 0.8
Explanation: 12/(5 * 3) = 0.8
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
29) How long does it take for an average technology from winning a patent to start the
development process?
Answer: 33.25 months
Explanation: Inter arrival time for new technology = a = 5 months.
CVa = 1
Activity Time = p = 12 months
CVp = 2
Number of servers = 3
Tq = 33.25 months
Difficulty: 3 Hard
Topic: Processing Time Variability
AACSB: Analytical Thinking
Blooms: Analyze
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30) How many years of patent life are left for an average product launched to the market?
Answer: 8.229 years
Explanation: Total Patent Life is 12 years, or 144 months, and the time spent in the
system is 45.25 months, so patent life left = 98.75 months.
144 - 45.25 = 98.75
98.75/12 = 8.229 years.
Difficulty: 3 Hard
Topic: Processing Time Variability
AACSB: Knowledge Application
Blooms: Apply
31) On average how many patented products are undergoing development or waiting to
be developed?
Answer: 9.05 products
Explanation: Use Little's Law where the flow rate is 1/5 patents per month and time in
the system is 45.25 months, so 9.05 products are undergoing development or waiting to
be developed.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Knowledge Application
Blooms: Apply
32) Pharma Dev is considering leasing an additional development center to shorten the
time to market of patented products. If this center is used in addition to the three centers,
how will the total time-to-market (waiting time plus development time) of a patented
product change?
Answer: The total time will decrease by 27 months.
Explanation: U = 12/(5 * 4) = 0.6
m=4
u = .6
Tq = 6.21 months (approx.)
T system = 18.21 months
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
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33) After a product is launched to the market, it generates gross margins of $40 million
per year of patent life. After the patent expires, the product generates no gross margins.
Leasing the new facility would increase Pharma Dev's average total annual gross margins
by $ ________.
Answer: $216 million
Explanation: The new facility reduces the time to market by 27 months. The flow rate in
the market is 0.2 drugs per month. So, by applying Little's Law, we find that the
inventory of drugs in the market has increased by 0.2*27=5.4 drugs. On an annual basis,
this increases revenues by $216 million.
Difficulty: 3 Hard
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Analytical Thinking
Blooms: Analyze
34) Which of the following will increase the waiting time in a call center in which the
incoming call gets assigned to the first available server?
A) Add more servers
B) Implement the Shortest Processing Rule
C) Implement a First-In-First-Out (FIFO) system
D) Increase the service time coefficient of variation
E) Increase the average service time
F) Decrease the interarrival time
G) B, C, D, and E
H) Both D and E
J) D, E, and F
Answer: J
Explanation: Waiting time will increase if there is an increase in service time coefficient
variation if the average service time increases, and if there is a decrease in the interarrival
time at the call center.
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of One Resource
AACSB: Reflective Thinking
Blooms: Analyze
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35) Consider the following three process designs to organize a call center with 12
employees. The center handles calls for two customer types. Type 1 customers call with
credit card related questions and type 2 customers call with questions related to the online
account opening. On a busy day, the call center receives 60 calls per hour from type 1
customers and 30 calls per hour from type 2 customers. It takes, on average, 2 minutes to
service both kinds of calls.
Process design 1: 6 employees handle type 1 calls; the other 6 employees handle type 2
calls
Process design 2: 8 employees handle type 1 calls; 4 employees handle type 2 calls
Process design 3: 12 cross-trained employees handle all calls
Which of the three process designs leads to the shortest and longest average waiting time
for a random incoming request?
A) 1 is the shortest, 2 is the longest
B) 2 is the shortest, 1 is the longest
C) 3 is the shortest, 2 is the longest
D) 2 is the shortest, 3 is the longest
E) 3 is the shortest, 1 is the longest
F) 1 is the shortest, 3 is the longest
G) 3 is the shortest, 1 and 2 are the same
H) Cannot be determined
J) None of the above
Answer: E
Explanation: Among the three process design models, have all employees trained to
handle both call types would produce the shortest wait time while process design 1 would
produce queuing pools, thus longer wait times.
Difficulty: 2 Medium
Topic: Predicting the Average Waiting Time for the Case of Multiple Resources
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 10 The Impact of Variability on Process Performance: Throughput Losses
[The following information applies to questions 1-2.]
Airport Massage Station
A small company just opened a new massage station at the Philadelphia airport. The
company has a stand that offers massages to travelers. Customers can select a length of
time for a massage between 5 and 20 minutes, and there is a unique rate of $30
independent of the length of time chosen by customers. The average massage length,
requested by customers, is 15 minutes with a standard deviation of 10 minutes. There are
four employees delivering massages. The average number of potential customers
requesting a massage is 20 per hour. The interarrival times are assumed to be
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exponentially distributed. If spots are unavailable when the customers arrive, they leave
in order not to risk missing their flights.
1) What is the average number of customers being serviced per hour at the massage
station? Choose the closest answer.
A) 7
B) 8
C) 9
D) 10
E) 11
F) 12
G) 13
H) There is not sufficient information to answer the question.
Answer: F
Explanation: m = 4
p = 15 minutes
a = 60/20 = 3 minutes
r = p/a = 15/4 = 5
Pm = 0.3983
The average number of customers serviced per hour is 20 * (1 - Pm) = 12.034
Difficulty: 2 Medium
Topic: Motivating Examples: Why Averages Do Not Work; Throughput Loss for a
Simple Process
AACSB: Knowledge Application
Blooms: Apply
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2) The station manager is considering the option of hiring additional employees to deliver
massages. The hourly wage of an employee is $50/hr. How many ADDITIONAL
employees should the manager hire to maximize profits?
[Profit = revenues from customers - labor cost]
Suppose that there exists sufficient equipment to accommodate as many new employees
as needed.
A) none
B) 1 additional employee
C) 2 additional employees
D) 3 additional employees
E) 4 additional employees
F) There is not sufficient information to answer the question.
Answer: C
Explanation: With no hire, the profit rate [$/hr] is 30 * 20 * (1 - Pm) - 4 * 50 = 161.
With the addition of one employee: m = 5, Pm = 0.2849, and the profit can be computed
as before which yields 179.
With the addition of two employees: m = 6, Pm = 0.1918, and the profit can be computed
as before which yields 185.
With the addition of three employees: m = 7, Pm = 0.1205, and the profit can be
computed as before which yields 178.
The profit rate is maximized when hiring two additional employees.
Difficulty: 2 Medium
Topic: Throughput Loss for a Simple Process
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 3-6.]
Hospital Trauma Bays
The local hospital's emergency department has 6 trauma bays. On average, patients
requiring a trauma bay arrive every 30 minutes with a coefficient of variation of 1 (no
seasonality exists). If the hospital has an available trauma bay, it is immediately allocated
to a needy patient. If there are no trauma bays available, the patient is sent to another
hospital. On average, a patient's length of stay in a trauma bay is 1.5 hours (with a
standard deviation of 1.5 hours). The hospital's emergency department operates 24 hours
a day.
3) What percentage of the patients requiring trauma bays end up being sent to another
hospital?
Answer: 5.22%
Explanation: Use the Erlang Loss Formula Pm(r). The interarrival time (a) is 30 minutes,
or .5 hours. The processing time (p) is 1.5 hours for each patient.
r = p/a = 1.5/.5 = 3
P6 * 3 = 5.22
The percentage of patients who are sent to another hospital is 5.22%.
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
AACSB: Knowledge Application
Blooms: Apply
4) How many patients are treated in the trauma bays on an average 24-hour day? (Round
to the nearest whole number).
Answer: 45 patients
Explanation: One patient is treated every 30 minutes which means 2 patients per hour.
The demand of trauma bays each hour is 2 * (1 - Erlang Loss) * 24 hours each day.
2 *(1 - 0.0522) * 24 = 45.49.
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
AACSB: Knowledge Application
Blooms: Apply
5) The hospital updated the operating procedures for its staff. This led to a reduction in
the coefficient of variation of the length of stay in a trauma bay from 1.5 to 1.25 and a
reduction in the mean to 1 hour. How will this training program affect the number of
patients who have immediate access to a trauma bay?
Answer: There will be no impact on the number of patients who have immediate access
to a trauma bay because the coefficient of variation for the arrival does not change.
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
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AACSB: Reflective Thinking
Blooms: Analyze
6) New state regulations require that every emergency department be able to
accommodate at least 90% of all patients needing a trauma bay without any waiting.
What is the minimum number of trauma bays necessary to meet this requirement? (Note:
Assume that the time spent in the trauma bay cannot be changed.)
Answer: 6 trauma bays
Explanation: The minimum number of trauma bays needs to remain at 6 because the
hospital serves 100% - 5.22% = 94 - 78%. If the hospital only had 5 trauma bays, that
would fall below the state regulated 90%.
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
AACSB: Reflective Thinking
Blooms: Analyze
[The following information applies for questions 7-9.]
Doc on call
A company has started a phone service that uses overseas doctors to provide emergency
medical consultations. The responding doctors are based in a country with low wages but
with a highly skilled pool of physicians. Responding to each call takes, on average, 15
minutes. At any given time, there are 4 doctors overseas on duty. Calls arrive every 5
minutes on average (standard deviation is 5 minutes). The company receives $50 from
the patient's insurance company for each consultation. If one of the 4 overseas doctors is
available, the firm pays $20 to the doctor and makes $30 in profit. If no doctor is
available overseas, the call is rerouted to the U.S. where a local physician answers the
question. A local physician is always available to take a call. In this case, the firm pays
the $50 to the local physician, so there's no profit for the company.
7) What is the probability of a call being answered by a physician in the U.S.? (Round to
four decimal places)
Answer: 0.2061
Explanation: P4(3) = 0.2061
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
AACSB: Knowledge Application
Blooms: Apply
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8) What would be the additional revenue per hour obtained if the company managed to
have 10 doctors overseas on duty at any given time?
Answer: $0/hour
Explanation: Revenue per hour is the same (customers pay the same).
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
AACSB: Reflective Thinking
Blooms: Analyze
9) What would be the additional profit if the company managed to have 10 doctors
overseas on duty at any given time?
Answer: $73.91/hour
Explanation: P10(3) = 0.0008
Δprofits = (0.2061 - 0.0008) * 12 * 30 = $73.91/hour
Difficulty: 3 Hard
Topic: Throughput Loss for a Simple Process
AACSB: Knowledge Application
Blooms: Apply
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 11 Scheduling to Prioritize Demand
1) When working with any scheduling system, what is the common objective across
operations?
Answer: Matching demand to resources.
Explanation: The scheduler needs to consider when a particular resource will be used to
process the demand. Scheduling can span across a variety of time ranges (long, medium,
and short). Resources and time demands vary across many operations such as
manufacturing, transportation, and patient scheduling. The goal for any operation that
involves scheduling is to make sure that the resources are utilized as much as possible
and that demand is served within a reasonable amount of time.
Difficulty: 3 Hard
Topic: Scheduling Timeline and Applications
AACSB: Analytical Thinking
Blooms: Analyze
2) Aurelina Hair Salon has a busy morning ahead of them. During the first 3 hours of the
day, their top hair stylist, Marcos, has 9 clients to serve. What is the flow rate in clients
per minute that Marcos has to serve?
Answer: .05 jobs per minute.
Explanation: To figure out the flow rate (R) we need to divide the inventory (I) by the
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flow time (T) or (R = I/T).
The first 3 hours of the day is equivalent to 180 minutes (3 * 60 = 180). If Marcos serves
9 clients during this time, then you calculate 9/180 = .05 jobs per minute.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 3-6.]
Qi at Sun City Title Company
Qi is an underwriter who works at Sun City Title Company where she processes loans
daily. She usually takes an average of 40 minutes to process each loan or job and can
identify how long each one will take based on a few key indicators within the application.
Today, she has five loans that she must process by the end of the day. Each job is labeled
in alphabetical order based on the order in which it arrived. For example, A arrived first,
and B came in second, etc. (See table below)
Job
Processing Time (minutes)
A
50
B
40
C
60
D
30
E
25
F
35
3) Qi's colleague suggests that she work through each job in a first-come-first-served
(FCFS) sequence. Why would this not be the best method to use in this situation?
Answer: FCFS doesn't take into consideration the varying process times which leads to
long flow times.
Explanation: Each job has a different set of circumstances that complicate the length of
time to process it. Although FCFS may seem like the quickest way to get started and
work through each job, rearranging the order can organize a flow to these jobs in a more
time-efficient way.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Analytical Thinking
Blooms: Analyze
4) Let's say, Qi's office requires underwriters to follow the shortest-processing-time
(SPT) rule. In what order will Qi complete the jobs with SPT?
A) A, B, C, D, E, F
B) E, D, F, B, A, C
C) C, D, E on Day 1 and A, B, F on Day 2
D) D, E, F on Day 1 and A, B, C on Day 2
E) C, A, B, F, D, E
Answer: B
Explanation: With SPT or shortest-processing-time, jobs are performed in an order that
is based on the amount of time each one takes to complete. The quickest job is
undertaken first, while the longest job is saved for last. In Qi's case, Job E should be the
first one she works on because it is a 25-minute process. She will then work on Job D for
30 minutes, Job F for 35 minutes, and so on. Her last job for today should be Job C
because it will take a full hour to complete.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
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5) Let's say Qi decided not to waste a minute of her day and immediately starts the jobs
according to the FCFS rule. What would the average flow time be after these five jobs?
A) 910
B) 160
C) 162
D) 150
E) 152
Answer: E
Explanation: Looking at the chart, FCFS means that jobs are completed in the order in
which they arrive: A, B, C, D, E, F. Job A has a flow time equal to its processing time of
45 minutes. Job B has a 90-minute flow time (45 minutes waiting for A plus 50 minutes
for its own processing time). Job C has a flow time of 150 minutes (90 minutes waiting
and 60 minutes for processing). Job D has a flow time of 180 minutes (150 minutes
waiting plus 30 minutes to process). Job E has a flow time of 205 minutes (180 minutes
waiting plus 25 minutes to process). Finally, Job F has a flow time of 240 minutes (205
minutes waiting plus 35 minutes to process). The average flow time of all six jobs is
calculated by 45 + 90 + 150 + 180 + 205 + 240 = 910/6 = 151.67 = 152.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
6) Before starting her work, Qi decides to take a moment to calculate average flow times.
After she learns that the average flow time under FCFS is 152 minutes, she predicts that
the SPT rule must yield a shorter average flow time. Is she correct?
Answer: Yes.
Explanation: SPT, or shortest-processing-time, would have the job order of E, D, F, B,
A, C. Let's calculate the SPT average flow time to determine if it would be less than 152
minutes. The flow time (and processing time) for E is 25 minutes. Job D has a flow time
of 55 minutes (25 minutes of waiting plus 30 minutes to process). Job F has a flow time
of 90 minutes (55 minutes waiting plus 35 minutes to process). Job B has a flow time of
130 minutes (90 minutes waiting plus 40 minutes to process). Job A has a flow time of
180 minutes (130 minutes waiting plus 50 minutes to process). Job C has a flow time of
240 minutes (180 minutes waiting plus 60 minutes to process). The average flow time is
calculated by 25 + 55 + 90 + 130 + 180 + 240 = 720/6 = 120. The average flow time
under FCFS (above) was 152 minutes. Thus, 152 - 120 = 32, so SPT is 32 minutes less
than the average flow time of FCFS.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Analytical Thinking
Blooms: Analyze
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7) Brianna is a software developer who has four programs to complete this season. She
estimates that one program will take two weeks to complete, two of them will take three
weeks to complete and the other one will take her four weeks. Brianna plans to use some
of her vacation time this season, so she will not accept any more program requests
beyond these four this season.
What is Brianna's flow rate, or projects per week, during the time these programs are
worked on?
Answer: .33.
Explanation: Flow rate (R) is determined by R = I/T. I represents inventory and T is for
flow time. Brianna has 4 jobs to complete within 12 weeks (2 + 3 + 3 + 4 = 12). Calculate
4/12 = .33 flow rate.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Analyze
[The following information applies to questions 8-10.]
Last season, Brianna had one of the busiest periods of her career in software
development. Take a look at the table below to see the number of programs she agreed to
build. Once Brianna accepts a collection of jobs, or programs to build, at the beginning of
a season, she does not accept any more until the next season. Brianna utilizes the
shortest-processing-time (SPT) scheduling application.
Job (programs to build)
Processing time (weeks)
A
2
B
1
C
4
D
6
E
3
F
5
8) Recall that Brianna uses the SPT rule. In what sequence did she build these six
programs?
Answer: B, A, E, C, F, D.
Explanation: When using shortest-processing-time (SPT), jobs are completed according
to the length of time they take. In other words, SPT begins with the quickest job and ends
with the one that will consume the most amount of time.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
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9) What was Brianna's flow time of job F? (Enter your answer in weeks).
Answer: 15 weeks.
Explanation: Recall that flow time is the sum of the wait time plus the process time. Job
B had a flow time of 1 week. Job A was 3 weeks (1 waiting and 2 for processing). Job E
took 6 weeks (3 weeks waiting and 3 weeks of processing). Job C was 10 weeks (6 weeks
waiting and 4 weeks to process). Finally, Job F had a flow time of 15 weeks (10 weeks
waiting and 5 weeks to process). In this situation, we do not look at Job D because it was
worked after job F under the SPT rule.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
10) What was Brianna's average flow time of jobs in the system?
Answer: 9.33.
Explanation: Let's continue with the calculations above and figure out the flow time for
the last job that Brianna undertook according to the SPT rule, Job D. Job D waited 15
weeks and then required 6 more weeks of its own processing time, which is a total of 21
weeks. To understand the average flow time, we need to add the flow time of all her jobs
and divide the total by 6.
Hence, 1 + 3 + 6 + 10 + 15 + 21 = 56/6 = 9.33. Brianna's average flow time of jobs in the
system was 9.33 weeks.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
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11) Which of the following would be a reason to use first-come-first-served (FCFS)
rather than shortest-processing-time (SPT)?
A) A sandwich shop has a long line of customers to serve.
B) A new tax accountant has to process a pile of income tax returns but isn't familiar with
how to determine the length of time each one will take to process.
C) An insurance adjuster has just received several cases to process, but some of the
information in the files may be biased in hopes of a faster processing time.
D) All of the above are reasons to use FCFS.
E) None of the above are reasons to use FCFS.
Answer: D
Explanation: Generally, the shortest-processing-time (SPT) is a preferable model to
follow, but there are a few cases in which first-come-first-served (FCFS) is the better
option. A sandwich shop should serve each customer as they enter the establishment to be
fair to their patrons who can probably see the order of meals coming out. A new tax
accountant may not be able to determine, at this point, how long each return will take and
should get started under the FCFS rule to avoid a delay. Finally, potentially biased
processing times, in the case of the insurance adjuster, is a reason to work in the order of
FCFS because the estimated processing times may be purposefully distorted.
Difficulty: 3 Hard
Topic: Resource Scheduling-Shortest Processing Time
AACSB: Analytical Thinking
Blooms: Analyze
12) What scheduling system should be used when a company has to pay $0.50 for every
hour it holds onto its inventory?
A) FCFS
B) SPT
C) WSPT
D) EDD
E) LPT
Answer: C
Explanation: This is a situation where the priority of jobs is weighted heavily due to
inventory holding costs. It would be in the company's best interest to not only follow the
shortest-processing-time rule but to prioritize it by the weight of how much inventory
each job is responsible for.
Difficulty: 3 Hard
Topic: Resource Scheduling with Priorities-Weighted Shortest Processing Time
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 13-14]
Southern States Bank has five small business loans to process and only one loan
processor at this location. See the table below for more information on each loan's
processing time and weight, or cost per unit of time).
Job
Processing time (hours)
Weight/priority (cost per unit of time)
A
12
2
B
20
5
C
8
1
D
18
6
E
25
5
13) What scheduling system should Southern States Bank use to process these small
business loans?
A) WSPT
B) EDD
C) FCFS
D) SPT
E) LPT
Answer: A
Explanation: In this case, it is best to use the weighted-shortest-processing-time (WSPT)
rule because the loans have varying priorities based on the size of the loan. It would be
preferable to process the loans not only by their length of processing time, but also by the
weight, or cost per unit of time that they carry.
Difficulty: 3 Hard
Topic: Resource Scheduling with Priorities-Weighted Shortest Processing Time
AACSB: Analytical Thinking
Blooms: Analyze
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14) In what order will Southern States Bank process these loans if they use the weightedshortest-processing-time (WSPT) rule?
A) E, D, B, A, C
B) A, B, C, D, E
C) D, B, E, A, C
D) E, D, C, B, A
E) C, A, B, D, E
Answer: C
Explanation: To determine the order of these jobs using WSPT rule, the ratio of its
weight to its processing time should be calculated. Job A is calculated by 2/12 = .17. Job
B is calculated by 5/20 = .25. Job C is calculated by 1/8 = .13. Job D is calculated by 6/18
= .33. Finally, Job E is calculated by 5/25 = .2. After calculating the ratio for each job, we
then put them in decreasing order of their weight to ensure that the jobs of the highest
weight are the first to be processed. Hence, the order should be: D (.33), B (.25), E (.2), A
(.17), and C (.13).
Difficulty: 3 Hard
Topic: Resource Scheduling with Priorities-Weighted Shortest Processing Time
AACSB: Knowledge Application
Blooms: Apply
15) When would it be most appropriate to sequence a series of jobs by earliest-due-date?
A) The weight of the jobs varies substantially.
B) The weight of the jobs varies minimally.
C) The shortest-processing-time pushes the jobs beyond the due date.
D) The shortest-processing-time does not take due-dates into consideration.
E) The jobs are on a strict completion timeline.
Answer: E
Explanation: Although SPT might work in the situation of due-dates, if you are working
with a strict timeline, the earliest-due-date (EDD) rule should apply. The benefit of using
EDD when working with due dates is because it is based on the calculation of deadlines,
lateness, and tardiness.
Difficulty: 3 Hard
Topic: Resource Scheduling with Due Dates-Earliest Due Date
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 16-19]
The following jobs need to be processed using the earliest-due-date (EDD) rule.
Job
Processing time (days)
Due dates (days)
A
5
15
B
7
13
C
4
16
D
9
14
E
6
18
16) What would be the lateness of Job A?
Answer: 6.
Explanation: First, we would sequence these jobs by order of their due date: B, D, A, C,
and 18. Then, we work through the jobs, starting with Job B. Job B has a processing time
of 7 days, which also means a flow time of 7 days because it will be the first job
according to the EDD rule. Job B was due within 13 days, so its lateness is -6. Next, we
look at Job D. Job D has a flow time of 16 days (7 waiting and 9 processing). It is due
within 14 days, so we are now at a lateness of 8. Finally, we look at Job A. Job A has a
flow time of 21 days (16 waiting and 5 processing). Job A is due within 15 days, so we
are now at a lateness of 6.
Difficulty: 3 Hard
Topic: Resource Scheduling with Due Dates-Earliest Due Date
AACSB: Analytical Thinking
Blooms: Analyze
17) What would be the tardiness of Job A?
Answer: 6
Explanation: Tardiness looks at how much time has elapsed since the due date. If the
amount is negative, meaning that the job was completed early, then tardiness would be 0.
In the case of Job A, it has a tardiness amount of 6 days. This is because it has a flow
time of 21 days while the due date is within 15 days (21 - 15 = 6)
Difficulty: 3 Hard
Topic: Resource Scheduling with Due Dates-Earliest Due Date
AACSB: Knowledge Application
Blooms: Apply
18) What is the maximum tardiness?
Answer: 13
Explanation: If we continue to work through the jobs, we see that C was tardy by 9 days
(25 days flow time minus 16 days of being due). Job E has a tardiness of 13 because of
31 days flow time minus 18 days due. The maximum tardiness is 13 days.
Difficulty: 3 Hard
Topic: Resource Scheduling with Due Dates-Earliest Due Date
AACSB: Knowledge Application
Blooms: Apply
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19) Let's take the job information above and see how lateness would differ if the jobs are
processed with SPT. Which of the following jobs would have a lateness amount greater
than 0?
A) None of the jobs because they would all be completed in time.
B) All of the jobs would be late because SPT does not take into consideration due dates.
C) Jobs B and D would be late.
D) Only Job D would come in late.
E) Only Job C would come in late.
Answer: C
Explanation: The order of jobs would now change to C, A, E, B, D. Job C has a flow
time of 4, and it is due with 16 days, so it has a lateness factor of -12. Job A has a flow
time of 9 (4 days waiting and 5 processing). It is due within 15 days, so it comes in 6
days early (-6). Job E has a flow time of 15 (9 days waiting and 6 days to process). It is
due within 18 days, so its lateness is -3. Job B has a flow time of 22 days (15 days
waiting and 7 to process). It is due within 13 days, meaning it is 9 days late. Finally, Job
D has a flow time of 31 days (22 days waiting and 9 to process). It is due within 14 days,
so it is 17 days late. Jobs B and D would both be late under the SPT rule.
Difficulty: 3 Hard
Topic: Resource Scheduling with Due Dates-Earliest Due Date
AACSB: Knowledge Application
Blooms: Apply
20) Bridgeport Electronics is a small facility that distributes integral circuits throughout
the Northeastern United States. It has seen an increase in orders recently due to the
collapse of its biggest competitor. The management team is trying to decide on a more
efficient workflow order to keep up with the demand. The customers have not designated
due-dates, and fortunately, Bridgeport Electronics does not have to pay any inventory
holding costs. The only issue at this point is that there has been a delay in producing
circuit boards because a buffer behind one of its smaller machines has been filling up.
What scheduling system should Bridgeport Electronics utilize to improve this process?
Answer: Longest Processing Time (LPT)
Explanation: In this situation, the longest processing time (LPT) would be the
recommended scheduling rule to follow. According to the theory of constraints, the flow
rate is determined by the rate that jobs are flowing through the bottleneck. The small
machine that has a backup occurring behind it is the bottleneck. As the buffer fills, it
increases the risk of the bottleneck becoming backed up. By following the LPT rule, jobs
will come to the small machine at a slower rate which will decrease the collection behind
it.
Difficulty: 3 Hard
Topic: Theory of Constraints
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
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(Cachon)
Chapter 12 Project Management
1) Building Brothers Construction Company has just been awarded a contract to build a
commercial building in Seattle, Washington. Their team of project managers has started
the process of listing the work that is required for the completion of this project. They
have broken plans down into ten smaller activities that will each require the following
amount of days: 7, 4, 9, 14, 26, 12, 8, 5, 19, and 3. Based on this information, how long
will this construction project take to complete?
A) Exactly 26 days
B) Exactly 107 days
C) More than 26 days
D) More than 107 days
E) More information is needed to make this determination.
Answer: E
Explanation: At first glance, the duration of this project may appear to require 26 days
since that is the longest activity or 107 days if all of the activities are added. At this point
though, the anticipated duration of this project cannot be determined because more
information is needed. For example, some of these activities may be able to start
concurrently, while other "downstream" activities may require the completion of a
previous, or "upstream" activity. The team needs to create a chart that shows what each
activity is dependent upon before its commencement.
Difficulty: 3 Hard
Topic: Motivating Example
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 2-3.]
The following five activities need to be completed in the development of an interactive
website for children. Activity 1 begins first and Activity 2 is dependent upon its
completion before it can begin. Activity 3 is dependent upon the completion of both
Activities 2 and 1. Activity 4 is not dependent on information from any other activities,
but Activity 5 is reliant on the completion of Activity 4.
2) Build a dependency matrix to represent these five activities.
Answer:
Explanation: Activities 1, 2, 3, and 5 are all dependent upon previous activities for
completion. This chart depicts the upstream and downstream activity for the development
of the website.
Difficulty: 3 Hard
Topic: Motivating Example
AACSB: Knowledge Application
Blooms: Apply
3) Based on the dependency matrix above, which of the following activities is likely not
to be a part of the critical path?
A) Activity 1
B) Activity 2
C) Activity 3
D) Activity 4
E) Activity 5
Answer: D
Explanation: Activity 4 is not an information-providing activity for any others and likely
has some wiggle room associated with its completion as a result of this.
Difficulty: 3 Hard
Topic: Motivating Example
AACSB: Knowledge Application
Blooms: Apply
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4) Which of the following is a reason for the use of an activity-on-node (AON) diagram?
A) To create a visual of the project's critical path.
B) To manage a project.
C) To sequence activities based on their dependency on other activities.
D) To examine expected activity duration times.
E) All of the above are reasons to use AON.
Answer: E
Explanation: Activity-on-node is a visual tool that project managers use to determine the
critical path of a project. It provides a visual representation of the order that activities can
be completed in, based on what other activities they are relying on, and the duration of
time that they take to complete.
Difficulty: 3 Hard
Topic: Critical Path Method
AACSB: Reflective Thinking
Blooms: Analyze
5) Which of the following is observed within the area of project management, not process
management?
A) The completion time of the whole project.
B) The resources with the highest capacities.
C) The longest and shortest activity times.
D) The bottleneck of the activities.
E) The resources with the lowest capacities.
Answer: A
Explanation: Project management is concerned with the project in its entirety which
would include the final completion time of the entire project. Observing the capacity of
the resources and individual activity duration times falls under the process management
role.
Difficulty: 3 Hard
Topic: Computing Project Completion Time
AACSB: Reflective Thinking
Blooms: Analyze
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[The following information applies to questions 6-7.]
A hotel renovation company has recently accepted an extensive renovation project in
downtown Raleigh, NC. The project manager has listed the following paths after creating
and analyzing an activity-on-node representation with a total of 6 activities.
Path 1: A1-A2-A5-A6 with a duration of 7 + 4 + 10 + 3 = 2 days
Path 2: A1-A3-A5-A6 with a duration of 7 + 5 + 10 + 3 = 25 days
Path 3: A1-A3-A4-A6 with a duration of 7 + 5 + 12 + 3 = 27 days
6) What is the activity with the longest duration?
A) Activity 1
B) Activity 2
C) Activity 3
D) Activity 4
E) Activity 5
Answer: D
Explanation: The activity with the longest duration is A4, which will require a duration
of 12 days. This activity can also serve as a risk of being the bottleneck and affects the
completion time of the entire project.
Difficulty: 3 Hard
Topic: Computing Project Completion Time
AACSB: Knowledge Application
Blooms: Apply
7) What is the critical path?
Answer: Path 3.
Explanation: The path with the longest duration is considered the critical path. Activity 3
will consume the longest amount of time with a total of 27 days.
Difficulty: 3 Hard
Topic: Computing Project Completion Time
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 8-9.]
Consider the following table of activities for a minor project on a construction site.
Earliest Start Time Expected Durations
Activity
(EST)
(days)
A1
0
5
A2
ECT(A1) = 5
2
A3
ECT(A2) = 7
6
A4
ECT(A2)
4
Earliest Completion
Time (ECT)
5
7
13
8) What is the earliest start time (EST) for activity 4 (A4)?
Answer: 7 days.
Explanation: Activity 4 is dependent upon the completion of activity 2. Activity 2 has
the earliest completion time of 7 days. Thus, for activity 4, we plan an EST of 7 days.
Difficulty: 3 Hard
Topic: Finding the Critical Path and Creating a Gantt Chart
AACSB: Knowledge Application
Blooms: Apply
9) What is the earliest completion time (ECT) for the final activity (A4)?
Answer: 11 days.
Explanation: Activity 4 can commence after the completion of activity 2, which is 7
days. The anticipated duration of activity 4 is 4 days. Thus, we use the equation ECT(A4)
= EST(A2) + Duration(A4) to determine the ECT of activity 4 which is 7 days plus 4
days. For activity 4, we have ECT of 11 days.
Difficulty: 3 Hard
Topic: Finding the Critical Path and Creating a Gantt Chart
AACSB: Knowledge Application
Blooms: Apply
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10) Which of the following is true about the critical path of activities?
A) The activity with the longest duration is always on the critical path.
B) The entire project is delayed if any activity on the critical path is delayed.
C) The critical path is the path with the longest duration of activities.
D) Answer choices B and C are correct.
E) None of the above answer choices are correct.
Answer: D
Explanation: The critical path is determined by the path that has the longest duration of
combined activities. It is very important to pay attention to this path as a delay in any one
of its activities can affect the timeline of the entire project. Whereas, other paths that are
not the critical path may have slack time and a delay may not affect the completion time
of the project. This path does not always necessarily have the single activity with the
longest duration within it.
Difficulty: 3 Hard
Topic: Critical Path Method; Computing Slack Time
AACSB: Reflective Thinking
Blooms: Analyze
11) The following activities are on the critical path of a project. A1 with a duration of 3
days and immediate start time. A2 can begin after A1 with a duration of 5 days, and A3 is
dependent upon the completion of A2. What is the slack time for the completion of the
entire project?
A) 0
B) 1
C) 2
D) 3
E) 4
Answer: A
Explanation: All activities within the critical path have a slack time of 0. Other paths that
are not the critical path may or may not have slack time.
Difficulty: 3 Hard
Topic: Computing Slack Time
AACSB: Analytical Thinking
Blooms: Analyze
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12) Which of the following would be a reason to incorporate slack time?
A) Slack time should not be considered at any time because it can delay an entire project.
B) To allocate available resources at more pressing times in the process.
C) When other activities are dependent upon activities before they can begin.
D) To delay the sequence of activities along the critical path.
E) If you are trying to rush the completion date of the project.
Answer: B
Explanation: Slack time can be incorporated, if the activities are not on the critical path,
although, it will not help the project finish earlier. A reason to calculate and incorporate
slack time will be if there is wiggle room with activities that are not on the critical path.
Slack time can be useful to dedicated resources to other activities that are more pressing.
Difficulty: 3 Hard
Topic: Computing Slack Time
AACSB: Reflective Thinking
Blooms: Analyze
[The following information applies to questions 13-15.]
Consider the following project that has uncertainty in activity duration. Activity 1 has a
completion time of 7 or 10 days, each with a 50% probability. Activity 2 has a
completion time of 9 or 13 days, each with a 50% probability. Both activities 1 and 2 can
start immediately and must be completed before activity 3, which has a deterministic
duration of 4 days.
13) What is the best-case scenario completion for this project?
Answer: 13 days.
Explanation: The earliest completion time for activity 1 is 7 days, but for activity 2, the
earliest completion is 9 days. Activity 3 cannot start until activity 2 has finished. Hence, 9
days for the first set of activities plus 4 deterministic days for activity 3 is a total of 13
days.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Knowledge Application
Blooms: Apply
14) What is the worst-case scenario completion time for this project?
Answer: 17 days.
Explanation: Both activities 1 and 2 can start at the same time, with activity 2 having the
latest possible completion of 13 days. The 13 days combined with the 4 days for activity
3 brings the latest completion time of 17 days.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Knowledge Application
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Blooms: Apply
15) What is the expected completion time for this project?
Answer: 15 days.
Explanation: We calculate the probability of the four possible completion times. If both
activities finish early, there is a 25% probability of a 13-day completion. If both activities
finish late, there is a 25% probability of a 17-day completion. If activity 1 finishes late
and activity 2 finishes early, there is a 25% probability of a 13-day completion. Finally, if
activity 1 finishes early and activity 2 finishes late, there is a 25% probability still of a
17-day completion time. So, we calculate .25 * 13 days + .25 * 17 days + .25 * 13 days +
.25 * 17 = 15 days.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 16-18.]
The Three Marketeers is a startup company that has just secured its first account with an
established corporation. The project manager who is assigned to this account
acknowledges that there a great deal of uncertainty with two of the activities within the
project. Activity 1 has a 50:50 probability of finishing within 12 or 15 days. Activity 2
has a 50:50 probability of finishing within 13 or 17 days.
16) What is the best-case scenario completion date for this project?
Answer: 25 days.
Explanation: If both activities can finish at the earliest possible time, they will be
completed at 12 days and 13 days respectively. This will bring the project completion
time to a total of 25 days.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Analytical Thinking
Blooms: Analyze
17) What is the worst-case scenario completion date for this project?
Answer: 32 days.
Explanation: The worst-case completion date for this project has activity 1 being
completed at 15 days and activity 2 finishing at 17 days for a combined amount of 32
days. Hopefully, the project will not take this long, but it is helpful for the project
managers to plan for this possibility.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Analytical Thinking
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Blooms: Analyze
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18) What is the expected completion time for this project?
Answer: 14.25 days
Explanation: Calculate .25 * 12 days + .25 * 15 days + .25 * 13 days + .25 * 17 days
= 14.25 days.
The four possible completion times are each calculated at a 25% probability which brings
this projected to an expected completion time of 14.25 days.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Analytical Thinking
Blooms: Analyze
19) Under what circumstance would the use of a Gantt chart and the critical path method
be useful?
A) Projects with high uncertainty.
B) Projects that will likely require iteration.
C) Projects with low uncertainty or high certainty.
D) Projects that have activities with multiple rework loops.
E) Projects that are innovative and uncommon.
Answer: C
Explanation: The use of Gantt charts and the critical path method provide the most
benefit toward projects that have a stronger level of certainty assigned to them. These two
methods become less helpful in situations where there already exists risk associated with
uncertainty.
Difficulty: 3 Hard
Topic: Dealing with Uncertainty
AACSB: Reflective Thinking
Blooms: Analyze
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20) Windy City Construction Company is seeking to accelerate one of its smaller
construction projects so that the team and resources are available in time for a much
larger project. What should the project manager consider as a viable option to speed
activities up within this project?
A) Assign team members to begin preliminary activities while waiting for information
providing activities to begin.
B) Front load early activities extra funding in order to prevent them from stretching on
during longer durations.
C) Have plans in place to ensure high levels of productivity as soon as the project is able
to begin.
D) Very carefully analyze and finalize the scope of the project and have plans in place in
case of the event of a needed change.
E) All of the above are viable options for helping the project finish in time.
Answer: E
Explanation: All of the options listed can assist in moving the project along at a
productive rate. Starting the project early with a plan of the scope can kick the work off
to a strong start. Dedicating funding toward activities early on instead of allowing them
to lag and working to complete some preliminary activities can also help to rush the
project.
Difficulty: 3 Hard
Topic: How to Accelerate Projects
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 13 Forecasting
[The following information applies to questions 1-2.]
A relatively young trampoline park company, named Wiggles Out, has been studying the
market-demand within a large city and surrounding area for years. It has recently opened
up a location between the city and a large suburb that has a substantial population of
young families.
1) Wiggles Out has utilized a system that includes automated and expert panel
forecasting. What time horizon did they work under to determine the forecasted demand
for this new location?
A) Short-term forecasts
B) Mid-term forecasts
C) Long-term forecasts
D) Time-series analysis
E) Generational analysis
Answer: C
Explanation: The trampoline park studied the industry and local market for years. This
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falls under the time horizon category of long-term forecasts, which is especially
important to do for the more substantial investment of entering a new market with a
building location.
Difficulty: 3 Hard
Topic: Forecasting Framework
AACSB: Reflective Thinking
Blooms: Analyze
2) The co-owners of Wiggles Out have been attempting to forecast the number of
jumpers each week for the last three months since the park opened. Now, they are trying
to tighten up spending as they enter the second quarter. For week twelve, for example, the
co-owners forecasted an optimistic amount of 370 jumpers but only ended up welcoming
245. What was their forecast error for week 12?
Answer: 125 jumpers.
Explanation: Forecast error is equal to the forecast minus the actual value, so 370 - 245 =
125. The co-owners were off by 125 customers (jumpers).
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 3-9.]
The co-owners of Wiggles Out have contracted a business demand forecast expert to help
them with the forecasting so that they can better prepare for the crowd fluctuations. This
expert includes variables such as weather, advertising, and school sessions to create her
forecasts. View the table below for a comparison between the co-owners' forecasts and
the expert's forecasts for the next four weeks.
Week 1
Week 2
Week 3
Week 4
Co-Owners' Forecast
370
270
250
390
Expert's Forecast
260
275
330
380
True Demand
245
260
375
400
3) What is the co-owners' forecast error on average?
Answer: 0.
Explanation: First, we compute the co-owners forecast on average:
370 + 270 + 250 + 390 = 1,280/4 weeks = 320. Then, we compute the true demand on
average over the 4 weeks: 245 + 260 + 375 + 400 = 1,280/4 = 320. Lastly, we compute
the difference to find 320 - 320 = 0.
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Knowledge Application
Blooms: Apply
4) What is the expert's forecast error on average?
Answer: 8.75.
Explanation: We need to calculate the difference between the expert's average forecast
over the 4 weeks and the four-week true demand average. So, for the expert's forecasted
amounts, we add 260 + 275 + 330 + 380 = 1,245/4 weeks = 311.25. We know from
above that the average of the true demand over the 4 weeks was 320, so the difference is
320 - 311.25 = 8.75.
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Knowledge Application
Blooms: Apply
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5) Based on the forecast error averages above, what can we determine?
A) The expert's forecast error is wrong, on average.
B) The co-owners forecast error is right, on average.
C) The co-owners forecast on average is unbiased, and the expert's forecast on average is
biased.
D) All of the above.
E) None of the above.
Answer: D
Explanation: When looking at the chart above, the expert's forecasts appear closer to the
true demand of jumpers per week. However, when averages are considered, we see that
the co-owners have an unbiased forecast because the amounts that the over or
underpredicted balance each other out.
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Analytical Thinking
Blooms: Analyze
6) In order to gain a better understanding of whose forecast is more accurate, the coowners decide to analyze forecast errors during the four weeks. What is the mean
absolute error, or MAE, of the co-owners' four-week forecast?
Answer: 67.5.
Explanation: To find the MAE, we first subtract the true demand from the forecast to
determine the forecast error, and then take its absolute value. So, for week 1, 370 - 245 =
125. For week 2, 270 - 260 = 10. For week 3, 250 - 375 = -125 = |125|. For week 4, 390 400 = -10 = |10|.
We then calculate the average of these values, 125 + 10 + 125 + 10 = 270/4 = 67.5. This
means that the average forecast error of the co-owners is 67.5 jumpers per week.
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Analytical Thinking
Blooms: Analyze
7) What is the mean absolute error, or MAE, of the expert's four-week forecast?
Answer: 23.75.
Explanation: Again, to find the MAE, we first subtract the true demand from the forecast
to determine the forecast error, and then take its absolute value. So, for week 1 is 260 245 = 15. For week 2 is 275 - 260 = 15. For week 3 is 330 - 375 = -45 = |45|. For week 4
is 380 - 400 = -20 = |20|. We then calculate the average of these values, 15 + 15 + 45 + 20
= 95/4 = 23.75. This means that the average forecast error of the expert is 23.75 jumpers
per week.
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Analytical Thinking
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Blooms: Analyze
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8) Based on the MAE data for both the co-owners and the expert, who is doing a better
job with forecasting the number of jumpers per week?
Answer: The Expert.
Explanation: Based on the MAE data, the expert has a lower mean absolute error (MAE)
value, which means a better forecast. Albeit, she is still 23.75 jumpers off, her forecasting
is closer than the 67.5 that the co-owners were off by.
Difficulty: 3 Hard
Topic: Evaluating the Quality of a Forecast
AACSB: Reflective Thinking
Blooms: Analyze
9) If the co-owners use the naïve forecasting model, how many jumpers will Wiggles Out
welcome during the course of week 5?
A) 400
B) 320
C) 311.25
D) 390
E) 380
Answer: A
Explanation: The naïve model uses data from the last measurement period. Thus, since
the actual demand of jumpers during week 4 was 400, the naïve model would declare a
forecast of 400 jumpers in week 5.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 10-15.]
A city in South Florida is tracking traffic accident data during its peak season for tourism.
View the chart below to see these dismal numbers.
Week
1
2
3
4
5
6
7
8
9
Traffic
Accidents
19
24
27
20
29
31
21
26
28
10) Based on the traffic accident data, how many traffic accidents are forecasted for week
10 using the naïve method?
Answer: 28.
Explanation: The naïve method simplistically uses data from the previous period. Week
9 saw 28 accidents so that the naïve method would assume another 28 in week 10.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
11) Based on the table provided, what is the three-week moving average forecast for
week 10?
Answer: 25.
Explanation: For moving average forecasts, the actual demands of the preceding periods
are equally averaged. Since this question asks for the three-week moving average, we
consider the data from weeks 9, 8, and to determine the forecast for week 10. Hence, 28 +
26 + 21 = 75/3 = 25.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
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12) Based on the table provided, what is the four-week moving average forecast for week
10?
Answer: 26.5.
Explanation: Again, for moving average forecasts, the actual demands of the preceding
periods are equally averaged. Since this question asks for the four-week moving average,
we consider the data from weeks 9, 8, 7, and 6 in determining the forecast for week 10.
Hence, 28 + 26 + 2 + 31 = 106/4 = 26.5.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
13) Assume a smoothing parameter of .1 and a forecasted amount of accidents for week 9
was 24. What is the exponential smoothing forecast for week 10?
A) 28.4
B) 28
C) 24
D) 24.2
E) 24.4
Answer: E
Explanation: For exponential smoothing, we apply more weight to the current period
than the past. Calculate (0.1 * 28) + [(1 - 0.1) * 24] = 24.4 is the forecast for week 10.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
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14) Historically, the second week of the peak tourist season has some of the highest
amounts of traffic accidents as travelers come into the area. The forecast for week 2 was
originally 35. Assuming a .5 smoothing parameter, what was the forecast for week 3
(before we knew the actual demand)?
A) 35
B) 29.5
C) 24
D) 24.5
E) 35.5
Answer: B
Explanation: Although this demand has already been realized, we can go back to the
table to determine what the forecasted demand for week 3 was under the exponential
smoothing method. We know the actual amount of accidents was 24, so we calculate (0.5
* 24) + [(1 - 0.5) * 35] = 29.5 was the week 3 forecast.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
15) Let's say the forecast for week 7 was 29 and assume the smoothing parameter is .3.
Based on this information, what was the forecast for week 8 before the actual amount was
realized?
Answer: 26.6.
Explanation: For this, we know the actual amount of accidents during week 7 was 21, so
we calculate (0.3 * 21) + [(1 - 0.3) * 29] = 26.6 was the forecast for week 8. Notice that
the actual amount of traffic accidents was very close to this forecasted amount.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
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16) Which of the following is a reason why forecasting based on time-series analysis
might limit accuracy?
A) Expert insight is omitted.
B) Based on past data alone.
C) Seasonality.
D) Long-term pattern trends.
E) All of the above.
Answer: E
Explanation: Although time-series analysis can provide some insight when forecasting, it
should not be solely relied upon as it doesn't consider some valid information. For
example, it does not provide expert insight, seasonal fluctuations, and trend fluctuations.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Reflective Thinking
Blooms: Analyze
17) An aging theatre company has seen a steady decrease in audience members each
weekend (when it is open). During the first week of the summer season, 190 people
bought tickets for their production. Week 2 yielded 180 people, 175 tickets were sold in
week 3, and week 4 only produced 166. Based on the two-week moving average forecast,
how many theatre tickets might sell in week 5?
Answer: 170.5.
Explanation: For the two-week moving average, we take into consideration the data from
week 4 and week 3 only. Thus, 166 + 175 = 341/2 = 170.5. Notice, that this amount does
not follow the steady decreasing trajectory.
Difficulty: 3 Hard
Topic: Eliminating Noise from Old Data
AACSB: Knowledge Application
Blooms: Apply
18) A current demand was forecasted to be 595 with an actual demand of 578. Assuming
a smoothing parameter of 0.3, a trend smoothing parameter of 0.5, and an initial trend
forecast of 4, what is the smoothed demand forecast for the next period?
Answer: 593.9.
Explanation: To capture this forecast, we calculate the following:
(0.3 * 578) + [(1 - 0.3) * 595] + 4 = 593.9. The smoothed demand forecast for the next
period.
Difficulty: 3 Hard
Topic: Time Series Analysis —Trends
AACSB: Knowledge Application
Blooms: Apply
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19) With the information above, what is the exponentially smoothed trend?
Answer: 1.45.
Explanation:
In order to capture the trend, we calculate [0.5 * (593.9 - 595)] + [(1 - 0.5) *4] = 1.45.
Difficulty: 3 Hard
Topic: Time Series Analysis —Trends
AACSB: Knowledge Application
Blooms: Apply
20) What benefit can a subjective forecast offer supply managers?
A) Factual data.
B) Automated information.
C) Time-saving efficiency.
D) Insight that goes beyond the present time.
E) The suggestion that the future will be like the past.
Answer: D
Explanation: While mathematical forecasting uses objective data to make assumptions
about future demand, they are only using past or current data. Subjective forecasts though
are unique in that they provide expertise and human intuition into what demands may
come.
Difficulty: 3 Hard
Topic: Expert Panels and Subjective Forecasting
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 14 Betting on Uncertain Demand: The Newsvendor Model
[The following information applies to questions 1-5.]
Goop Inc. needs to order a raw material to make a special polymer. The demand for the
polymer is forecasted to be normally distributed with a mean of 250 gallons and a
standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop
purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose
of unused raw material due to government regulations. (One gallon of raw material yields
one gallon of polymer.) If demand is more than Goop can make, then Goop sells only
what they made, and the rest of demand is lost.
1) Suppose Goop purchases 150 gallons of raw material. What is the probability that they
will run out of raw material? (Enter the answer as a percentage)
Answer: 78.8%
Explanation:
z = (150 - 250)/125 = -0.8. From the Distribution Function Table, F(-0.8) = 21.2%. They
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will run out of raw material if demand exceeds this quantity, which has a 1 - 21.2% =
78.8% change.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
2) Suppose Goop purchases 300 gallons of raw material. How many gallons of demand
on average would remain unfulfilled?
Answer: 28.8
Explanation: z = (300 - 250)/125 = 0.4. From the loss function table, L(0.4) = 0.2304.
Lost Sales = sigma × L(z) = 28.8 gallons.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
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3) Suppose Goop purchases 400 gallons of raw material. How much should they expect
to spend on disposal costs?
Answer: $785
Explanation: z = (400 - 250)/125 = 1.20.
Lost Sales = sigma × L(1.20) = 7.01.
Expected Sales = mu - Lost Sales = 250 - 7.01 = 243.
Expected left over inventory = Q - Expected Sales = 400 - 243 = 157.
Disposal cost = $5 * 157 = $785.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Analytical Thinking
Blooms: Analyze
4) Suppose Goop wants to ensure that there is a 92% probability that they will be able to
satisfy the customer's entire demand. How many gallons of raw material should they
purchase?
Answer: 426
Explanation: Look up 0.92 in the distribution function table and we find that z = 1.41.
Convert to an order quantity Q = 250 + 1.41 * 125 = 426 gallons.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Knowledge Application
Blooms: Apply
5) How many gallons should Goop purchase to maximize its expected profit?
Answer: 250
Explanation: The underage cost is $25 - $10 = $15. The overage cost is $10 + $5 = $15.
The critical ratio is 0.5, z = 0, Q = 250 gallons.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 6-7.]
Betty Cooker runs a bakery in San Francisco that specializes in her famous Black Forest
cakes. These cakes come with four kinds of frostings: vanilla, chocolate, raspberry and
devilicious. She estimates that the daily demand for each type of cake is independent and
is normally distributed with a mean of 50 and a standard deviation of 20. Each customer
wants to buy exactly one cake. Customers who favor a particular type of frosting will not
buy any other if their preferred frosting is out of stock. Every day in the morning, Betty
Cooker and her team of bakers prepare a fresh batch of the cakes for sale that day. Her
costs to bake and top each cake are $5. Each cake sells for $15. Betty's Bakery prides
itself on its fresh assortment, so cakes not sold by the end of that day are given away to a
soup kitchen for the homeless.
6) Suppose Betty wants to bake enough cakes so that she can be 97.5% sure that she can
satisfy the demand of all of her customers. How many cakes with devilicious frosting
should she prepare daily in the morning? (Enter the answer as a whole number, do not
round)
Answer: 89
Explanation: From the Standard Normal Distribution Function Table Φ(1.96) = 0.975.
The desired order quantity is Q = 50 + 1.96 * 20 = 89.2 cakes.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
7) She hires a consultant, Trump McDonald, who advises her to, "Focus on maximizing
your expected daily profits, and the customer demand will take care of itself." In order to
maximize profits, Trump advises Betty to bake 60 Devilicious cakes. What would be
Betty's expected profit from Devilicious cakes if she followed Trump's advice?
Answer: $390.60
Explanation: z = (60 - 50)/20 = 0.5, Expected Lost Sales = 3.96, Expected Sales = 46.04,
and Expected Leftover = 13.96. Expected profit = 10 * 46.04 - 5 * 13.96 = 390.60.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Analytical Thinking
Blooms: Analyze
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8) Bob's Fly catalog collected forecasts, sales, and demand data for 20 items in one
category from its previous catalog. The data is provided below in the table.
For example, their forecast for the first item in the table was 100 units, but it
unfortunately only sold 26 units. However, with the last item listed, they sold 341 units
but could have sold 569 units if they had ordered enough inventory.
For the next catalog, they have an item for which they forecast demand to be 400 units.
Suppose they will use that forecast along with the data in the above table to choose a
normal distribution to model demand for this product. What mean and standard deviation
should they choose? (Separate your answers with a comma)
Answer: 368, 168
Explanation: Mean = 400 * 0.92 = 368. Standard deviation = 400 * 0.42 = 168
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 9-10.]
The Penn Bookstore sells several magazines. A single stocking quantity is ordered for
each issue. When a new issue arrives, any remaining copies of the old issue are returned
to the publisher. If a magazine sells out, then it remains unavailable until the next issue
arrives.
Consider the following data on Bits and Bytes magazine at the Penn Bookstore:
The forecast column lists their forecast of demand for that issue (when they ordered
copies for that issue). It is generated by an internal computer system that accounts for
seasonality and other events in the store (which is why the forecast varies from issue to
issue). The quantity column is the actual number of issues stocked that week, and the
sales column provides the number of units actually sold. The estimated demand column
provides an estimate of what sales could have been, had there been no stockouts. (If sales
are less than or equal to the order quantity, the estimated demand equals sales; otherwise,
it can be greater.)
9) The system forecasts that week 37 demand at this location will be for 25 copies.
Suppose they were to choose a normal distribution to represent demand in week 37. What
mean and standard deviation should they choose? (Separate your answers with a comma)
Answer: 27, 9.5
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Explanation: Mean: µ = µA/F * forecast = 1.08 * 25 = 27;
Standard Deviation: σ = σA/F * forecast = 0.38 * 25 = 9.5
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
10) Suppose the week 39 forecast is for 20 copies. What would be the coefficient of
variation of demand? Again, assume a normal distribution is chosen to model demand.
(Include all decimal places in your answer)
Answer: 0.352
Explanation: C.O.V. = σ/µ = (0.38 * 20)/(1.08 * 20) = 0.38/1.08 = 0.352.
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
11) Consider Modern Active MBA, a periodical dedicated to selecting an MBA program
and getting the most out of the experience. The publisher charges the Penn Bookstore
$1.50 for each copy of MAMBA sold. It costs the publisher $0.35 to print and deliver
each copy of the magazine. Leftover copies are discarded at a cost of $0.05 per copy to
the publisher. If it were up to the publisher, how many copies of a particular issue of
MAMBA should the publisher stock at the bookstore when the forecast of demand is
normally distributed with a mean of 40 and a standard deviation of 22? (Enter the answer
as a whole number, do not round)
Answer: 54
Explanation:
Cu = 1.50 - 0.35 = $1.15;
Co = 0.35 + 0.05 = $0.4;
F(z) = Cu/(Cu + Co) = 1.15/(1.15 + 0.4) = 0.742
=> z = 0.65 => Q = 40 + 0.65 * 22 = 54.3 copies.
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
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12) The Penn Bookstore is doing an audit of the magazine procurement process. A
consultant recommends an in-stock probability of 80% for all of the magazines they
stock. If they follow the consultant's recommendation (and achieve an 80% in-stock
probability), what is the expected percentage of their magazines that will experience a
stock-out? (Enter the answer as a percentage)
Answer: 20%
Explanation: 100% - 80% = 20%
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Knowledge Application
Blooms: Apply
13) National Geographic still sells a considerable number of copies. Its demand for the
April issue is forecasted to be normally distributed with a mean of 80 and a standard
deviation of 35. If the Penn Bookstore stocks 100 copies, how many copies can they
expect to return to the publisher at the end of the month? (National Geographic is a
monthly periodical.) (Enter the answer as a whole number, do not round)
Answer: 26
Explanation:
z = (Q - µ)/σ = (100 - 80)/35 = 20/35 = 0.57;
L(z) = L(0.57) = 0.1771;
Expected lost sales = σ * L(z) = 35 * 0.1771 = 6.2;
Expected sales = µ - expected lost sales = 80 - 6.2 = 73.8;
Expected leftover inventory = Q - expected sales = 100 - 73.8 = 26.2 copies.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
14) Consider another magazine, Green Business. The forecast for an issue is Poisson with
mean 4.25. How many issues should the Penn Bookstore stock if they want to ensure a
99.6% in-stock probability?
Answer: 11
Explanation: Use the Poisson distribution function table with µ = 4.25 to find the
smallest S such that F(S) ≥ 0.996 => S = 11 issues.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
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15) If they happen to order 6 copies of Green Business, how many copies of Green
Business should they expect to sell (i.e., expected sales)? (Recall, demand is Poisson with
mean 4.25.)
Answer: 4
Explanation: Expected lost sales = 0.25412 copies from the Poisson loss function table
with µ = 4.25 and S = 6; Expected sales = 4.25 - 0.25412 = 4 copies.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Analytical Thinking
Blooms: Analyze
16) Demand for Surf World is Poisson with mean 2.5. If they happen to stock 5 copies,
what is the expected number of customers who will want to purchase Surf World but will
be unable to do so because the bookstore runs out of copies? (Include all decimal places
in your answer)
Answer: 0.062
Explanation: Expected lost sales = 0.06195 copies from the Poisson loss function table
with µ = 2.5 and S = 5 = 0.062.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Knowledge Application
Blooms: Apply
17) Mensa and Muscles is a weight training and fitness magazine for cerebral men and
women. Demand for the March issue is forecasted to be Poisson with a mean of 8.0, and
9 copies of M&M are stocked. What is the probability that all demand for M&M will be
satisfied? (Enter the answer as a percentage)
Answer: 71.7%
Explanation: Use the Poisson function table with µ = 8 and S = 9 => F(S) = 0.7166 =
71.7% of satisfied demand.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 18-21.]
Share&Care is a nonprofit car share company that rents cars. When a customer makes a
reservation, they specify their pickup time and the number of time slots they will hold the
vehicle, where each time slot equals 15 minutes. For example, if the pickup time is 1 pm,
then possible drop off times are 1:15 (1 slot), 1:30 (2 slots), etc. Share&Care charges
$1.50 for each time slot in the reservation. To discourage customers from returning the
rented cars beyond their drop off time, they charge $20 per time slot used beyond the
drop off time. For example, if a customer's drop off time is 2:30 and he returns the
vehicle at 2:47, then he is charged $40 for the 2 time slots he used beyond his reservation
(and of course, $1.50 per slot that he reserved).
Larry runs a small business that makes deliveries on Fridays. The number of time slots he
needs is well modeled by a Poisson distributed with mean 4. He books his car 2 days in
advance before he knows his needs exactly. (He does this to ensure availability of a car.).
Assume on the day of the reservation Larry learns his needs and has little control over the
number of slots he needs. For example, if he needed 5 slots but booked 4 slots, then he
uses the car for 5 slots, for a total charge of 4 * $1.50 + $20 = $26. If he ends up booking
the car for more time than he needs, the extra time on the car has no value to him.
18) What is the probability that Larry needs exactly 2 time slots? (Enter the answer as a
percentage)
Answer: = 14.6%
Explanation: Based on his demand distribution, the probability he will need the car for
exactly 2 time slots = Prob(D = 2) = Prob(D <= 2) - Prob(D <= 1) = F(2) - F(1)
= 0.238 - 0.092 = 0.146, or 14.6%.
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
19) Suppose he books the car for 2 time slots. How likely is he to pay $40 or more in late
fees? (Enter the answer as a percentage)
Answer: = 57%
Explanation: If he books for 2 time slots (30 minutes) and incurs $40 or more in late fees
(cost of 2 more slots), then his demand is for 4 time slots or more.
= Prob(D >= 4) = 1 - Prob(D <=3 ) = 1 - 0.43 = 0.57.
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
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20) To minimize his rental costs, how many time slots should Larry reserve the car for?
Answer: = 7
Explanation: Use Poisson with mean 4. If he under reserves then he pays $20 instead of
$1.5, so Cu = $18.5. If he reserves but doesn't need the slot, he loses the $1.5: Co = 1.50.
Critical Ratio is 0.925. F(6) = 0.889, F(7) = 0.949. He should reserve Q = 7 time slots. (1
hour and 45 minutes).
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
21) Larry has a new plan. Whenever his need for the car exceeds the number of slots he
has rented the car for, he returns the car on time to avoid the fine and uses his bicycle for
the remaining deliveries. Unfortunately, bike deliveries take 3 times longer than car
deliveries. Suppose he rents the car for 5 slots (75 minutes). If he needs 7 slots, then he
uses the car for 5 slots, and the remaining 2 slots are done by bicycle, which takes 6 slots
(1.5 hours). How much time does he expect to bicycle on average (in terms of slots)?
(Round answer to the nearest tenth)
Answer: = 1.2
Explanation: Based on the Poisson distribution with mean 4, and Q = 5 (75 minutes),
Expected Lost Sales = 0.41 slots. But each "car slot" takes 3 times longer than bike, so
this is equivalent to 3 * 0.41 = 1.23 slots, which is 1.23 * 15 = 18.45 minutes.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 22-24.]
Montanso is a large bio firm that sells genetically modified seed to farmers. They need to
decide how much seed to put into a warehouse to serve the demand for the next growing
season. They will make one quantity decision. It costs Montanso $8 to make each
kilogram (kg) of seed. They sell each kg for $45. If they have more seed than demanded
by the local farmers, the remaining seed is sent overseas. Unfortunately, they only earn
$3 per kg from the overseas market (but this is better than destroying the seed because it
cannot be stored until next year). If demand exceeds their quantity, then the sales are lost,
and the farmers go to another supplier. As a forecast for demand they will use a normal
distribution with a mean of 300,000 and a standard deviation of 106,000.
22) How many kilograms should they place in this warehouse before the 2011 growing
season?
Answer: 425,080
Explanation: Cost of underage = $45 - $8 = $37. Cost of overage = $8 - $3 = $5.
F(z) = 37/(37 + 5) = 0.881. Using the Standard Normal Distribution Function table, we
get z = 1.18. Q = (1.18 * 106,000) + 300,000 = 425,080 kg.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
23) Ignoring the analysis in the previous question, how many kilograms should they place
in this warehouse if they want to minimize their inventory while ensuring that the
stockout probability is no greater than 10%?
Answer: 436,740
Explanation: F(z) = 0.9. Using the Standard Normal Distribution Function table,
we get z = 1.29. Q = (1.29 * 106,000) + 300,000 = 436,740 kg.
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Knowledge Application
Blooms: Apply
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24) A senior executive at the company asks the following "Suppose we were to place
500,000 kilograms in this warehouse. What is the probability that our total revenue will
be at least $18,000,000?" (Note: The revenue comes from both local sales and overseas
sales. Furthermore, you are concerned with revenue and not profit, so you can ignore
costs). (Enter the answer as a percentage)
Answer: 97%
Explanation: Optimal order quantity = mean + z * standard deviation
= 500,000 = 300,000 + z *106,000
z = 500,000 - 300,000/106,000
z = 200,000/106,000
z = 1.887 The probability corresponding to z = 1.887 is approximately 97%
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 25-26.]
Dan's Independent Book Store is trying to decide on how many copies of a book to
purchase at the start of the upcoming selling season. The book retails at $28.00. The
publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of
the book at 50% off the retail price, at the end of the season. Dan estimates that demand
for this book during the season is Normal with a mean of 1000 and a standard deviation
of 250.
25) Suppose Dan wants to maximize his expected profits from the sale of this book. How
many copies should he order from the publisher?
Answer: 1045
Explanation:
Underage cost, Cu, is 28 - 20 = 8
Overage cost, Co, is 20 - (28/2) = 6
Critical ratio = Cu /(Co + Cu ) = 8/14 = 0.5714
Look up the z-statistic in the Standard Normal Distribution Function Table that
corresponds to the critical ratio: Φ(0.18) = 0.5714, so choose z = 0.18 copies.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
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26) Suppose Dan orders 1500 copies. What is Dan's expected profit?
Answer: $4,970.60
Explanation: Evaluate the z-statistic: z = (1500 - 1000)/250 = 2.0
Look up L(z) in the Standard Normal Loss Function Table: L(2.0) = 0.0085
Expected lost sales = σx L(z) = 250 * 0.0085 = 2.1
Expected sales = μ - Expected lost sales = 1000 - 2.1 = 997.9
Expected leftover = Q - Expected sales = 1500 - 997.9 = 502.1
Profit = Profit margin * Expected sales - Loss on leftover inventory * Expected leftover =
8 * 997.9 - 6 * 502.1 = $4970.60 in profit.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 27-28.]
Consider a new anthology of Greek poetry from the 1930s. The publisher is selling the
book for $82.50, and Dan plans a 25% gross margin on this book, i.e., the price will be
$110. Dan estimates that demand over the next year has a Poisson distribution with mean
2.5. At the end of the year, Dan will sell leftover books to a discounter and probably will
only get 20% of the wholesale price for each copy.
27) Suppose Dan orders four copies of the poetry book. What are Dan's expected sales?
(Round answer to the nearest whole number)
Answer: 2
Explanation: Look up L(Q) in the Poisson Distribution Loss Function Table: L(4) =
0.17077. Expected sales = mean - Expected lost sales = 2.5 - 0.17077 = 2.33 expected
sales.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Analytical Thinking
Blooms: Analyze
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28) How many copies of the poetry book should Dan order to maximize his expected
profit?
Answer: 2
Explanation:
Underage cost, Cu, is 110 - 82.50 = 27.5
Overage cost, Co, is (1 - 0.2) * 82.50 = 66
Critical ratio = Cu /(Co + Cu) = 27.5/133.5 = 0.2941
Look up in the Poisson Distribution Function Table with mean 2.5 the quantity that
corresponds to the critical ratio:
F(1) = 0.28730 and F(2) = 0.54381, so choose Q = 2 copies.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
29) Woot! specializes in "one day - one deal" selling. Every day they sell a product that is
not available the next day. If the item sells out, all the excess demand is lost, and if items
are left over, they are salvaged and not sold again on a future day. On a particular
Monday, Woot! sells Creative Labs blue-tooth adapter for only $15, buying them at $9
each. All unsold adapters are sent back to the supplier at $7 each. If Woot! estimates
demand to be normally distributed with mean 500 and standard deviation of 70 units,
how many adapters should Woot! order from its supplier to maximize its expected profit?
(Enter answer as whole number, do not round)
Answer: 547
Explanation:
Overage Cost, Co = $9 - $7 = $2
Underage Cost, Cu = $15 - $9 = $6
Critical Ratio=Cu/(Cu + Co) = 6/(2 + 6) = 0.75
F(0.67) = 0.7486, F(0.68) = 0.7517, thus z = 0.68
Purchase quantity = Q = μ + z * σ = 500 + .68 * 70 = 547.6 adapters.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
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30) Elite Couture, a high-end fashion goods store has to decide on the quantity of Luella
Bartley handbags to sell during the Christmas season. The unit cost of the handbag is
$28.50, and the handbag sells for $150. A discounter purchases all handbags remaining
unsold at the end of the season for $20 each. Further, there is a significant 40% inventory
holding cost incurred for each unsold bag. Demand for bags is distributed normally with
mean 150 and standard deviation 20. How many bags should be purchased to maximize
the expected profit? (Enter answer as whole number, do not round)
Answer: 171 bags
Explanation:
Overage Cost, Co = $28.50 - $20 + 0.40 * 28.50 = $8.5 + $11.40 = $19.90
Underage Cost, Cu = $150 - $28.50 = $121.50
Critical Ratio = Cu/(Cu + Co) = 121.5/(121.5 + 19.9) = 0.8593
F(1.07) = 0.8577, F(1.08) = 0.8599, thus z = 1.08
Purchase quantity = Q = μ + z * σ = 150 + 1.08 * 20 = 171.6 bags.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Analytical Thinking
Blooms: Analyze
31) Zaza Fashions' demand for the Polka Dot silk skirt during the Fall season is Poisson
with a mean of 6.5. Zaza calculates the order quantity that maximizes its expected profit
using the news vendor model and determines that the stock-out probability with that
order quantity is 0.32724. What is the in-stock probability corresponding to that order
quantity? (Answer should include all decimal places)
Answer: 0.67276
Explanation:
The in-stock probability is 1 - stock-out probability, so the in-stock is 1 - 0.32724 =
0.67276 in-stock probability.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 32-34.]
Alpha Airlines has to decide how many meals to load on its daily 6 pm non-stop flight
from Philadelphia to Los Angeles. The meals are sold on board to economy class
passengers for $10.00 and cost the airline $4.00 each. All meal orders must be made at
least 48 hours before the flight departs. Any meals left over at the end of the flight are
tossed into the trash by the ground clean-up crew. Alpha estimates that the demand for
the meals on this flight is Poisson distributed with a mean of 9.
32) How many meals should Alpha order?
Answer: 10
Explanation: Cu = $10 - $4 = $6. Cu/(Cu + Co) = 6/(6 + 4) = 0.6. From the Poisson
Distribution Function Table with mean 9, Q = 10 meals.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
33) Suppose that Alpha wants to achieve a 75% in-stock probability. How many meals
should Alpha order?
Answer: 8
Explanation: From the Poisson Distribution Function Table with mean 9, Q = 8 meals.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Knowledge Application
Blooms: Apply
34) Alpha has decided to use all left-over meals on its local flight from Los Angeles to
Phoenix. They have determined that the cost of re-stocking such meals from the
Philadelphia-Los Angeles flight to the Los Angeles-Phoenix flight is $1.50. Any extra
meals used on the flight to Phoenix are sold for $5, and there will not be leftover meals
on that flight. How many meals should Alpha order for its flight to Los Angeles?
Answer: 13
Explanation: Cu = $10 - $4 = $6. Co = $4 - ($5 - $1.5) = $0.5.
Cu/(Cu + Co) = 6/(6 + 0.5) = 0.923. From the Poisson Distribution Function Table with
mean 9 we have Q = 13 meals.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Analytical Thinking
Blooms: Analyze
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35) WebFlix is an Internet DVD rental service. Customers mail back DVDs to the
company after watching them and then receive new ones in the mail based on their
preference lists that they maintain via the web. WebFlix currently has 10,000 customers,
and an average customer's daily DVD demand is Poisson with mean 0.25 (and each
customer's demand is independent of the other customers' demands). The existing DVD
processing facility is capable of handling 2600 DVDs on a given day without overtime.
What is the probability that this facility cannot handle daily demand without overtime?
(Recall that, when mean demand is large, Poisson distribution can be approximated by
the Normal distribution.) (Enter the answer as a percentage)
Answer: 2%
Explanation: Demand for WebFlix is normal with mean 2500 and standard deviation =
sqrt(10000 × 0.25) = 50; z = (2600 - 2500)/50 = 2 and the probability of having demand
less than 2600 is 0.9772 (from the Standard Normal Distribution Function Table).
Therefore, the stockout probability is about 2%.
Difficulty: 3 Hard
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Analytical Thinking
Blooms: Analyze
36) Suppose the news vendor model describes a firm's operations decision. Is it possible
to have positive expected lost sales and positive expected leftover inventory? Choose the
best answer.
A) No, if there is leftover inventory, then there should not be lost sales.
B) No, if expected lost sales are positive, then expected leftover inventory must be
negative.
C) No, actual demand can differ from sales.
D) Yes, they are both expectations over numerous possible outcomes, among which there
will be no outcome in which both are positive.
E) Yes, as long as the underage cost is greater than the overage cost.
Answer: D
Explanation: Since expected lost sales and expected sales are averages over all possible
outcomes, they are both positive. However, in each outcome, there will be no lost sales if
items are left over, and a sale would never be lost if there are items left over. However, if
averages are taken over all possible outcomes, they are both positive.
Difficulty: 2 Medium
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Reflective Thinking
Blooms: Analyze
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37) A firm is considering the use of the A/F method in the upcoming season to forecast
their demand and to choose order quantities. They collected data from last year's products
in the category. (See the table.) Based on these data, they plan to fit a normal distribution
to each of the current products. The mean of the normal will equal their forecast, and the
standard deviation will equal 28% of their forecast. What is likely to be a problem with
their approach to the A/F method? Choose the best answer.
A) They shouldn't use the normal distribution to model demand and should instead use
the empirical demand distribution.
B) There must be something wrong with their data because the average A/F ratio is rarely
equal to 1 (in which case it is unbiased).
C) They did not sort their A/F ratios from least to greatest.
D) Their order quantities are likely to be too low because they didn't keep track of actual
demand.
E) They need more data because at least 20 observations are needed to implement this
method.
F) They need to have more than one forecast per product because they need to estimate
standard deviations.
Answer: D
Explanation: Their calculations are assuming sales equals demand, but because of
stockouts, sales can be less than demand. Consequently, this will lead to a bias in their
forecasts. (a) it is not the best answer because there is no compelling reason to assume the
data isn't normally distributed. (b) is incorrect because the average A/F can be 1.0. (c) is
incorrect because you don't need to sort the A/Fs if you are using the data to fit a normal
distribution. (e) is incorrect because while more data would be useful, it is not necessary
— there is no formal cutoff. (f) is incorrect because you can implement the approach with
one observation per product.
Difficulty: 3 Hard
Topic: How to Construct a Demand Forecast
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AACSB: Reflective Thinking
Blooms: Analyze
38) Suppose a firm uses an A/F ratios approach (similar to Le Club case) to come up with
demand forecast. The average A/F ratio from historical data turns out to be 0.8. What is
the best conclusion that can be drawn from this observation?
A) The optimal order quantity should be 0.8 times the forecast.
B) The critical ratio of the product in the past was 0.8.
C) The coefficient of variation of demand will be 0.8.
D) There is a bias in the forecasting process: forecasts are on average higher than
demand.
E) There is a bias in the forecasting process: forecasts are on average lower than demand.
F) None of the above
Answer: D
Explanation: Since an A/F ratio is lower than 1 it means that the actual demand is lower
than the forecasted demand. (a) is incorrect because the optimal order quantity also
depends on the critical ratio. (b) and (c) are incorrect since the A/F ratio determines
neither the critical ration nor the coefficient of variation. (e) is incorrect, since the bias is
in the opposite direction as described in (d).
Difficulty: 2 Medium
Topic: How to Construct a Demand Forecast
AACSB: Reflective Thinking
Blooms: Analyze
39) In a particular setting where the news vendor model applies, demand is normally
distributed, and the critical ratio is known to be 0.8. Then, if the profit-maximizing
quantity were ordered,
A) The expected sales are less than expected demand;
B) The expected sales are greater than expected demand;
C) The expected sales are exactly equal to expected demand;
D) The expected sales could be less than, equal to or greater than expected demand.
Answer: A
Explanation: Expected sales are ALWAYS less than expected demand, i.e., no matter the
critical ratio or the demand distribution. (It only equals expected demand if the quantity is
unlimited.)
Difficulty: 2 Medium
Topic: How to Choose and Order Quantity
AACSB: Reflective Thinking
Blooms: Analyze
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40) For products with slow-moving demand, e.g., 1 unit per week, the Poisson
distribution is likely to be a better model for demand than the normal distribution because
(choose the best answer).
A) The Poisson's standard deviation is equal to the square root of its mean.
B) The normal distribution does not allow the freedom to choose any standard deviation
for any given mean.
C) The Poisson distribution is a continuous distribution.
D) Only the standard normal distribution would apply in this setting.
E) The Poisson distribution does not assign any probability to negative outcomes.
Answer: E
Explanation: Normal distribution assigns positive probabilities to negative demand;
however, if the mean is significantly higher than the standard deviation, these
probabilities become negligibly small. However, if the items are slow moving (mean low
compared to standard deviation), there is a significant probability of having negative
demand under normal distribution. Poisson distribution does not assign any probability to
negative outcomes. Answers in (b), (c) and (d) are incorrect, while the answer in (a) is
not relevant.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
AACSB: Reflective Thinking
Blooms: Analyze
41) Consider two products A and B that have identical cost, retail price and demand
parameters and the same short selling season (the summer months from May through
August). The news vendor model is used to manage inventory for both products. Product
A is to be discontinued at the end of the season this year, and the leftovers will be
salvaged at 75% of the cost. Product B will be re-offered next summer, so any leftovers
this year can be carried over to the next year while incurring a holding cost on each unit
left over equal to 20% of the product's cost. How do the stocking quantities for these
products compare?
A) Stocking quantity of product A is higher.
B) Stocking quantity of product B is higher.
C) Stocking quantities are equal.
D) The answer cannot be determined from the data provided.
Answer: B
Explanation: The salvage value of Product A is 75% of its cost. The overage cost, Co, is
the difference between Product A's cost and its salvage value, which is then 100% - 75%
= 25% of the cost. Product B's overage cost is 20% of its cost. Both products have the
same underage cost, Cu, so Product A has a higher overage cost, which means it has the
lower critical ratio, Cu/(Co + Cu). Given they have the same demand distribution,
Product A's optimal order quantity must be lower, or, Product B's stocking quantity is
higher.
Difficulty: 3 Hard
Topic: How to Choose and Order Quantity
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AACSB: Analytical Thinking
Blooms: Analyze
42) O'Neill sells the same 3mm boot for surfing every year. Because this is a functional
product with little fashionable content, O'Neill believes that this is a stable product, i.e.,
expected demand doesn't change from year to year. However, sales are concentrated in a
short period during the summer. O'Neill plans to use sales data from the last five years to
forecast demand this year. Those data are 850, 1025, 1000, 990 and 875. Note, due to the
short selling season, in two of the seasons O'Neill ran out of boots, whereas in three of
those seasons O'Neill had boots left over at the end of the season and they were held over
until the next season. What is the mean of the demand forecast?
A) The mean of O'Neill's demand forecast should equal 948.
B) The mean of O'Neill's demand forecast should be greater than 948.
C) The mean of O'Neill's demand forecast should be less than 948.
D) It is not possible to determine whether O'Neill's forecast should be 948, greater than
948 or less than 948.
Answer: B
Explanation: The mean of the data is 948, but in two of the season's actual demand must
have been larger than sales. Hence, the mean of actual demand must be higher. (In the
three seasons with leftover boots, sales = demand.)
Difficulty: 2 Medium
Topic: How to Construct a Demand Forecast
AACSB: Reflective Thinking
Blooms: Analyze
43) A reseller supports a sales team that is responsible for selling a group of products.
The reseller plans to use the news vendor model to guide ordering decisions for these
products. How should the total salaries of the sales force be incorporated into the news
vendor model analysis? (Focus only on salaries, i.e., ignore sales bonuses or other forms
of compensation.)
A) Salary costs should be prorated across products based on expected sales, and that
prorated amount should be added to the product's variable cost.
B) Salary costs should be prorated across products based on expected sales, and that
prorated amount should be added to the product's overage cost.
C) Salary costs should be prorated across products based on expected purchase quantities,
and that prorated amount should be added to the product's variable cost.
D) Salary costs should be prorated across products based on expected purchase
quantities, and that prorated amount should be added to the product's overage cost.
E) Salary costs should not be included in the news vendor analysis.
Answer: E
Explanation: Salaries of the sales force is a fixed cost and therefore should not be
included in the marginal analysis and thus should not be included in the newsvendor
analysis.
Difficulty: 3 Hard
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Topic: The Newsvendor Model: Structure and Inputs
AACSB: Analytical Thinking
Blooms: Analyze
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44) Suppose a company uses the news vendor model to manage its inventories and faces
normally distributed demand with a coefficient of variation = 1. The company decides to
order a quantity that exactly equals its mean demand forecast. Which of the following is
true regarding this company's performance measures?
A) The probability of serving all the demand is 50%.
B) Expected lost sales are 50% of mean demand.
C) Expected sales are equal to mean demand.
D) Expected leftover inventory is 0.
Answer: A
Explanation: The critical ratio is then 50%, and the corresponding z is 0. The in-stock is
then 50%.
Difficulty: 2 Medium
Topic: How to Construct a Demand Forecast
AACSB: Reflective Thinking
Blooms: Analyze
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45) A company collected data on the performance of their forecasts of 38 items in the
previous season. The average A/F ratio across this sample is 1.02, and the standard
deviation of the A/F ratios is 0.40. The average forecast is 2405 units. The data is plotted
in the following graph.
What comment best describes the quality of their forecasting process?
A) Their forecasts are too optimistic.
B) Their forecasts are too pessimistic.
C) Their forecast errors are small because the average A/F ratio is close to 1.00.
D) Their high forecasts are too pessimistic and low forecasts are too optimistic.
E) Their high forecasts are too optimistic and low forecasts are too pessimistic.
F) It is not possible to assess the quality of their forecasts because of the inherent
randomness of the forecast errors.
Answer: D
Explanation: Choice A is incorrect because forecasts greater than 3000 tend to be too
low. Choice B is incorrect because forecasts less than 3000 tend to be too high. Choice C
is incorrect because their forecasts could have large errors, even when on average, the
errors compensate each other, and the average A/F ratio is close to 1.00. Choice E is
incorrect because the high forecasts (above 3000) are too pessimistic. Choice D fits the
pattern of pessimistic high forecasts and optimistic low forecasts. Choice F is incorrect
because while there is randomness, it is unlikely that the pattern has been produced
merely by chance (i.e., the probability this pattern emerges if there is no bias in the
forecasts is quite small).
Difficulty: 2 Medium
Topic: How to Construct a Demand Forecast
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AACSB: Analytical Thinking
Blooms: Analyze
46) In the Le Club Français du Vin case study, the following change would increase the
ordering quantity for red wines.
A) Increase the shipping and handling cost per bottle.
B) Increase the end-of-season discounts.
C) Increase the time to sell-off slow-moving wines from 12 months to 24 months.
D) Increase the cost of capital.
E) None of the above.
Answer: D
Explanation: Answer options A-C lead to higher cost of overage or lower cost of
underage and, as a result, smaller ordering quantity.
Difficulty: 2 Medium
Topic: How to Choose and Order Quantity
AACSB: Reflective Thinking
Blooms: Analyze
47) Suppose the news vendor model is used to manage inventories. Which of the
following can happen when the order quantity is increased by one unit?
A) Expected sales increases by more than one unit.
B) Expected lost sales increases by more than one unit.
C) Expected leftover inventory increases by more than one unit.
D) Expected sales decreases by less than one unit.
E) Expected lost sales decreases by less than one unit.
F) Expected leftover inventory decreases by less than one unit.
G) None of the above.
Answer: E
Explanation: If the order quantity is increased by one unit, expected lost sales clearly
decrease, but by less than one unit because demand is uncertain.
Difficulty: 2 Medium
Topic: The Newsvendor Model: Structure and Inputs
AACSB: Reflective Thinking
Blooms: Analyze
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48) O'Neill uses A/F ratios to measure the quality of their forecasting of seasonal items.
They use the news vendor model to choose order quantities. O'Neill improves its
forecasting with time. After several seasons of implementing this process which of the
following should O'Neill observe?
A) The average A/F ratio should get closer to the average critical ratio of the products.
B) The average A/F ratio should get closer to the target in-stock probability (which is the
same across all products).
C) The average A/F ratio should get closer to the stock-out probability (which is the same
across all products).
D) The standard deviation of the A/F ratios should get closer to 1.
E) The maximum A/F ratio should decrease, and/or the minimum A/F ratio should
increase.
F) None of the above.
Answer: E
Explanation: If forecasting improves, A/F ratios should be getting closer and closer to 1.
In other words, the maximum A/F ratio should decrease, and/or the minimum A/F ratio
should increase.
Difficulty: 2 Medium
Topic: How to Construct a Demand Forecast
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 15 Assemble-to-Order, Make-to-Order, and
Quick Response with Reactive Capacity
1) BASF sells customized petrochemical catalysts that are produced in a plant in
Germany. Many of their customers are in North America and transportation is done via
ocean carrier. They can purchase container capacity in advance at the price of $2500 per
container. However, if they advance purchase containers, they bear the risk of not
knowing their exact needs for containers. In particular, here is a forecast of their needs
for June (i.e., a density and distribution function):
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If they purchase a container in advance and don't actually need it, then they will fill it
with some excess "filler" product and store it in North America until it can be sold. The
expected extra storage cost is $325 per container. For example, if their needs are for 2
containers but they advanced purchased 3 containers, then they ship all three containers
and incur an extra $325 charge for the 1 container filled with "filler" product. Containers
purchased on the spot market (after they learn their needs) are expected to cost $3000 per
container. For example, they may advance purchase 1 container but discover that they
need 3 containers, in which case they would purchase an additional 2 containers at $3000
each. How many containers should they advance purchase to minimize their costs?
Answer: 5 containers
Explanation: Cu = 3000 - 2500 = $500; Co = $325;
The critical ratio = Cu/(Cu + Co) = 500/(500 + 325) = 0.61
The quantity they should purchase in advance is the smallest quantity Q such that
F(Q) ≥ 0.61 => Q = 5
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Knowledge Application
Blooms: Apply
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2) PECO has an idea to reduce the consumption of electricity by residential users. It
normally charges customers $0.11 per kWh. With a new plan, the customer pays $0.10
per kWh for the first 800 kWhs of the month, $0.15 per kWh for the next 200 kWhs (i.e.,
kWhs 800 through 1000) and $0.35 per kWh for all additional kWhs (i.e., all kWhs above
1000). If a household's monthly usage is normally distributed with a mean of 900 and a
standard deviation of 400, what would be the household's average monthly bill under this
new plan?
Answer: $123.63
Explanation: It is equivalent to think of another pricing scheme where the customer pays
$0.10 per kWh for all the usage incurred during the month; $0.05 per kWh on top of that
for every kWh consumed beyond 800 kWhs; $0.20 on top of the first two for every kWh
consumed beyond 1000 kWhs. The expected monthly bill for this household = $0.10 * µ
+ $0.05 * L(800) + $0.20 * L(1000), where L(800) = σ * L((800 - µ)/σ) = 400 * L(-0.25)
= 400 * 0.5365 = 214.52 and L(1000) = σ * L((1000 - µ)/σ) = 400 * L(0.25) = 400 *
0.2863 = 114.52 =>
The final answer = $0.1 * 900 + $0.05 * 214.52 + $0.20 * 114.52 = $123.63
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Analytical Thinking
Blooms: Analyze
[The following information applies to questions 3-5.]
A small retailer is considering various monthly plans for purchasing electricity. With one
plan they are charged 5 cents per kWh no matter what their consumption is. With a
second plan, they can pre-purchase kWhs at the cost of 4.5 cents per kWh. If they don't
use all of the kWhs they purchase, then there is no refund for the unused electricity. If
they need more kWhs than they purchase, the extra kWhs are purchased at the rate of 6
cents per kWh. Their forecast for kWh usage per month is normally distributed with a
mean of 6,000 and a standard deviation of 2,500.
3) Suppose they choose the first plan, the flat rate of 5 cents per kWh. What will be their
expected monthly bill?
Answer: $300
Explanation: Their expected monthly bill is 6,000 * 5cents = $300.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Knowledge Application
Blooms: Apply
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4) Suppose they choose the second plan, 4.5 cents per pre-purchased kWh which is nonrefundable and 6 cents per additional kWh. How many kWs should they pre-purchase?
Answer: 4,325 kWs
Explanation: The cost of underage is 6 - 4.5 = 1.5cents. The cost of overage is 4.5 cents.
Using the newsvendor formula, F(z) = 1.5/(1.5 + 4.5) = 0.25. z = -0.67. Thus, the amount
of kWs to pre-purchase Q = mu + z * sigma = 6,000 + 2,500 * (-0.67) = 4,325.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Analytical Thinking
Blooms: Analyze
5) Suppose they choose the second plan, 4.5 cents per pre-purchased kWh which is nonrefundable and 6 cents per additional kWh. If they were to pre-purchase 6000 kWhs, then
what would be their expected monthly bill?
Answer: $329.84
Explanation: The expected monthly bill = 4.5 * 6000 + 6 * expected shortage. We can
get expected shortage using the standard normal loss table.
Z = (6000 - 6000)/2500 = 0. L(0) = 0.3989.
The expected shortage is L(0) * sigma = 0.3989 * 2,500 = 997.25.
$0.045 * 6000 + $0.06 * 997.25 = $329.84.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 6-7]
Purchasing road salt for towns in the Northeast is a challenging task. The town of Homer,
New York, has calculated a forecast of their annual salt needs using historical data. The
forecast is summarized in the table below (Q is the quantity needed):
6) For example, there is a 60.6% chance they will need 50,000 tons or fewer, there is a
3.3% chance they will need exactly 100,000 tons, and there is a very small chance they
will need more than 200,000 tons. Suppose Homer wanted to minimize the amount of
inventory it purchases while at the same time having no more than a 6% chance of
running out of salt (which would force it to purchase salt on the spot market for a
premium). At the start of the season, how much salt (in tons) should Homer have
available in its storage sheds? Assume salt must be purchased in increments of 10,000
tons.
Answer: 130,000 tons
Explanation: The stockout probability cannot exceed 6%, which means the in-stock
probability should be at least 94%. Thus, 120,000 tons only gives an in-stock of 93.7%,
which means a stockout probability of 1 - 0.937 = 6.3%. Thus, to minimize inventory to
have no more than a 6% stockout probability, they should have 130,000 tons. In that case,
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they will have a 1 - 0.952 = 4.8% chance of running out.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Knowledge Application
Blooms: Apply
7) Now suppose Homer has been offered the following deal from American Salt Mine
(ASM). ASM will sell Homer salt options for $30 per option with an exercise price of
$40 for each option Homer purchases in advance of the season. Homer can "exercise" it
during the season to receive one ton of salt during the season. For example, if Homer
purchases 100,000 options before the season starts, then it pays ASM $30 * 100,000 =
$3,000,000 for those options. As Homer needs salt during the season, ASM will deliver,
up to the number of purchased options, for a price of $40 per ton. Options are good only
for this season—any unexercised options at the end of the season have no value. Finally,
if Homer exercises all of its options and still needs more salt, then it will have to purchase
salt in the spot market, for an estimated $80 per ton. Given this deal, how many options
should Homer purchase from ASM? Assume options must be purchased in increments of
10,000 tons.
Answer: 30,000 options
Explanation: If an option is purchased but not used, then Homer could have avoided
buying the option in the first place, i.e., Co = $30. If an option is not purchased but could
have been used, then Homer spends $80 to buy the ton when it could have spent $30 +
$40 to purchase it if it had an option, i.e., Cu = $80 - $70 = $10. The critical ratio is
10/(10 + 30) = 0.25. Looking at the forecast, F(20K) = 0.239 and F(30K) = 0.379. Use
the round-up rule and purchase 30,000 options.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Knowledge Application
Blooms: Apply
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8) Dan's Independent Book Store is trying to decide on how many copies of a book to
purchase at the start of the upcoming selling season. The book retails at $28.00. The
publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of
the book at 50% off the retail price, at the end of the season. Dan estimates that demand
for this book during the season is normal with a mean of 1,000 and a standard deviation
of 250. Suppose Dan orders 1,415 copies of the book. What would be his expected
mismatch cost?
Answer: $2,560.35
Explanation: Mismatch Cost = C0 * Expected leftover inventory + Cu * Expected lost
sales
Calculating z-statistic: (Q-µ)/σ = (1,415 - 1,000)/250 = 1.66
Looking up the loss function table: L(1.66) = 0.0201
Expected Lost sales: σL(z) = 250 * 0.0201 = 5.025
Expected leftover inventory = Q - Expected sales = Q - (µ - Lost sales) = 420.025
Expected mismatch costs = (20 - 14) * 420.025 + (28 - 20) * 5.025 = $2,560.35
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Analytical Thinking
Blooms: Analyze
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9) SEC, a Semiconductor (fabrication) Equipment Company, has a central spare parts
warehouse to support its chip fabrication plant customers located around the world. As
new generations of fab equipment are introduced, the installed base of older models
declines and ultimately disappears. As a consequence, SEC must at some point retire
support for the older model. Once a model has been scheduled for retirement, SEC makes
a "final buy" for service parts that are required to maintain support of the equipment until
the retirement date. If the inventory of a part runs out before retirement, then an
emergency order is placed with the part vendor. Inventory remaining in the warehouse at
the retirement date is scrapped for salvage materials.
Consider one model that has 50 machines installed throughout the world and SEC has
just announced the model will be retired in one year. Focus on part A in this machine.
Part A's current cost to purchase is $10,000. The expected cost for an emergency order of
part A after the final buy is $25,000. Part A's estimated salvage value is $2,000 and its
total annual demand (across the 50 machines) is estimated to be Poisson with mean 3.5.
Suppose there are currently 2 of these parts in inventory.
How many part A's should SEC order in the final buy to minimize its expected cost?
(Recall, there are currently two parts in inventory.)
Answer: 2
Explanation:
Overage Cost, Co = $10,000 - $2,000 = $8,000
Underage Cost, Cu = $25,000 - $10,000 = $15,000
Critical Ratio =Cu/(Cu + Co) = 15/(15 + 8) = 0.6522
F(3) = 0.53663, F(4) = 0.72544, thus Q = 4
Purchase quantity: Q-Inventory = 4 - 2 = 2
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Analytical Thinking
Blooms: Analyze
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10) A construction company has signed a contract to build an office tower. The contract
stipulates that the project will be completed in 1,500 days from today and also includes a
penalty on the construction company of $30,000 per day the project is late. In addition,
the construction company estimates that its internal cost is $60,000 for each day the
project is late. However, completing the project early is costly to the firm as well: each
day the project is early costs the firm $45,000. (This includes the opportunity cost of
capital and idle capacity.) The firm estimates the project will take 1,200 days to complete
with a standard deviation of 500 days. How many days should the firm wait to begin
construction?
Answer: 80 days
Explanation: This is similar to a newsvendor problem in time (instead of quantity),
where "overage" is early ("allotting too many days to the project"), and "underage" is late
("allotting too few days to the project"). Overage/Early Cost, Co = $45,000 per day.
Underage/Late Cost, Cu = $30,000 + $60,000 = $90,000 per day. Critical Ratio = Cu/(Cu
+ Co) = 90/(90 + 45) = 0.6667.
From the Standard Normal Distribution Function Table, Φ(0.44) = 0.6664 and Φ(0.44) =
0.6700, so choose z = 0.44. Hence, start 1,200 + 0.44 * 500 = 1,420 before the project
due date. Therefore, start in 1,500 - 1,420 = 80 days.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Analytical Thinking
Blooms: Analyze
11) Montgomery County, PA (MC) predicts that its total road salt needs during the next
winter will be normally distributed with a mean of 3,400 tons and a standard deviation of
1,800 tons. MC currently has no road salt in inventory. MC and the supplier American
Salt Inc. (ASI) have signed the following contract. MC will receive salt on an as needed
basis during the winter season (in other words, MC will buy in sufficiently small
quantities, and ASI will deliver with a sufficiently small lead time that MC's total
purchase for the season will be essentially equal to its total road salt needs). MC will pay
$62 per ton for the first 3,600 tons purchased and $75 per additional ton above 3,600.
For example, if MC purchases 2,500 tons, then their total payment to ASI is 2,500 * $62
= $155,000, and if MC purchases 4,000 tons, then its total payment to ASI is 3,600 * $62
+ 400 * $75 = $253,200. How much can MC expect to pay ASI?
Answer: $218,899
Explanation: MC pays at least $62 for every ton purchased, which means a payment of
$62 * 3,400 = $210,800. MC pays an additional $75 - $62 = $13 for every ton in excess
of 3,600. The z-statistic that corresponds to 3,600 is (3,600 - 3,400)/1,800 = 0.11. The
expected demand above 3,600 is 1,800 * L(0.11) = 623. MC pays $13 * 623 = $8,099 for
those tons. The total payment is $210,800 + $8,099 = $218,899.
Difficulty: 3 Hard
Topic: When is Mismatch Cost High?
AACSB: Analytical Thinking
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Blooms: Analyze
12) WebFlix is an Internet DVD rental service. Customers mail back DVDs to the
company after watching them and then receive new ones in the mail based on their
preference lists that they maintain via the web. For next year, WebFlix projects that
demand at its processing facility is normally distributed with mean 3,600 DVDs per day
and standard deviation of 60. WebFlix needs to set a capacity for this facility, which is
measured in DVDs per day. If the capacity is Q, then the cost per day incurred for this
capacity is $0.1Q, no matter whether the capacity is fully utilized or not. If demand on a
day exceeds the chosen capacity, then WebFlix processes the entire excess using
overtime. In that case, each DVD handled with overtime costs $0.15 to process. What is
the optimal processing capacity that WebFlix will need?
Answer: 3,574
Explanation: The overage cost is $0.1 because having one unit of unneeded capacity
costs the firm $0.1. The underage cost is $0.05 because having one unit too few of
capacity means overtime is used (at a cost of $0.15) instead of regular capacity (which
costs $0.10 per unit) so the extra cost of overtime capacity is $0.15 - $0.10 = $0.05.
Cu/(Cu + Co) = 0.3333 and therefore z = -0.43 (from the Normal Distribution Function
Table).
The corresponding optimal capacity Q = 3,600 - 60 * 0.43 = 3,574.
Difficulty: 3 Hard
Topic: Quick Response with Reactive Capacity
AACSB: Knowledge Application
Blooms: Apply
13) Zazz, a maker of a hot new MP3 player, is concerned about the availability of flash
memory chips, a key component in the Zazz3 player. It is the start of April and Zazz must
commit to a flash memory chip quantity for delivery in July. Each chip ordered now will
cost Zazz $40. Zazz expects that demand for chips in July is normally distributed with a
mean of 250,000 and a standard deviation of 200,000. If Zazz's demand in July exceeds
its regular order (the amount ordered in April), then Zazz can obtain additional units on
the spot market. The spot market price for these chips in July is estimated to be $50.
Chips not used in July will certainly be used in August. However, chips ordered in May
for August delivery are expected to cost $36. Furthermore, there is a $1 cost to hold each
chip from one month to the next (due to the opportunity cost of capital and physical
storage costs). How many chips should Zazz order in April?
Answer: 338,000
Explanation: The key is to realize that Cu = $50 - $40 = $10 (if chips are not ordered in
April, then they will have to be purchased in July on the spot market) and Co = $40 + $1
- $36 = $5 (if chips are not sold in July they will stay in inventory for one month
incurring the $1 charge and then sold in August instead of purchasing them for $36 in
August).
Cu/(Cu + Co) = $10/($10 + $5) = 0.667. From the Normal Distribution Function Table,
we find z = 0.44 and Q = 250,000 + 0.44 * 200,000 = 338,000.
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Difficulty: 3 Hard
Topic: Quick Response with Reactive Capacity
AACSB: Knowledge Application
Blooms: Apply
[The following information applies to questions 14-16.]
You operate a small tee-shirt silk screening company. Your local professional football
team has just made it to the NFC Championship game, which will be played in one week.
You are considering selling tee-shirts with "NFC Champions" blazed across the top of the
shirt along with the local team's name and mascot. If the team indeed wins, these shirts
will sell extremely well, but if they lose, then there will be no demand for these shirts.
Unfortunately, you must print the shirts before the game because otherwise there will not
be enough time to take advantage of the hype. You estimate that there is only a 40%
chance the local team will win, but if they win, you figure your demand will be normally
distributed with mean 15,000 and standard deviation 6,000. It costs $5.50 to buy and
silkscreen each shirt, you will sell these shirts for $12.50 each, and any leftover shirts
(whether the team wins or loses) can be sold to a liquidator for $0.50 each.
14) Suppose you print 18,000 shirts and suppose you get lucky and the team wins. What
is your expected profit?
Answer: $75,756
Explanation: If your team wins, the mean demand is 15,000 with a standard deviation of
6,000. Q = 18,000
Thus, z = (Q - μ )/σ = (18,000 - 15,000))/6000 = 0.5
Then, from the Normal Loss Function table, L(0.5) = 0.1978
Expected lost sales:
σ * L(z)
= 6000 * 0.1978
= 1,186.8
Expected sales:
μ - Expected lost sales
= 15,000-1,187
= 13,813
Expected left over inventory: Q - Expected sales
= 18,000 - 13,813
= 4,187
Expected profit
= Revenue + Liquidation - Cost
= 13,813*$12.50 + 4,187*$0.50 - 18,000*$5.50
= $172,663 + $2,094 - $99,000
= $75,756
Alternatively,
Expected profit = (p-c) * Expected sales-(r-c) * Expected left over inventory
= ($12.50 - $5.50) * 13,813 - ($5.50 - $0.50) * 4,187
= $75,756
Difficulty: 3 Hard
Topic: When is the Mismatch Cost High?
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AACSB: Analytical Thinking
Blooms: Analyze
15) Suppose you print 15,000 shirts, and again, you are lucky, and the team wins. Given
that the team wins, what is the probability you lose money on this venture?
Answer: 0.0735
Explanation: Let D be the number of shirts sold. If D > 15,000, then you stock out and
clearly make a positive profit. We wish to determine the demand D such that we break
even. When we know that value, we can determine the probability that demand is that
value or lower.
If D < 15000, then Profit is ($12.50 - $5.50) * 15,000 - ($5.50 - 0.50) * 0 > 0
Therefore, D must be less than 15,000 in order to lose money.
So, if D < 15,000, then
Profit = ($12.50 - $5.50) * D- ($5.50 - $0.50) * (15,000 - D)
= $12.00 * D - $75,000
Hence, we break even if D <= $75,000/$12 = 6,250
The z statistic for 6,250 is z = (6,250 - 15,000)/6,000 = -1.4583
From the Standard Normal Distribution Function table, F(1.46) = 0.0721 and F(1.45) =
0.0735
Difficulty: 3 Hard
Topic: When is the Mismatch Cost High?
AACSB: Analytical Thinking
Blooms: Analyze
16) How many shirts should you print to maximize your expected profit? (Unlike in the
previous two parts, do not assume the team necessarily wins.)
Answer: -0.2
Explanation: The overage cost is Co = $5.50 - $0.50 = $5
The underage cost is Cu = $12.50 - $5.50 = $7
The critical ratio is Cu/(Co + Cu) = 7/12 = 0.58
We want to find a quantity Q in which the probability demand is Q or lower than 0.58.
We know that if they lose, which has a probability 0.60, then demand is 0, and if they
win, demand can be greater than 0. So, the probability demand is 0 or lower is at least
60%. Given that our critical ratio is 58%, the optimal order quantity is Q = 0. Put another
way, the marginal benefit of ordering the first unit is negative. To see this, the probability
the first unit is sold is approximately 40%, and the profit is $7, for an expected gain of
0.4 * 7 = 2.8. The expected loss, however, is 0.6 * 5 =3 because there is a 60% chance it
doesn't sell. Hence, the expected profit for that unit is 2.8 - 3 = -0.2.
Difficulty: 3 Hard
Topic: Quick Response with Reactive Capacity
AACSB: Analytical Thinking
Blooms: Analyze
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17) Patagonia sells outdoor wear. The margin, the loss due to salvaging, and the
coefficient of variation of the demand distribution for each of several products are
provided below. Among the following products, which product is likely to have the
lowest demand-supply mismatch cost per unit?
Product
Snow
Ice
Freeze
Blizzard
Powder
Chill
Margin, $ per unit Loss due to salvaging, $ Coefficient of
per unit
variation
900
100
0.20
1600
400
0.25
100
200
0.85
500
1000
0.40
400
100
0.25
800
200
0.20
A) Snow
B) Ice
C) Freeze
D) Blizzard
E) Powder
F) Chill
Answer: E
Explanation: Demand supply mismatch cost per unit for Snow = (900 + 100) * 0.2 = 200
Demand supply mismatch cost per unit for Ice = (1600 + 400) * 0.25 = 500
Demand supply mismatch cost per unit for Freeze = (100 + 200) * 0.85 = 255
Demand supply mismatch cost per unit for Blizzard = (500 + 1000) * 0.4 = 600
Demand supply mismatch cost per unit for Powder = (400 + 100) * 0.25 = 125
Demand supply mismatch cost per unit for Chill = (800 + 200) * 0.2 = 200
Thus, lowest supply-demand mismatch cost is for Powder.
Difficulty: 3 Hard
Topic: When is Mismatch Cost High?
AACSB: Analytical Thinking
Blooms: Analyze
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18) Which of the following normal demand distributions would result in the highest
expected profit for the news vendor model (keeping cost/revenue parameters the same)?
Choose the best answer.
A) Mean 20, standard deviation 0
B) Mean 20, standard deviation 10
C) Mean 20, standard deviation 20
D) Mean 10, standard deviation 0
E) Mean 10, standard deviation 10
F) Mean 10, standard deviation 20
G) It is not possible to determine which of the above has the highest expected profit
because it would depend on the particular cost and revenue parameters.
Answer: A
Explanation: Higher average demand and lower standard deviation would lead to higher
profit in the newsvendor model. Therefore (A) yields to the highest profit.
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Reflective Thinking
Blooms: Analyze
19) Why does Sport Obermeyer place two production orders with their suppliers, each
comprising 50% of their total season needs? Choose the best single answer.
A) This lowers their carbon footprint.
B) This increases their odds of not suffering from quota restrictions.
C) This allows them to take advantage of the positive correlation between early orders
from retailers and total demand.
D) This allows them to defer production of their lowest value and easiest to forecast
items until after the Las Vegas trade show.
E) This gives them more time to refine their product designs.
F) They would be better off ordering just once because then they would face a news
vendor problem for which the optimal solution is known.
Answer: C
Explanation: This has nothing to do with their carbon footprint. It would increase the
odds of suffering from a quota restriction, and they would defer the highest value and
hardest to forecast. It would reduce the time they have to design products (or have no
effect on it), and the single ordering opportunity would not be beneficial.
Difficulty: 3 Hard
Topic: Reducing Mismatch Costs with Make-to-Order
AACSB: Reflective Thinking
Blooms: Analyze
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20) Which kind of product is likely to have the highest mismatch cost as a % of its
maximum profit:
A) High demand variability, large gross margin, high salvage value
B) High demand variability, large gross margin, low salvage value
C) High demand variability, low gross margin, high salvage value
D) High demand variability, low gross margin, low salvage value
E) Low demand variability, large gross margin, high salvage value
F) Low demand variability, large gross margin, low salvage value
G) Low demand variability, low gross margin, high salvage value
H) Low demand variability, low gross margin, low salvage value
Answer: D
Explanation: Products with low critical ratios and high coefficient of variation will have
the highest mismatch cost as a % of their maximum profit. Recall that CR = (cost of
underage)/(cost of underage + cost of overage). Products with low gross margin will have
low costs of underage, while products with low salvage value will have high costs of
overage, which together yield to low critical ratios. Answer D yields too low CR and high
COV due to the above-mentioned factors.
Difficulty: 3 Hard
Topic: When is the Mismatch Cost High?
AACSB: Reflective Thinking
Blooms: Analyze
21) You are deciding which demand forecasting system to use for a line of products: A/F
approach (see LLBean) or a panel of experts (see Sport Obermeyer). Which of the
following considerations will support the panel of experts' approach?
A) Demand has to be forecasted for a large number of items.
B) All items in the product line have approximately the same coefficient of variation.
C) news vendor model will be used to make stocking decisions.
D) Items in the product line differ significantly in the coefficient of variation.
E) Reactive capacity is available to make the second ordering decision.
Answer: D
Explanation: Choices A and B favor the A/F approach since the A/F approach can
aggregate data across the entire product line. Choice C is relevant for both alternative
approaches. Choice E is irrelevant to both alternative approaches. If D holds, aggregate
data across all products are less useful. Hence, the panel of experts will be preferable to
using A/F over the entire product line.
Difficulty: 3 Hard
Topic: When is the Mismatch Cost High?
AACSB: Reflective Thinking
Blooms: Analyze
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22) National Bike's mass customization model is a good business model because (choose
the best one)
A) it did not make money in its bike business in the past.
B) it can bypass the retailers.
C) it can completely avoid holding component and finished goods inventory.
D) it needs to reduce the manufacturing cost.
E) the mismatch cost is high for high-end bikes.
F) all the above.
G) none of the above.
Answer: E
Explanation: Choices B, C, D, and F are factually incorrect because retailers are still
used. Choice A is vague and needs more information to be considered. Choice E is the
strongest reason in favor of customization overproducing to forecast.
Difficulty: 3 Hard
Topic: Summary
AACSB: Reflective Thinking
Blooms: Analyze
23) In order to make reactive capacity useful,
A) the unit cost of the second order must not be higher than that of the first order.
B) the critical ratios of different products must be different.
C) the coefficient of variation (COV) of different products must be different.
D) the mismatch costs of different products must be different.
E) the lead time of the second order is not too long.
F) all the above are needed.
G) none of the above is needed.
Answer: E
Explanation: If the lead time of the second order is long enough, regular capacity would
be adequate, and reactive capacity would not be needed. Choices A through D are red
herrings, and not necessary to make reactive capacity useful. Choice D (and partially,
choices B and C) are relevant only for the production of multiple products, whereas
reactive capacity can be useful in a single-product context as well.
Difficulty: 3 Hard
Topic: Quick Response with Reactive Capacity
AACSB: Reflective Thinking
Blooms: Analyze
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24) Suppose the news vendor model is appropriate for each of the following products.
Which one of them is most likely to have the largest difference between its maximum
profit and its expected profit? Assume all products have the same mean forecasts and
underage/overage costs.
a)
b)
c)
d)
e)
Coefficient of variation
0.4
0.4
0.8
1.2
1.2
Stock-out probability
0.25
0.05
0.15
0.25
0.05
A) a
B) b
C) c
D) d
E) e
Answer: D
Explanation: A high stock-out probability implies a low in-stock probability and a low
critical ratio. The mismatch costs are highest with a high coefficient of variation and a
low critical ratio (high stock-out probability).
Difficulty: 3 Hard
Topic: Evaluating and Minimizing the Newsvendor's Demand-Supply Mismatch Cost
AACSB: Reflective Thinking
Blooms: Analyze
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25) The process of using a committee to forecast, as in the Sport Obermeyer case,
becomes more useful if:
I) The committee begins to generate a single consensus forecast rather than individual
forecasts.
II) The number of items to be forecasted increases.
III) The firm has more reactive capacity.
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
F) II and III only
G) I, II, and III
H) None of the above
Answer: H
Explanation: Option I is not true because the point of the committee is to determine the
uncertainty in the forecasts, which is not provided if a single consensus forecast is
generated. II is not true because committee forecasting is labor intensive, thus increasing
the number of products may increase the workload too much. III is not true because, with
more reactive capacity, forecasting is less necessary—in the extreme, the firm only uses
reactive capacity (make-to-order) and then forecasting is less important.
Difficulty: 3 Hard
Topic: Quick Response with Reactive Capacity
AACSB: Reflective Thinking
Blooms: Analyze
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26) Taboo! Inc makes shirts for women at its plant in Costa Rica, and sells to wholesalers
and distributors in the U.S. Due to long lead times; it makes its production commitments
for each season using the news vendor model. Unsold shirts are salvaged at the end of the
season at a heavy loss.
Now the firm is considering opening a second factory in Fall River, Massachusetts,
where production costs are much higher, but production lead times shrink. Taboo! Inc
plans to produce a baseline number of shirts in Costa Rica, and then respond to demand
during the season by producing in the Fall River plant at a higher cost. Which of the
following statements must be true under the new strategy (choose the best answer)?
i. Expected sales will go up.
ii. The total expected production of shirts for the season will go up.
iii. Expected leftover inventory of shirts at the end of the season will decline.
A) i only.
B) ii only.
C) iii only.
D) i and ii.
E) i and iii.
F) ii and iii.
G) i, ii, and iii.
Answer: E
Explanation: Options i and iii are clearly the answers if Taboo! Inc is willing to produce
shirts at a higher cost. Option ii, however, may not be the case as this depends on how the
newsvendor order quantity relates to the mean of the distribution.
Difficulty: 3 Hard
Topic: Quick Response with Reactive Capacity
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 16 Service Levels and Lead Times in Supply Chains:
The Order-up-to Inventory Model
[The following information applies to questions 1-4.]
Jim is a CFO of a mid-sized construction company. One of his key tasks is to ensure that
the company has sufficient cash to pay its daily and hourly workers who are hired
whenever the need arises. The company operates all 365 days a year, and Jim estimates
that on any day his payroll is normally distributed with mean $25,000 and standard
deviation $7,000. Jim manages his cash reserves using the order-up-to model: each
morning he places an order for cash with the bank, and the armored vehicle arrives 2 days
later with the money. It is the company's policy to pay all workers on the same day, but in
rare cases when the company runs out of cash, it pays workers as soon as possible while
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increasing their paycheck by 1% for each day of delay. For each dollar carried, the
company incurs 15% cost annually, which includes the cost of capital and insurance.
1) What is the profit-maximizing order-up-to level for cash?
Answer: $96,339.
Explanation: h. 0.15/365 = 0.00041, b = 0.01 so that the critical ratio is b/(b + h) = 0.96,
z = 1.76, S = 25,000 * 3 + 7,000 * sqrt(3) * 1.76 = $96,339.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
2) Suppose Jim is interested in ensuring that the company immediately satisfies all
employee salary requirements with a 95% probability. What is the corresponding orderup-to level?
Answer: $95,005.
Explanation: The appropriate z for an in-stock probability of 95% is 1.65.
S = 25,000 * 3 + 7,000 * sqrt(3) * 1.65 = $95,005.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
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3) Suppose Jim uses the order-up-to level of $150,000. One of these days the armored car
is robbed. What is the probability that more than $30,000 is stolen?
Answer: 24%.
Explanation: The question is asking to calculate a chance that the next delivery (or
equivalently order) is larger than $30,000. Since the distribution of orders is the same as
distribution of demand, we have Pr(Order > 30,000) = 1 - Pr(Orde r < 30,000),
z = (30,000 - 25,000)/7,000 = 0.71, Φ(z) = 0.76 so 1 - Φ(z) = 24%.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
4) To reduce lines and move payroll closer to workers, Jim considers opening another
payroll office. Exactly half of the workers will receive payments at one office, and the
other half will receive payments at the other office. What will be the coefficient of
variation of daily demand for cash at each of these offices?
Answer: 0.39.
Explanation: Each office will have mean demand of 25,000/2 = 12,500 and standard
deviation of demand 7,000/sqrt(2) = 4,950, so the coefficient of variation is 4,950/12,500
= 0.39.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 5-7.]
Supreme Cola is a supplier of fountain equipment to restaurants, bars, and cafeterias. The
fountain equipment is manufactured at their York PA plant site. A national distribution
center (DC) for the fountain equipment is also maintained adjacent to the plant. Supreme
has one common platform design to which they add various features and accessories to
create 10 different product options. The lead time for manufacturing and delivering a
batch of products to the distribution center is 2 weeks. They review inventory and order
weekly.
For product ACola, Supreme uses a normal distribution with mean 25 and standard
deviation 20 to model weekly demand. Demands across weeks are independent. ACola
sells for $15,000, and they enjoy a 50% gross margin. The annual holding cost for
inventory in the DC is 25% of the product's cost. In the event that a customer order
cannot be filled from the warehouse due to an out-of-stock situation, Supreme expedites
the manufacture and delivery of the item. It estimates that such expediting increases their
cost by $770 per unit.
5) What order-up-to level should Supreme choose to minimize their inventory for ACola
while achieving at least a 99.25% in-stock probability?
Answer: 159.1.
Explanation: Mean demand over l + 1 periods is (2 + 1) * 25 = 75 The standard deviation
over this time is sqrt(2 + 1) * 20 = 34.6. From the table of the Standard Normal
Distribution function, z = 2.43 (corresponds to 99.25%).
S = mu + z * sigma = 75 + 2.43 * 34.6 = 159.1
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
6) Suppose Supreme wants to minimize its holding and backorder (i.e., expediting) costs
for ACola. What stockout probability should they target? Assume 52 weeks per year.
Answer: 4.5%.
Explanation: The holding cost is 0.25 * 0.5 * 15,000/52 = $36 per unit per week. The
backorder cost is $770. The optimal in-stock is 770/(770 + 36) = 0.955. The stockout
probability is 1 - 0.955 = 4.5%.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
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7) Supreme uses an order-up-to policy with a base stock level equal to 250 for ACola.
What is the probability that Supreme will have more than 40 units on order of that
product at the start of any given week?
Answer: 64%.
Explanation: Demand over two periods (the lead time) has mean 2 * 25 = 50 and
standard deviation sqrt(2) * 20 = 28.28.
The z that corresponds to 40 is then (40 - 50)/28.28 =- 0.35.
F(-0.35) = 0.36. So, there is a 36% chance demand is 40 or lower over two periods.
There is a 1 - 0.36 = 64% chance that it is greater than 40.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Analytical Thinking
Blooms: Analyze
8) An industrial company requires argon gas cylinders for its work. Weekly demand is
normally distributed with a mean of 35 and a standard deviation of 15. Demands are
independent across weeks. Orders are placed weekly and the lead time to receive an order
is 1 week. They want to hold enough cylinders to ensure a 99.75% in-stock probability. If
they use an order-up-to model, what base stock level should they implement? (Do not
round to an integer value, i.e., leave your response in decimal form.)
Answer: 129.6 base stock level.
Explanation: F(z) = 0.9975 => z = 2.81
Demand for l + 1 periods is normally distributed with a mean of 2 * 35 = 70 and a
standard deviation of sqrt(2) * 15 = 21.213 => Q = 70 + 2.81 * 21.213 = 129.6.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 9-11.]
Radio Shack sells a 32GB flash drive. Weekly demand for the 32GB flash drive in one of
their stores is Poisson distributed with a mean of 1.25. The store places orders weekly,
and there is a one-week lead time to receive orders.
9) On average, how many units will the store have on order?
Answer: 1.25 units.
Explanation: Expected number of units on order=expected demand in one period x lead
time=1.25 units per period*1 period=1.25.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Knowledge Application
Blooms: Apply
10) Suppose that they have 5.5 units of this flash drive on average in inventory in the
store. What are the annual turns of this item in this store? Assume 52 weeks per year.
Answer: 23.64 annual turns.
Explanation: Annual Turns = Total weeks * demand / Avg inv per week
= 52 * 2.5 /5.5 = 23.64 times.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
11) Suppose they operate with a base stock level of 4. What in-stock probability would
they achieve?
Answer: 89.12%.
Explanation: Lead time is 1 period (one week) => l + 1 = 2. So, the in-stock probability
is the probability that demand over 2 periods (two weeks) is less than or equal to 4. The
demand over two weeks is Poisson distributed with mean 2 * 1.25 = 2.5. Use the Poisson
function table with µ = 2.5 and S = 4 on page 423 of the textbook to find F(S) = 0.89118
= 89.12%.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
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12) Radio Shack sells the same 32GB flash drive on their e-commerce site which has a
single distribution center. Daily demand at their e-commerce DC is forecasted to be
normally distributed with a mean of 150 and a standard deviation of 75. The lead time to
receive a replenishment at the distribution center from their supplier is 2 days. They
review their inventory and place orders every two days, on the same day that they receive
deliveries of new inventory. They operate 7 days a week. If they were to implement an
order-up-to model, what base stock level should they choose for the DC if they want to
achieve a 99.3% in-stock probability? (Leave your answer in decimal form, i.e., no need
to round to an integer value.)
Answer: 969 base stock level.
Explanation: Notice that Radio Shack reviews their inventory and places orders every
two days, so one period is two days. The mean and standard deviation for demand over
one period is therefore 2 * 150 = 300 and sqrt(2) * 75, respectively. The lead time is 2
days, namely 1 period => l = 1 => demand over l + 1 = 2 periods is then normally
distributed with mean 2 * 300 = 600 and standard deviation sqrt(2) * sqrt(2) * 75 = 150.
Finally, Φ(z) = 0.993 => z =2.46. S = µ + z * σ = 600 + 2.46 * 150 = 969.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
13) A retailer uses the order-up-to model to manage inventory of an item in a store. The
lead time for replenishment is 4 weeks, and they can place orders weekly. Weekly
demand is Poisson with mean 0.10 units. Their base stock level is 5, and unfilled demand
is backordered. What is the coefficient of variation of their orders?
Answer: 3.16.
Explanation: Since order size = demand, C.O.V. of the orders = C.O.V. of the demands =
σ/µ= sqrt(0.1)/0.1 = 3.16.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 14-18.]
A large toy company Müttel currently allows toy retailers to place orders with delivery in
2 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Müttel has
introduced. Müttel charges a wholesale price of $10 for the Gipokmon. The manager of a
small boutique toy retail company, TOYS-are-MINE, plans to sell the toy for $20 and
incurs a holding cost of $0.1 per toy, per week. At this price, demand per week for the toy
at one of their stores is estimated to be Poisson distributed with a mean of 1.5 units.
Assume that the backorder cost is equal to the product's retail margin. Assume TOYSare-MINE uses the order-up-to model to plan orders and deliveries to this store.
14) Suppose TOYS-are-MINE uses an order-up-to level of 10. After receiving their
delivery for this week, they have 2 units on-hand. Last week's order was for 5 units. How
many units will they order this week?
Answer: 3 units.
Explanation: Recall that S = On hand + on order - backorder.
S = 10 = 2 + 5 + (this week's order) + 0.
Hence this week's order is equal to 3 units.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
15) Suppose they use an order-up-to level of 10 for this store. On average, how many
units will this store have on-order?
Answer: 3 units.
Explanation:
On order = (lead time) * (average demand) = (2 weeks) * (1.5 units/week) = 3 units.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
16) Given their cost and price for the Gipokmon, what is the optimal in-stock probability
that TOYS-are-MINE should target?
Answer: 0.9901.
Explanation: The optimal in-stock probability is equal to the critical ratio, which is given
as CR = (backordering cost)/(backordering cost +holding cost) = (10)/(10 + 0.1) =
0.990099.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
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17) Suppose an order-up-to level of 5 is established. What is the resulting in-stock
probability?
Answer: 99.55%
Explanation: From the Poisson distribution function table for mean = 1.5, we find the instock probability for S = 5 as 99.55%.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Knowledge Application
Blooms: Apply
18) Suppose an order-up-to level of 3 is established. What would be the expected end-ofperiod on-hand inventory of Gipokmons?
Answer: 0.245.
Explanation: End-of-period on-hand inventory = S - Expected Sales.
Expected Sales = μL + 1- Lost Sales. From the Poisson Loss Function Table we find the
Lost Sales for S = 3 and μL + 1 = 4.5 as 1.745 units. Therefore,
expected sales = 2.755 and end end-of-period on-hand inventory = 0.245.
Difficulty: 3 Hard
Topic: The End-of-Period Inventory
AACSB: Analytical Thinking
Blooms: Analyze
19) Locus Computer, based in California, is planning to manufacture its entry into the
tablet space, the Lpad, in Taiwan. One option is to ship Lpads via ocean carrier. It is
estimated that the lead time will be 2.5 months. Alternatively, the company can use air
shipments which only have a lead time of 1/4 months. Annual holding costs are estimated
to be 30% of the value of the product. As a percentage of the value of the product, how
much would air shipments save in holding costs if you only consider pipeline inventory
and ignore the cost of air shipments?
Answer: 5.625%.
Explanation: Annual holding costs are 30% of the value of the product. Monthly holding
costs are 30/12 = 2.5% of the value of the product.
Under the ocean carrier option, the pipeline inventory cost per unit as a percentage of the
value of the product will be: 2.5 * 2.5% = 6.25%.
Under the air shipments option, the pipeline inventory cost per unit as a percentage of the
value of the product will be: 0.25 * 2.5% = 0.625%.
Therefore, the savings with air shipments option is equal to 6.25 - 0.625 = 5.625% of the
value of the product.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 20-21.]
Timbuk2 Inc. manufactures over 100,000 different versions of a messenger bag
(illustrated on the right). Suppose Timbuk2 implements an order-up-to model to manage
its inventory of a particular plastic buckle. The lead time to receive these buckles is three
weeks. Demand is approximately normally distributed with a mean of 2,300 units per
week and a standard deviation of 1,300. Each week's demand is independent of the
demand in the other weeks.
20) What is the order-up-to level that achieves a target in-stock probability of 99.6%?
Answer: 16,090.
Explanation: From the Standard Normal tables, F(2.65) = 0.996.
We saw that Dl+1 ~ N(2,300 * 4, 1,300 * sqrt(4)) ~ N(9200, 2600).
S = 9,200 + 2,600 * 2.65 = 16,090.
Difficulty: 3 Hard
Topic: Choosing an Order-up-to Level to Meet a Service Target
AACSB: Analytical Thinking
Blooms: Analyze
21) Suppose Timbuk2 operates with an order-up-to level of 16,000. At the start of a week
(before shipments are received for that week, before an order is placed that week and
before any demand occurs), what is the probability there is at least 3,500 units on order?
Answer: 93%.
Explanation: With a three-week lead time there will be on average three weeks worth of
demand on order. The distribution of three weeks of demand is normally distributed with
mean 2,300 * 3 = 6,900 and standard deviation 1,300 * sqrt(3)
= 2,252.
The z-statistic for 3,500 units is then (3,500 - 6,900)/2,252 = -1.51.
The probability the outcome of a standard normal is -1.51 or high is
1 - Φ(-1.51) = 93%.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 22-25.]
Craig is a self-proclaimed movie buff who uses WebFlix, an Internet DVD rental service,
to satisfy his movie needs. Craig watches movies in the evening and mails movies back
the following morning. Upon receipt of a DVD, WebFlix mails Craig a new movie. To
make sure that new movies are mailed to him without delays, Craig maintains a very long
list of movies he desires to watch in his WebFlix account. It takes 4 days on average for
Craig to receive a new movie from the moment he mails the previous movie. (For
example, he receives Friday afternoon the replacement for a movie he mailed Monday
morning.) Craig's daily thirst for movies is Poisson-distributed with mean 0.5. If on a
given day, Craig is unable to watch the number of movies he desires because they are not
available, then he watches them as soon as they become available.
22) Suppose Craig uses a rental plan allowing him to have up to 5 DVDs at home or in
the mail at any point in time. What is the probability that, on a given day, Craig cannot
satisfy his movie-watching needs?
Answer: 5%.
Explanation: Use the Poisson Distribution Function Table with mean 0.5(1 + 4) = 2.5.
For S = 5, the in-stock probability (from the table) is .95798, and the corresponding
stockout probability is about 5%.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Knowledge Application
Blooms: Apply
23) How many DVDs, on average, does Craig have in the mail (on the way to or from
WebFlix)?
Answer: 2.
Explanation: From Little's Law, on-order inventory is 0.5 × 4 = 2.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Knowledge Application
Blooms: Apply
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24) Craig decides that his current plan is too expensive, so he switches to the cheaper
plan that only allows him to have up to 4 DVDs at home or in the mail. On average, how
many movies does Craig have at the end of the day at his home that he hasn't watched?
Answer: 1.67.
Explanation: Expected backorder = 0.17077 (from the Poisson Loss Function Table for S
= 4 and mean demand = 0.5(1 + 4) = 2.5).
End-of-period inventory is 4 - 2.5 + 0.17077 = 1.67.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Analytical Thinking
Blooms: Analyze
25) Instead of an ad hoc way of deciding which plan to buy, Craig decides that he would
like to be able to fulfill all of his moving watching needs in a month with at least an 80%
probability while minimizing his monthly fee (fees are increasing in the number of DVDs
held). In this case, how many DVDs should Craig's plan allow him to have?
Answer: 4.
Explanation: We seek an order-up-to level that yields an 80% in-stock probability.
From the Poisson Loss Function Table with mean demand = 0.5(1 + 4) = 2.5, we obtain S
= 4.
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Knowledge Application
Blooms: Apply
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26) For products with slow-moving demand, e.g., 1 unit per week, the Poisson
distribution is likely to be a better model for demand than the normal distribution because
(choose the best answer)
A) the Poisson's standard deviation is equal to the square root of its mean.
B) the normal distribution does not allow the freedom to choose any standard deviation
for any given mean.
C) the Poisson distribution is a continuous distribution.
D) only the standard normal distribution would apply in this setting.
E) the Poisson distribution does not assign any probability to negative outcomes.
Answer: E
Explanation: Normal distribution assigns positive probabilities to negative demand,
however, if the mean is significantly higher than the standard deviation these
probabilities become negligibly small. However, if the items are slow moving (mean low
compared to standard deviation), there is a significant probability of having negative
demand under a normal distribution. Poisson distribution does not assign any probability
to negative outcomes. Answers in b, c, and d are incorrect, while the answer in a is not
relevant.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
Blooms: Evaluate
27) A retailer is considering two possible definitions of "in-stock":
(I) A product is in-stock if it has at least one unit on-hand at the end of the day.
(II) A product is in-stock if it has satisfied all demand during a day.
For a given order-up-to level, which definition yields the higher in-stock probability?
A) Definition I, because if one unit is on-hand, then all demand must have been satisfied.
B) Definition II, because the firm is more likely to satisfy all demand than to end the day
with one unit on hand.
C) Definition II, because if all demand is satisfied, then there must be some inventory left
over.
D) Either one is possible because it will depend on the particular order-up-to policy
chosen, the distribution function of demand, and the lead time.
Answer: B
Explanation: Definition II yields higher in-stock because there will be days when there
are no items left over, but all the demand was satisfied. In such cases, Definition II will
be in-stock but will be out of stock by Definition I.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
Blooms: Analyze
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28) A firm manages its inventory with an order-up-to model. Each period is one day, the
lead time is 2 days, the base stock level is 10 and their inventory position at the start of a
day (before they submit an order for that day) is -4. Which of the following is definitely
true?
A) Demand was 4 units yesterday.
B) Demand was 10 units yesterday.
C) There are 4 units backordered.
D) There are 14 units on-order before they order today.
E) After today's order there will be 14 units on-order.
F) They will receive more inventory today.
G) None of the above.
Answer: G
Explanation: With an inventory position of -4, we know they have no on-hand inventory,
and the sum of on-order minus backorders is -4. We don't know how many are on-order
or backordered. Therefore, they have at least 4 units backordered, but they could have
more, in which case the amount on-order would vary, ruling out c, d, and e. We don't
know when those backorders occurred, so there are many possibilities for demand
yesterday (ruling out a and b). We also don't know how many were ordered 2 days ago,
so we don't know how much will arrive today (ruling out f).
Difficulty: 3 Hard
Topic: Performance Measures
AACSB: Reflective Thinking
Blooms: Analyze
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29) A firm uses the order-up-to model to manage its inventory. It wants to increase its instock probability while decreasing its holding costs (i.e., reduce its average inventory).
Which of the following will help to achieve this goal? (Consider each one on its own.)
(i) Decrease the lead time.
(ii) Increase the base stock level.
(iii) Increase the average quantity on-order.
A) Only (i)
B) Only (ii)
C) Only (iii)
D) (i) and (ii)
E) (i) and (iii)
F) (ii) and (iii)
G) Any of them will help (that is (i), (ii) or (iii).
H) None of them will help.
Answer: A
Explanation: Decreasing the lead time will reduce inventory for a given base stock level
and increase the in-stock probability. The others are not correct. If the base stock is
increased, the in-stock will increase but so will inventory. If the average quantity onorder increases, then it must be that the average lead time increases, which is not good for
the in-stock.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Evaluate
30) A firm implements the order-up-to model with weekly ordering. In week 11 they
observe that demand is much lower than expected demand. At the start of week 12
(before they order), they decide to lower their forecast of mean demand per week while
keeping the standard deviation the same as well as the target in-stock probability. Their
order in week 12 will:
A) be less than the demand they observed in week 11.
B) equal to the demand they observed in week 11.
C) be greater than the demand they observed in week 11, but less than their updated
expected demand.
D) be greater than their updated expected demand.
E) equal to their updated expected demand over their lead time plus one period.
F) none of the above.
Answer: A
Explanation: The firm has decided to reduce the order in week 12 due to their
observation of demand falling below the expected demand in week 11.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
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Blooms: Analyze
31) Assume a firm implements an order-up-to inventory model with an order-up-to level
of 10. The lead time is 5 time periods, demand is normally distributed, and the target fill
rate is 95%. Suppose the order has just been placed. Which of the following is definitely
not true?
A) The last order was 12.
B) The backorder in the previous period was 14.
C) There are 11 units in on-hand inventory.
D) Demand in the previous period was 71.
E) There are 12 units in the pipeline, and 2 units are backordered.
F) There are 8 units on-hand and 2 units in the pipeline.
Answer: C
Explanation: If the maximum inventory position that we allow is 10, it is impossible to
have 11 units in on-hand inventory. Since there is on-hand inventory, there cannot be any
backorders so that the inventory position exceeds 10 even without accounting for the
pipeline inventory.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
Blooms: Analyze
32) Suppose inventory is managed using the order-up-to model. Your inventory position
is 20 and demand in the last period was 10. Your optimal order quantity is 10 units. Your
target in-stock probability is
A) 95%
B) 96%
C) 97%
D) 98%
E) 99%
F) Could be any of the above a-e.
G) Cannot be any of the above a-e.
Answer: F
Explanation: The target in-stock is not related to any one order.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Analytical Thinking
Blooms: Analyze
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33) Suppose you are managing inventory using the order-up-to model, the order-up-to
quantity is 10 and you have already received several replenishments. Which of the
following statements is definitely false?
A) On-order inventory is 9.
B) Inventory position is 9.
C) Backorder is 11.
D) On-hand inventory is 11.
E) Inventory position is -11.
F) Pipeline inventory is 11.
Answer: D
Explanation: Order-up-to level = inventory on-hand + on order inventory - backorders.
On-hand inventory cannot be greater than order-up-to level. So D is false. On-hand
inventory is less than order-up-to level, so A is true. Inventory position can be lower than
order-up-to level before ordering, hence B can be true. Backorders can be arbitrarily
large. Inventory position can be negative (before ordering) because of large backorders.
Hence, C and E could be true. Pipeline inventory can be 11 if there is no on-hand
inventory and there are 11 backorders. So, the order would be 11 units, and pipeline
inventory would be greater than or equal to 11. Option F could be true.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
34) Suppose the order-up-to model is used. The probability that you end any given period
with no on-hand inventory equals
A) the in-stock probability.
B) the critical ratio.
C) lost sales.
D) the gross margin.
E) the ratio of inventory turns to days-of-supply.
F) none of the above.
Answer: F
Explanation: Probability of ending a period with no inventory is stockout probability,
which isn't any of the above choices.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
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35) A firm sells a product whose demand over the next couple years will be stable so the
order-up-to model is used to manage its inventory. When the demand uncertainty is small
(for example, the weekly demand has a mean of 100 and a standard deviation of 5), the
main benefit of reducing the lead time is
A) to do more lead time pooling.
B) to reduce the expected on-hand inventory at the end of every period.
C) to enable us to use the reactive capacity.
D) to reduce the pipeline stock.
E) none of the above.
Answer: D
Explanation: Pipeline stock is directly proportional to lead time (by Little's law), and
hence is reduced by reducing the lead time. Reducing lead time has a small effect on the
expected on-hand inventory when uncertainty is small. Similar arguments apply for gains
from pooling.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
Blooms: Analyze
36) In the order-up-to model, assume that the mean of demand in a period remains the
same and the order-up-to level is kept at a constant level. If the demand uncertainty (the
standard deviation of demand in each period) increases,
A) the expected inventory at the end of each period would increase.
B) the expected inventory at the end of each period would decrease.
C) the expected inventory at the end of each period would remain unchanged.
D) the expected inventory at the end of each period may go up or down.
Answer: A
Explanation: The demand fluctuates more. When demand shoots up in a period and the
firm runs out of stock, the inventory at the end of the period is zero, no matter how much
the demand overshoot is. When demand falls in a period, the inventory at the end of the
period increases proportionally. Reduction in inventory levels is bounded from below by
zero. Since the mean demand is the same, and the uncertainty has gone up, the average
(or expected) inventory at the end of each period would increase.
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
Blooms: Analyze
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37) Suppose the order-up-to model is used to manage inventories. The firm is planning
changes that will reduce the lead time to receive replenishments, but the firm is also
planning on making its assortment more "fashionable," which essentially means that
forecast uncertainty is likely to rise for all products. What can be said about the likely
change in the firm's on-order inventory?
A) It will surely decrease.
B) It will remain the same.
C) It will surely increase.
D) More information is needed to determine the impact of these changes.
Answer: A
Explanation: From Little's Law, on-order inventory = lead time * expected demand in
one period. A change in forecast uncertainty influences the standard deviation of demand
but does not influence either the length of the lead time or the expected demand in one
period. Hence, these changes (reducing the lead time and making products more
fashionable) will reduce the on-order inventory due to the reduction in the lead time
(more fashionable products has no impact on the on-order inventory).
Difficulty: 3 Hard
Topic: Choosing Demand Distributions
AACSB: Reflective Thinking
Blooms: Evaluate
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38) Suppose in the order-up-to model the target in-stock probability is 0.95 and demand
across periods are independent and normally distributed. If the lead time is doubled but
the target in-stock probability remains 0.95, what happens to the order up-to level?
A) It more than doubles (increases by more than a factor of 2).
B) It doubles (increases exactly by a factor of 2).
C) It increases, but by less than a factor of 2.
D) It decreases.
E) The answer cannot be determined with the given information.
Answer: C
Explanation: S = μ + z * σ where μ is the mean of demand over l + 1 periods and σ is the
standard deviation of demand over l + 1 periods. Since the target in-stock probability
remains the same, the z statistic will remain the same. Furthermore, the z statistic is
positive because the target in-stock is 0.95. Hence, only the mean and standard deviation
of demand change.
Let L be the initial lead time and 2L be the doubled lead time.
Let μdaily be the expected demand in one period.
Let σdaily be the standard deviation of demand in one period.
With L as the lead time SL = (L + 1) * μdaily + z *
×σ daily
With 2L as the lead time S2L = (2L + 1) × μdaily + z *
× σdaily
Because z is constant and positive, it is clear that the order-up-to level increases.
There are two parts to the order-up-to equation.
The first part increases by less than a factor of 2:
(2L + 1) * μdaily < 2 (L + 1) * μdaily
The second part also increases by less than a factor of 2:
* σdaily < 2
* σdaily
Hence, the order-up-to level increases by less than a factor of 2.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Analytical Thinking
Blooms: Analyze
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39) In the order-up-to model the standard deviation of orders
A) is higher than the standard deviation of demand.
B) is lower than the standard deviation of demand.
C) is equal to the standard deviation of demand.
D) cannot be compared to the standard deviation of demand.
Answer: C
Explanation: In the order-up-to-model, items are ordered on a one-for-one basis. Thus,
the variance of orders equals the variance of demand.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
40) In the order-up-to model, what is the relationship between lead time and inventory
turns?
A) Higher lead time leads to higher turns.
B) Higher lead time leads to lower turns.
C) Higher lead time leads to higher turns only if the in-stock probability is greater than
50%.
D) Higher lead time leads to lower turns only if the in-stock probability is greater than
50%.
Answer: B
Explanation: Inventory turns = cost of goods sold /inventory value, where "inventory
value" is the value of the inventory in $s (rather than in units) because cost of goods sold
is measured in $s. If lead time increases, then inventory increases and so turns decrease.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
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41) Regarding the performance of the order-up-to model, if the order-up-to level is
always chosen to minimize the sum of the expected holding and backorder costs, then as
the lead time decreases
A) pipeline inventory as a percentage of total inventory increases.
B) pipeline inventory as a percentage of total inventory decreases.
C) the optimal in-stock probability increases.
D) the optimal in-stock probability decreases.
E) none of the above.
Answer: B
Explanation: The optimal in-stock probability is determined by the critical ratio, and
hence remains unchanged as the lead time decreases. So, choices C and D are false. The
pipeline inventory falls proportionally as the lead time decreases. However, the rest of the
inventory decreases only in proportion to the square root of the lead time. Hence, the
pipeline inventory falls more steeply than the total inventory as the lead time decreases.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
42) Suppose inventory is managed using the order-up-to model. Which of the following
actions will certainly lead to a higher order-up-to level? In all cases assume the
characteristics of the demand process do not change.
A. Increase in the target in-stock probability (for the same lead time).
B. Decrease the target stock-out probability (for the same lead time).
C. Increase in the lead time (for the same service level).
A) A only.
B) B only.
C) C only.
D) A and B.
E) B and C.
F) A and C.
G) A, B and C.
H) None of the above.
Answer: G
Explanation: All three of these actions lead to higher order-up-to level.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
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43) Ana Litic, a new supply chain manager at HP, decides to check some data on the
supply chains she manages. She discovers that HP's in-transit inventory of printers
between Vancouver, WA and its Asian DC has increased from two quarters ago.
However, the distribution of demand at the Asian DC has not changed over this period of
time. Ana knows that the Asian DC manager is controlling inventory to achieve a fixed
in-stock probability target, so she is happy to see that indeed the in-stock at the Asian DC
has also not deviated off the target. Ana wonders what has happened to the Asian DC's
average inventory. What is she likely to discover regarding the Asian DC's on-hand
inventory?
A) On-hand inventory has not changed because the in-stock probability has not changed
at the Asian DC.
B) On-hand inventory has increased because the lead time from Vancouver WA to the
Asian DC must have increased.
C) On-hand inventory has not changed because average demand has not changed at the
Asian DC.
D) On-hand inventory has decreased because the variability of demand must have
decreased.
E) It is not possible to predict what Ana is likely to observe with respect to the change in
on-hand inventory, i.e., it could be lower, higher, or unchanged.
Answer: B
Explanation: If the pipeline inventory increases, it means that either the mean demand
increased or the lead time increased. Since we know that demand distribution has not
changed, it means that the lead time has increased, which leads to higher on-hand
inventory.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
AACSB: Reflective Thinking
Blooms: Analyze
44) Assuming that the order-up-to level stays constant, which of the following statements
is true about the order-up-to model?
A) As the lead time increases, the on-hand inventory increases, but the pipeline inventory
remains the same.
B) As the demand uncertainty (measured by σ) increases, both on-hand inventory and
pipeline inventory increase.
C) When the mean demand increases, both on-hand inventory and pipeline inventory
remain the same.
D) As the demand uncertainty (measured by σ) increases, on-hand inventory decreases,
but the pipeline inventory remains the same.
E) None of the above.
Answer: E
Explanation: None of the above apply as the order-up-to level remains constant.
Difficulty: 3 Hard
Topic: The Order-up-to Model Design and Implementation
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AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 17 Risk-Pooling Strategies to Reduce and Hedge Uncertainty
1) The amount of milk produced by dairy cows depends on a number of factors, including
average temperature and rainfall. A large dairy co‐op forecasts that production of milk
next month in its northern region will be normally distributed with a mean of 100,000
gallons and a standard deviation of 40,000 gallons. Production next month in its southern
region is forecasted to be normally distributed with a mean of 80,000 and a standard
deviation of 30,000. The correlation between the two regions is 0.4. What is the
coefficient of variation for total milk production across the two regions?
Answer: 0.31
Explanation: The mean of the total milk production is the sum of the mean of the
northern region and the southern region:
Northern Mean = 100,000
SD = 40,000
CV = SD / Mean
CV = 40,000 / 100,000
CV = 0.4
Southern Mean= 80,000
SD= 30,000
CV =SD / Mean
CV = 30,000 / 80,000
CV = 0.375
the coefficient of variation for total milk production across the two regions?
0.4 * 0.4 = 0.16
0.375 * 0.4 = 0.15
Total = 0.31
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Analytical Thinking
Blooms: Apply
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2) The table below provides monthly demand data for two products along with the
average monthly demand (2nd to the last column) and the standard deviation of monthly
demand (last column). Which of the following best describes the relationship between the
demands for these two products?
A) The products are negatively correlated.
B) The products are independent.
C) The products are positively correlated.
D) There is not enough evidence regarding the correlation between these products.
Answer: A
Explanation: The products are negatively correlated. The standard deviation of the total
demand, if they were independent, would be sqrt(1,127^2 + 1,019^2) = 1,519. This is
greater than the actual standard deviation of total demand, 1,040, which suggest that more
variability has been reduced than would be reduced with independent demand, i.e., they
are negatively correlated.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Analytical Thinking
Blooms: Analyze
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[The following information applies to questions 3-4.]
Aquaguard manufactures three models of water purifiers in three separate plants in
Taiwan. These plants serve the demand in Europe. All three models sell at a unit price of
$100, and the holding cost is 5% of the selling price per month. The monthly demand for
these models is normally distributed with the following parameters:
Model 1: Mean 1000, SD 300
Model 2: Mean 1000, SD 300
Model 3: Mean 1000, SD 300
The demand for Model 1 and Model 2 has a correlation coefficient of -0.35, while that for
Model 3 is independent of the other two models.
3) Consider Aquaguard's distribution in Europe. They have a central DC that caters to the
European market. The lead time from Taiwan to their DC is 2 months and orders are
placed every month. Determine the expected end-of-month inventory for each product
when a target in-stock probability is 98%.
Answer: 1,074.
Explanation: The mean demand over l + 1 periods is 3 * 1,000 = 3,000.
The standard deviation over l + 1 periods is 300 * = 519.6
Look up the z-statistic in the Standard Normal Distribution Function Table that
corresponds to the in-stock probability of 98%: z = 2.06.
Order-up-to level S = 3,000 + 2.06 * 519.6 = 4,070.
Look up L(z) in the Standard Normal Loss Function Table: L(2.06) = 0.0072.
Expected inventory for each product = S - (l + 1)μ + σL(z) = 4070 - 3000 + 519.6 *
0.0072 = 1074
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Analytical Thinking
Blooms: Apply
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4) Aquaguard has the option of redesigning its products. It can develop a "base" product
B and ship it to the DC. The base product can then be customized into any one of the
models and sold (delayed differentiation). The company chooses to redesign Models 1
and Models 2 while Model 3 remains untouched. The lead time, the in-stock target level,
and the ordering policies remain the same. Determine the expected end-of-period
inventory for product B.
Answer: 1,224
Explanation: For Models 1 and 2,
μ = 2 * 1000 = 2000, σ = 300 *
= 300 *
The mean demand over l + 1 periods is 3 * 2000 = 6000.
= 342.
The standard deviation over l + 1 periods is 342 * = 592.
Look up the z-statistic in the Standard Normal Distribution Function Table that
corresponds to the in-stock probability of 98%: z = 2.06.
Order-up-to level S = 6,000 + 2.06 * 592 = 7,219.52.
Look up L(z) in the Standard Normal Loss Function Table: L(2.06) = 0.0072.
Expected inventory for Models 1 and 2
= S - (l + 1)μ + σL(z) = 7219.52 - 6000 + 592 * 0.0072 = 1224
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Analytical Thinking
Blooms: Apply
5) Suppose that Supreme uses the same demand distribution for two of the 10 products,
i.e., each has a mean of 25 units per week and a standard deviation of 20 per week.
Supreme observes that the coefficient of variation of total demand for these 2 products is
0.70. Which of the following is true?
A) Demands for these products are positively correlated with each other.
B) Demands for these products are negatively correlated with each other.
C) Demands for these products are independent.
D) There is not enough information to answer this question.
Answer: A
Explanation: If the products were independently distributed, their combined demand
would have a mean of 25 * 2 = 50 and a standard deviation of sqrt(2) * 20 = 28.28. The
coefficient of variation would be 28.28/50 = 0.57. The actual coefficient of variation is
higher than this, 0.70, so less variability is reduced than expected for independence. The
products must be positively correlated.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Knowledge Application
Blooms: Apply
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6) Montanso is a large bio firm that sells genetically modified seed to farmers. They
currently have one warehouse in each of two different counties in Indiana, Grant, and
Wabash. Over the last three years, demand (in kg) for their seed in these two counties has
been
Montanso is considering consolidating their warehouses into a single one that would
serve both counties. Therefore, they would like to understand the correlation in demand
between these two counties. Given the data, which of the following do you think is most
likely?
A) The demands are negatively correlated.
B) The demands are independent.
C) The demands are positively correlated.
D) There is not enough information to determine with confidence whether the demands
are negatively correlated, independent, or positively correlated.
Answer: C
Explanation: If the demands were independent, then the standard deviation of the total
would be Sqrt(67,000^2 + 39,000^2) = 77,524. That is less than 106,000, so there is less
of a reduction in the standard deviation than we would expect if they were independent.
Consequently, they must be positively correlated.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Analytical Thinking
Blooms: Analyze
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7) Cross-training workers is most useful, from the perspective of matching supply with
demand when
A) average demand exceeds capacity.
B) average demand is approximately equal to capacity.
C) average demand is significantly less than capacity.
D) cross-training of workers is equally useful (from the perspective of matching supply
with demand) no matter the relationship between capacity and average demand.
Answer: B
Explanation: Cross training provides flexibility and flexibility is most useful when
capacity is approximately equal to demand.
Difficulty: 3 Hard
Topic: Capacity Pooling with Flexible Manufacturing
AACSB: Reflective Thinking
Blooms: Analyze
8) An insurance firm uses several types of agents to service different classes of insurance
customers. Demand from each class of customers is uncertain. The firm decides to invest
in the cross-training of agents so that an agent can serve multiple classes of customers.
Investment in cross-training is likely to have a large incremental value
A) when total expected demand for services far exceeds total capacity.
B) when total expected demand for services is close to the total capacity.
C) when total expected demand for services is far less than the total capacity.
D) when there is minimal uncertainty in demand.
E) when cross-training is very expensive.
F) in none of the above cases.
Answer: B
Explanation: Cross-training produces large value when total expected demand for
services is close to total capacity and full flexibility.
Difficulty: 3 Hard
Topic: Capacity Pooling with Flexible Manufacturing
AACSB: Reflective Thinking
Blooms: Analyze
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9) A firm sells two products, A and B. Both products have normally distributed demand.
Both have the same mean and standard deviation. Consequently, they have the same
coefficient of variation, which happens to be 0.50. If we were to measure the coefficient
of variation (COV) of total demand (i.e., the sum of demands for products A and B) then
we would find that the COV of the total demand
A) equals the sum of the individual COVs, i.e., it would be 1.0.
B) would be no greater than 1.0 and possibly less than 1.0.
C) would be 0.5.
D) would be no greater than 0.5 and possibly less than 0.5.
E) would be 0.35, i.e., 0.5 divided by the square root of 2.
F) would be 0.35 or lower.
Answer: D
Explanation: COV of total demand is given by (COVi) * SQRT(0.5 * (1 + Correlation)),
which is always less than or equal to COVi since the correlation coefficient can only take
values within [-1,1]. Therefore, the COV of the total demand will never exceed the COV
of individual demand, which is 0.5.
Difficulty: 3 Hard
Topic: Product Pooling
AACSB: Reflective Thinking
Blooms: Analyze
10) Recall the proposal in the HP case to stock generic printers in the European DC and
add to this generic printer an appropriate power supply and manual before shipping to a
specific country. This process is often called delayed product differentiation; the generic
printer is called the generic product, and the power supply and manuals the differentiating
components. It is claimed that delayed product differentiation will not change the
inventory of the differentiating components (holding the service level fixed). Is this claim
correct? Choose the best response.
A) No, inventory of the differentiating components will decrease because of lead-time
risk pooling.
B) No, inventory of the differentiating components will decrease because the target instock probability will decrease.
C) No, inventory of the differentiating components will increase because their
replenishment lead-time will increase.
D) Yes, inventory of the differentiating components will remain the same because the
characteristics of their demand distribution (e.g., mean and standard deviation) will not
change.
E) Yes, inventory of the differentiating components will remain the same because their
per unit holding cost and backorder cost will not change.
Answer: D
Explanation: Differentiating component inventory remains constant because the mean
and standard deviation is constant.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
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AACSB: Reflective Thinking
Blooms: Analyze
11) It is also claimed that delayed differentiation will reduce the inventory of the generic
product (holding the service level, such as the in-stock probability, constant) even if the
different product offerings have positively correlated demand (but not perfectly positively
correlated). Is this claim correct?
A) No, with positive correlation the coefficient of variability of the generic product will
not be reduced.
B) No, with positive correlation the in-stock probability of the generic product will have
to be increased.
C) No, with positive correlation the expected demand of the generic product will
increase.
D) Yes, lead time risk pooling is most effective with positively correlated demand.
E) Yes, the standard deviation of total demand (i.e., the sum of the demands across the
product offerings) will be reduced even with a positive correlation (assuming the
correlation is less than one).
Answer: E
Explanation: Positive correlation leads to a reduction in total demand standard deviation.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Reflective Thinking
Blooms: Analyze
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Aquaguard manufactures three models of water purifiers in three separate plants in
Taiwan. These plants serve the demand in Europe. All three models sell at a unit price of
$100 and the holding cost is 5% of the selling price per month. The monthly demand for
these models is normally distributed with the following parameters:
Model 1: Mean 1000, SD 300
Model 2: Mean 1000, SD 300
Model 3: Mean 1000, SD 300
The demand for Model 1 and Model 2 has a correlation coefficient of -0.35, while that for
Model 3 is independent of the other two models.
12) The company wishes to make two of the models in one plant by using flexible
technology. Which two models should Aquaguard choose in order to minimize
production variability in the new plant (as measured by the coefficient of variation)?
A) Models 1 and 2
B) Models 1 and 3
C) Models 2 and 3
D) All of the above.
Answer: A
Explanation: All else equal, pooling works better when demand correlation is low
(negative). Correlation is the lowest between Models 1 and 2.
Difficulty: 3 Hard
Topic: Capacity Pooling with Flexible Manufacturing
AACSB: Reflective Thinking
Blooms: Analyze
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13) Which of the following is NOT a benefit of pooling inventory across locations?
A) One can maintain the same on-hand inventory and increase the in-stock probability.
B) One can decrease pipeline inventory.
C) One can reduce on-hand inventory and increase the in-stock probability
simultaneously.
D) One can maintain the same in-stock probability with less on-hand inventory.
E) One can maintain the same on-hand inventory and increase the in-stock probability
and one can decrease pipeline inventory.
F) One can decrease pipeline inventory and one can reduce on-hand inventory and
increase the in-stock probability simultaneously.
G) One can maintain the same on-hand inventory and increase the in-stock probability,
one can decrease pipeline inventory and One can maintain the same in-stock probability
with less on-hand inventory.
Answer: B
Explanation: Pipeline inventory depends on the mean demand and lead-time. None of
these two components are affected by inventory pooling.
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Reflective Thinking
Blooms: Analyze
14) A company wants to standardize two of its products to take advantage of product
pooling. Under which demand conditions will the standardization be most effective?
A) If the demand for the two products is somewhat positively correlated.
B) If the demand for the two products is perfectly positively correlated.
C) If the demand for the two products is uncorrelated.
D) If the demand for the two products is negatively correlated.
E) The benefits of pooling do not rely on the underlying correlation.
Answer: D
Explanation: Product standardization is a variant of pooling, which is most effective
when demand correlation between pooled products is low (negative).
Difficulty: 3 Hard
Topic: Product Pooling
AACSB: Reflective Thinking
Blooms: Analyze
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15) Which of the following is a reason to delay the differentiation of a product?
A) There is less uncertainty with respect to demand for individual versions of a product
than there is for total demand.
B) Variety can be added late in the production process without a substantial cost increase.
C) The cost of a generic component is low, relative to the cost of the unique components.
D) Demand among end items is positively correlated.
E) a and b.
F) a and d.
Answer: B
Explanation: The first, second and third options would be reasons NOT to introduce the
delayed differentiation. At the same time, the ability to add variety late in the production
process (when most of the uncertainty has been resolved) and at a low cost, does increase
benefits of the delayed differentiation.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Reflective Thinking
Blooms: Analyze
16) A company is planning to design a new digital camera. One option is to produce two
different models: the "regular" model is suitable for taking pictures in dry conditions, and
the "underwater" model is suitable for taking pictures both on land and underwater. A
second option is the "Swiss army knife" approach: one model that is suitable for both
above and below water conditions. Which of the following is most likely to be true?
A) Due to its higher functionality, the option-two camera is likely to be lighter than both
the option-one cameras.
B) Assuming total demand is the same with either option, for a given amount of
inventory investment (in units), the in-stock probability with option two is likely to be
higher.
C) Manufacturing labor content per camera with option two is likely to be lower than
with option one.
D) Due to its integrated features, option two is likely to appeal to more consumers; hence,
total demand with option two is likely to be higher than with option one.
Answer: B
Explanation: Due to its higher functionality, the camera is likely to be heavier than either
of the option one cameras. Due to its higher complexity, the option two's labor content is
likely to be higher than with either option one camera. Total demand with two welldesigned cameras should be higher than with one well-designed camera. So that leaves b
as the only choice due to risk pooling. For the same inventory investment, option two
should have a higher in-stock probability than with option one.
Difficulty: 3 Hard
Topic: Product Pooling
AACSB: Reflective Thinking
Blooms: Analyze
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17) A manufacturing company is considering two options for adopting manufacturing
flexibility. Option 1 allows Factory 1 to produce both Products 1 and 2 while Factory 2
can only produce Product 2. Option 2 allows Factory 2 to produce both Products 1 and 2
while Factory 1 can only produce Product 1.
Option 1 is preferable over Option 2 when
A) demand for Products 1 and 2 is positively correlated.
B) demand for Products 1 and 2 is independent.
C) demand for Products 1 and 2 is negatively correlated.
D) there is more uncertainty in demand for Product 1 than for Product 2.
E) there is equal uncertainty in demand for Products 1 and 2.
F) there is more uncertainty in demand for Product 2 than for Product 1.
Answer: F
Explanation: Positive or negative correlation does not necessarily make Option 1
preferable because both options offer equal amounts of flexibility. However, if demand
for Product 2 is more uncertain than demand for Product 1, Option 1 allows the company
to mitigate the harmful effect of uncertainty by shifting production of Product 2 to
Factory 1 if Factory 2 runs out of capacity.
Difficulty: 3 Hard
Topic: Capacity Pooling with Flexible Manufacturing
AACSB: Analytical Thinking
Blooms: Analyze
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18) Establishing a regional warehouse for a retailer network can (choose one)
A) reduce the total inventory required due to risk pooling.
B) be costly because of an additional facility and additional handling costs.
C) be less beneficial if the demands of stores are positively correlated.
D) be more beneficial if the distance between the supplier and the market is long.
E) be less beneficial if the number of stores is small.
F) all of the above.
G) none of the above.
Answer: F
Explanation: Establishing a regional warehouse can have each of the effects specified in
answer choices A-E.
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Reflective Thinking
Blooms: Analyze
19) Amazon started with one warehouse but now has seven warehouses. Amazon's
decision to increase the number of warehouses it operates resulted in
A) higher overhead costs and lower technology costs.
B) higher technology costs and lower inventory costs.
C) higher service level and lower inventory costs.
D) higher inventory costs and lower shipping costs.
E) higher labor costs and lower overhead costs.
F) none of the above.
Answer: F
Explanation: Since increasing the number of warehouses results in dis-economies in
inventory costs (one warehouse benefits from risk pooling) but at the same time brings
inventory closer to customers, thus reducing shipping costs.
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Reflective Thinking
Blooms: Analyze
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20) Capacity pooling in the form of flexible capacity is most valuable when
A) capacity is significantly greater than the expected demand.
B) capacity is significantly smaller than the expected demand.
C) capacity is approximately equal to expected demand.
D) the capacity size relative to demand does not matter.
Answer: C
Explanation: According to Figure 17.16, flexible capacity is most valuable when
capacity is approximately equal to expected demand. If capacity is much greater than
expected demand, then flexibility is not needed because there will always be sufficient
capacity. If capacity is much less than expected demand, then flexibility does not provide
much value because capacity will always be utilized.
Difficulty: 3 Hard
Topic: Capacity Pooling with Flexible Manufacturing
AACSB: Reflective Thinking
Blooms: Analyze
21) A firm currently operates a distribution center (DC) with weekly replenishments.
They are considering switching to daily replenishment. To evaluate this decision, demand
data was collected for one product. They found the following:
Demand over five days
Demand over one day
Mean
100
20
Standard deviation
40
11
Demand for this product over time (i.e., across periods) is
A) positively correlated.
B) independent.
C) negatively correlated.
D) This data is not sufficient to determine the correlation.
Answer: A
Explanation: If demand were independent across periods, the standard deviation over
five days would have been 11* = 24.6. Because the actual standard deviation is higher,
there must be a positive correlation.
Difficulty: 3 Hard
Topic: Product Pooling
AACSB: Reflective Thinking
Blooms: Analyze
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22) Consider two books sold by Amazon.com, A and B. Book A is shipped to customers
from the Delaware warehouse, and book B is shipped from the Seattle warehouse.
Inventories for these books are managed using an order-up-to policy with a target instock probability. Currently, the demand correlation between these two books is zero.
Suppose the demand correlation between these two books were to increase, but the means
and standard deviations of demand for the books remain the same. Assume any necessary
adjustments are made to the base stock levels to maintain the same target in-stock
probability. What would happen to each book's average inventory?
A) Both A and B's inventory would increase.
B) Both A and B's inventory would decrease.
C) They would not change.
D) A's inventory would decrease, and B's inventory would increase.
E) A's inventory would increase, and B's inventory would decrease.
F) It is impossible to tell from the information provided.
Answer: C
Explanation: No change. Since A and B are stocked at separate locations, the correlation
between the two books does not affect demand at either location.
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Reflective Thinking
Blooms: Analyze
23) A computer firm sells two versions of a computer, a "slow" and a "fast" version, at
two different prices. Because these are sophisticated pieces of equipment, no matter the
version purchased, a technician is required to install the computer at the customer's
location. The firm decides to manufacture only the fast version of the computer. When a
customer requests the slow version, a fast version is delivered to the customer, and during
the installation process, the technician damages several circuit boards to convert the fast
computer into a slow computer. This strategy is best described as
A) consolidated distribution.
B) location pooling.
C) universal design.
D) delayed differentiation.
E) capacity pooling.
Answer: D
Explanation: This strategy is delayed differentiation because a generic component is held
and only customized late in the process.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Reflective Thinking
Blooms: Analyze
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24) Which of the following is the least important part of the contract manufacturing
industry's value proposition?
A) Contract manufacturers can quickly establish production capacity for a firm.
B) Contract manufacturers take advantage of scale to procure components cheaply.
C) Contract manufacturers provide lower assembly cost because they can pool capacity
among multiple customers.
D) Contract manufacturers provide legal services because they have significant
experience with multiple suppliers and customers.
Answer: D
Explanation: Contract manufacturing's principal advantages are in the first three options.
The provision of legal services, as mentioned in option d is the least important part of the
contract manufacturing industry's value proposition.
Difficulty: 3 Hard
Topic: Capacity Pooling with Flexible Manufacturing
AACSB: Reflective Thinking
Blooms: Analyze
25) Suppose two versions of a product are made with a delayed differentiation strategy,
i.e., a generic version of the product is stocked and then converted into one of the two
final products as demand is realized. This strategy becomes more effective as the
correlation between the two products decreases because
A) the sum of the products' demands increases.
B) the mean demand for each product increases.
C) the standard deviation of the combined demand of the two products decreases.
D) the coefficient of variation of demand for each product decreases.
E) the standard deviation of demand for each product decreases.
Answer: C
Explanation: As the standard deviation of the combined demand decreases for both of
these products, the delayed differentiation strategy is more effective.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Reflective Thinking
Blooms: Analyze
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26) The following are the observed sales of free-range chicken eggs by the Wholesome
Foods grocery chain in the regions of Lilliput and Blefuscu (all numbers in dozens).
Week 1
Week 2
Week 3
Lilliput
120
140
180
Blefuscu
130
130
120
Based on the above numbers only, which of the following options is definitely true?
A) Demands in these two regions are definitely negatively correlated.
B) Demands in these two regions are definitely positively correlated.
C) Total demand in Blefuscu over the three weeks was at least 380 dozen.
D) Demands in these two regions are definitely independent of each other.
E) The store in Blefuscu carried not more than 130 dozen eggs each week on their
shelves.
F) The order quantity in the Lilliput region grocery store was at most 180 dozen in any
given week.
Answer: C
Explanation: Total demand is greater than sales since demand equals sales + lost sales.
So, the third option is supported by the data. The other choices are either untrue or
unsupported.
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Reflective Thinking
Blooms: Analyze
27) In the HP case, what is the best reason, not to implement DC localization in the Asian
market? (Choose the best answer.)
A) Total demand in Asia was not sufficiently large enough to justify the fixed expenses
associated with implementing DC localization.
B) The Asian market did not have the problem of variety.
C) Demand across products in the Asian market was positively correlated.
D) The necessary components were procured in North America, which meant long lead
times for replenishing those components in Asia.
E) Air shipments to Asia were more expensive than air shipments to Europe.
F) The cost of labor in Asia is lower than the cost of labor in Europe.
Answer: A
Explanation: The absolute savings must justify the fixed expenses, and Asia was too
small of a market for them at the time. The other choices are not supported in the case
data or not relevant to the analysis.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Reflective Thinking
Blooms: Analyze
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28) Which of the following is the best reason why Amazon opened more than one
warehouse?
A) Opening multiple warehouses allowed them to reduce their inventory investment.
B) Opening multiple warehouses reduced shipping costs.
C) Opening multiple warehouses allowed them to collect broader consumer data.
D) Opening multiple warehouses reduced the number of customers that would have to
pay sales tax.
E) Opening multiple warehouses simplified their logistics management software.
F) Opening multiple warehouses allows Amazon to forward buy.
Answer: B
Explanation: Multiple warehouses allowed them to position stock closer to customers,
which reduces shipping costs.
Difficulty: 3 Hard
Topic: Location Pooling
AACSB: Reflective Thinking
Blooms: Analyze
29) In the Hewlett-Packard case, if each of the following pieces of new information were
true, then which one would make postponement a less attractive option for the European
market?
A) Demand for printers in Europe will continue to grow.
B) Manufacturing one generic printer will become less expensive at the Vancouver
factory.
C) Accurate demand forecasting for different countries in Europe will become harder.
D) Demand correlation among the different countries will increase in the future.
E) Labor expenses for local (European) product assembly will become insignificant.
F) The power supply units will become cheaper with time.
G) Shipping one generic printer to Europe will be cheaper than shipping several versions.
Answer: D
Explanation: Risk pooling is less useful if demand for products is positively correlated.
Hence, if demand correlation were to increase, a postponement would become less
useful.
Difficulty: 3 Hard
Topic: Product Pooling
AACSB: Reflective Thinking
Blooms: Analyze
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30) Suppose a firm is currently selling three similar products with identical demand
distributions but different demand correlations among them. The firm is considering
designing a universal product that would replace all three of them. The firm will achieve
savings in inventory
A) only if at least two of the products have negatively correlated demand.
B) only if demands for all three products are positively correlated.
C) only if all demand correlations are different from zero.
D) only if all demand correlations are different from -1.
E) only if all demand correlations are different from 1.
F) none of the above applies.
Answer: E
Explanation: If demand for all three products is perfectly positively correlated, then there
are no benefits to risk pooling.
Difficulty: 3 Hard
Topic: Product Pooling
AACSB: Reflective Thinking
Blooms: Analyze
31) Suppose a firm has several factories that it can use to satisfy the demand for several
products. Furthermore, each factory is operating at close to 100% utilization. Which
action is likely to be most effective to increase sales?
A) Increase the mean demand.
B) Decrease the mean demand.
C) Reconfigure the factories so that they can produce a broader set of products.
D) Focus the factories so that they each produce one product.
E) Reduce the number of products sold.
F) Increase capacity.
G) Decrease capacity.
Answer: F
Explanation: When capacity is much smaller than demand (so that utilization is close to
100%), the most effective way to increase sales is through increasing capacity.
Difficulty: 3 Hard
Topic: Lead Time Pooling: Consolidated Distribution and Delayed Differentiation
AACSB: Reflective Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 18 Revenue Management with Capacity Controls
[The following information applies to questions 1-3.]
Inn at Penn has 200 rooms. For regular-fare customers, rooms are priced at $300 per
night, while the rooms are priced at $700 per night for the high-paying customers who
generally arrive at the last minute. The demand for such high-fare customers is
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distributed normally with mean 60 and standard deviation 50. Assume that there is ample
demand for regular-fare customers.
1) What should the protection level for the high fare be to maximize expected profit?
Answer: 69
Explanation:
Cu/(Cu + Co) = (700 - 300)/700 = 0.5714,
z = 0.18,
Q = 60 + 50 * 0.18 = 69
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
2) Suppose that Inn at Penn operates with the protection level of 80 rooms for high-fare
customers. On average, how many high-fare customers are turned away because of a lack
of rooms?
Answer: 11.5
Explanation: z = (80 - 60)/50 = .4.
Expected Lost Sales = 50 * L(z) = 50 * 0.23 = 11.5
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
3) Suppose again that the Inn at Penn operates with the protection level of 80 rooms for
high-fare customers. What is the probability that there are at least 5 rooms left
unoccupied?
Answer: 62%
Explanation: For 5 rooms to be left, demand for high-fare rooms should be less than 75.
z = (75 - 60)/50 = 0.3
Φ(z) = 62%
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
[The following information applies to questions 4-6.]
JetRed Airways flies several daily flights from Philadelphia to Chicago. Based on
historical data, the flight on Wednesday evening before Thanksgiving is always sold-out.
However, there are usually no-shows, so the airline decides to improve revenue by
overbooking. The no-shows are Poisson-distributed with mean 8, and the airline
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estimates that the cost of bumping a passenger is about 10 times more than the ticket
price.
4) How many seats should JetRed overbook?
Answer: 4
Explanation:
Co = 10Cu
Cu/(Cu + Co) = 1/11 = 0.091
Q=4
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
5) JetRed management is dreading bad publicity around Thanksgiving, so it decides
instead that it does not want to bump passengers more than 5% of the time. What is the
maximum number of seats that JetRed can overbook?
Answer: 3
Explanation: When Q = 4, the company faces a probability of 4% that there are 3 or
fewer no-shows.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
6) Suppose six seats are overbooked. How many seats can JetRed expect to have empty,
on average?
Answer: 2.35
Explanation: Empty seats are expected lost sales.
Q = 6.
Expected Lost Sales = 2.35.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 7-8.]
Jtrix Inc. offers high-end, specialized testing services to contract manufacturers (CM) of
semiconductor equipment. Its weekly testing capacity is 125 hours, and it is sold in 1hour blocks for $140/hour. The internal operating cost of its testing equipment is
$100/hour. Because of demand uncertainty induced by the recession, in the recent past,
CMs have often canceled their orders for testing at the last moment. Jtrix estimates that
the number of canceled hours can be approximated by a Poisson distribution with a mean
of 14 hours (see the table below). Jtrix does charge a cancelation penalty of $40 per
canceled hour (that is, if a CM books an hour but then cancels, they still pay Jtrix $40). If
Jtrix ends up with unused capacity due to cancellations, it is unable to sell that capacity to
another customer, but it also doesn't incur the operating cost of $100/hour (that is, the
$100 is incurred only when operating). If its available capacity is insufficient to meet the
booked demand, Jtrix has the option to cannibalize testing time from its sister facility.
However, doing so is expensive for Jtrix, and increases its operating cost to $150/hour.
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7) Suppose Jtrix decides to overbook by 10 hours each week, i.e., it sells exactly 135
hours of testing capacity each week. On average, how many hours of unused testing
capacity will it have in a given week?
Answer: 4.23
Explanation: The unused testing capacity is equivalent to the loss occurring due to too
many cancellations. We find the loss for 10 hours of overbooking as 4.23 from the table.
Difficulty: 2 Medium
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Understand
8) Suppose Jtrix decides to overbook its capacity. How many hours should Jtrix sell to
CMs?
Answer: 142
Explanation: The cost of underage is equal to the margin which is $40. The cost of
average is the loss incurred due to cannibalizing the sister facility, which is $150 - $140 =
$10. CR = $40/($40 + $10) = 0.8. The overbooking level of 17 is the lowest overbooking
level satisfying the critical ratio. Hence, it is the optimal overbooking level. As a result,
the optimal number of hours to sell is 17 + 125 = 142.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
9) Gamma Airlines operates a flight from Denver to Boston. Two fares are offered a low
fare of $175 and a high fare of $550. Low-fare demand books before high-fare demand,
and there is ample demand at the low fare. Demand for the high fare is estimated to be
normal with a mean of 35 and a standard deviation of 20. If the flight has 90 coach seats,
what is the optimal protection level for the high fare?
Answer: 44.6
Explanation: The cost of underage is equal to the lost opportunity of the additional
revenue from high fare customers, which is $550 - $175 = $375. The cost of overage is
the lost opportunity from not being able to sell to a low-fare customer due to protecting
too many seats, which is equal to $175.
Hence, CR = ($375)/($550) = 0.6818. The corresponding z value is 0.48 We find the
protection level PL = μ + zσ = 35 + 0.48 * 20 = 44.6.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 10-13.]
Hotel manager Basil Fawlty and his resourceful assistant, Manuel, run a 26-room hotel in
a quaint little town called Tourkey on the eastern sea coast. A combination of Mr.
Fawlty's friendly attitude and the absence of a respectable inn in the nearby vicinity imply
that Mr. Fawlty enjoys sufficient demand at his low fare of $159 per night. Manuel notes
that some customers will walk into the inn requesting a room for that evening and they
are willing to pay a high fare of $325 per night. Manuel knows this demand is variable.
(In reality, this demand is Poisson distributed with mean 7.5.) He suggests some rooms
should be kept unsold to the low-fare customers so that they can serve the high-fare
customers.
10) To maximize profits with Manuel's plan, what is the booking limit that should be set
for low fare customers?
Answer: 19 rooms
Explanation: Co = 159, Cu = 325 - 159. Critical ratio is 0.5108. Based on the critical
ratio, the protection level for the Poisson distribution with mean 7.5 is 7. The booking
limit is 26 - 7 = 19 rooms.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
11) On average, how many empty rooms will the hotel have under Manuel's plan, if the
protection level is 9 rooms?
Answer: 2
Explanation: Recall that left-over inventory means empty rooms. For Poisson demand
distribution with a mean of 7.5, the expected empty rooms with a protection level of 9 is
L(9) = 0.52292 and left-over inventory is 9 - 7.5 + 0.52292 = 2.023.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
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12) Basil scoffs at the idea. He says, "Empty rooms! A bird in the hand is better than two
in the bush. This brilliant idea of yours, Manuel, might work in Barcelona but definitely
not at Tourkey. Let me run the hotel my way. We will sell to everyone who reserves in
advance and ignore the walk-in demand."
If Basil has his way, what will be the hotel's expected revenue?
Answer: $4,134
Explanation: Revenue from Basil's plan is 26 * $159 = $4,134.
Difficulty: 3 Hard
Topic: Revenue Management and Margin Arithmetic
AACSB: Knowledge Application
Blooms: Apply
13) Manuel replies, "If you are going to forgo the opportunity to sell to last-minute
customers, let's at least accept more than 26 reservations for the evening." Checking the
data, Manuel observes that the number of "no-shows" is Poisson distributed with mean
2.75. (Recall, a "no-show" is when a customer makes a reservation but doesn't show up to
use the room that evening.) Manuel also notes that a $100 non-refundable deposit is
required with all reservations. However, if the hotel does not have a room for a
reservation holder, then they need to book that person in a B&B in the nearest town. They
decide that in those cases they would refund the customer's deposit and pay for the
customer's stay in the B&B, which is $450. The customer would not be happy, but they
are getting a free night, so Manuel figures that there would be no loss of goodwill.
Finally, if they have an empty room due to a no-show, they also figure that they would
not be able to fill the room with a last-minute customer. What is the critical ratio they
should use to choose an overbooking quantity to maximize revenue?
Answer: 0.26
Explanation: Cu is $159 because an empty room could have been filled by another
reservation that is worth $159. Co is $450 because over overbooking means a loss of
$450 relative to never accepting the reservation. Critical ratio is 159/(159 + 450) = 0.26.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 14-16.]
Le Meridien in San Francisco has 160 rooms. The hotel has an ample low-fare demand at
the room rate of $200 per night, but the demand from the high-fare class which pays $450
per night on average, is uncertain. The high-fare demand is normally distributed with
mean 60 and standard deviation 42.
14) How many rooms should Le Meridien protect for high-fare customers to maximize
expected revenue? (Leave your answer in decimal form, i.e., no need to round to an
integer value.)
Answer: 65.88
Explanation:
Cost of underage is $450 - $200 = $250
Cost of overage is $200
Critical ratio is Cu/(Cu + Co) = 250/450 = 0.556
We find the z-statistic in the Standard Normal Distribution Function Table such that F(z)
= critical ratio. The ratio 0.556 falls between F(0.13) and F(0.14); we choose the entry
with the higher z, i.e., z = 0.14.
Finally, we convert the chosen z into Q.
Q = µ + z * σ = 60 + 0.14 * 42 = 65.88
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
15) Suppose Le Meridien sets a booking limit of 100 for low-fare customers. How many
high-fare customers does the hotel expect to turn away due to a lack of rooms?
Answer: 16.75
Explanation: Setting the booking limit at 100 rooms implies a protection level of 60
rooms for the high-fare customers. The expected number of high-fare customers that
would be turned away is the expected loss sales of 60 = L(z) * σ = L((60 - 60)/42) * 42 =
0.3989 * 42 = 16.75.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
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16) When high-fare demand is less than their protection level, the Le Meridien assumes
rooms go empty because it is too late to sell the rooms to low-fare arrivals. However,
now they have an opportunity to sell those rooms at the last-minute to a third-party seller
of opaque goods (such as hotwire.com and price-line). The third-party seller buys the
room inventory on the day at $80 and assumes all the risk of selling those rooms on its
website. What critical ratio should the hotel use for setting the protection level for its
high-fare customer class (who continue to pay $450 per night, and whose demand is still
normally distributed with mean 60 and standard deviation 42) knowing that it now has
this opportunity to sell off remaining inventory at the last minute for $80? (Early demand
at the low fare of $200 remains ample, and Le Meridien still makes this decision to
maximize expected revenue.)
Answer: 0.676
Explanation:
Cost of underage is $450 - $200 = $250
Cost of overage is $200 - $80 = $120
Critical ratio is Cu/(Cu + Co) = 250/(250 + 120) = 250/370 = 0.676
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
[The following information applies to questions 17-21.]
San Francisco Express Airlines, SaFE for short, flies from PHL to SFO. On a Thursday
evening flight, the number of last-minute no-shows and cancellations is Poisson
distributed with mean 7.5. SaFE has an unlimited number of low fare travelers who pay
$300. The cost of bumping such a passenger is estimated to be $350 (due lost goodwill as
well as the cost of routing their itinerary through other airlines). SaFE offers this low fare
because it also comes with a cancellation/rebooking fee of $150 — if a customer doesn't
show up for the flight or cancels her reservation, she must pay $150 to use the ticket on
another flight.
17) To maximize revenue from this flight, how many seats should the airline overbook?
Answer: 7 seats
Explanation: Cost of underage is $300
Cost of overage is $350
Critical ratio is Cu/(Cu + Co) = 300/650 = 0.4615.
We find the Y in the Poisson Distribution Function Table (with mean equal to 7.5) such
that F(Y) = critical ratio. The ratio 0.4615 falls between F(6) and F(7). We choose the
entry with the higher Y, i.e., Y = 7. Therefore, the airline should consider overbooking 7
seats.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
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Blooms: Apply
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18) Customers are more reliable on the Friday evening flight. On that flight, the average
number of no-shows and cancellations is Poisson with mean 4.5. Suppose SaFE
overbooks that flight by 6 seats. What is the probability that at least 1 passenger will be
bumped from this flight? (Round answer to the nearest tenth percent)
Answer: 70.3%
Explanation: The probability that at least 1 passenger will be bumped from this flight is
equal to the probability that there are 5 or fewer no-shows. From the Poisson Distribution
Function Table (with mean equal to 4.5) we find that F(5) = 0.70293 = 70.3%.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
19) The flight from Philadelphia to Chicago has 250 seats. The airline offers a high and
low fare. There is ample demand for the low fare. Low fare customers buy in advance of
high fare customers. Demand for the high fare is normally distributed with a mean of 100
and a standard deviation of 40. The high fare is $700, and the low fare is $450.
What is the optimal protection level for the high fare?
Answer: 85.6
Explanation:
Cost of underage Cu is 700 - 450 = 250
Cost of overage Co is 450
Critical ratio is 250/(250 + 450) = 0.3571.
Look up the z-statistic in the Standard Normal Distribution Function Table that
corresponds to the critical ratio: Φ(-0.36) = 0.3594, so choose z = -0.36.
Q = 100 - 0.36 * 40 = 85.6.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
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20) What is the total expected revenue (including both low and high-fare passengers)
when the protection level is 110 seats?
Answer: $124,950
Explanation: Given that Q is 110, calculate z = (110 - 100)/40 = 0.25.
Expected sales of high-fare seats = μ - σ * L(z). Look up L(z) in the Standard Normal
Loss Function Table and find 0.2863.
Expected sales are 100 - 40 * 0.2863 = 88.5.
Expected revenue is $700 * 88.5 + $450 * (250 - 110) = 124,950.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
21) The number of no-shows on this flight has a Poisson distribution with a mean of 9.5.
The airline estimates the cost of bumping a passenger on this flight is $1500. What is the
optimal maximum number of reservations to accept on this flight?
Answer: 257
Explanation: Cost of underage Cu is 450.
Cost of overage Co is 1,500.
The critical ratio is 450/(450 + 1,500) = 0.2308.
Look up the protection level in the Poisson Distribution Table in the column
corresponding to the mean of 9.5. Find that when Y =7, the value in the table is 0.26866.
The maximum number of reservations to accept is 250 + 7 = 257.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
22) A hotel has 125 rooms that are sold at a high and low fare. The high-fare protection
limit is 30, and it is optimal for a hotel to overbook by 8. What is the low-fare booking
limit?
Answer: 103
Explanation: If 8 rooms are overbooked, a total of 133 rooms are offered for sale.
Furthermore, is 30 of these rooms are protected for the high-fare customers, the booking
limit for the low-fare customers is 133 - 30 = 103.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 23-26.]
A newly created NorthEast Airways (NE) flight from Philadelphia to Boston has 300
seats. The high fare on the flight is $800, and the restricted/low fare is $300. There is
ample demand for the low-fare class, but high-fare demand is random. Further, the
customers who buy low fares buy their tickets well in advance before high-fare
customers. Assume the demand for the high fare is normally distributed with mean 120
and standard deviation of 50.
23) Mr. Wright is in charge of the flight booking operations and decides to set a
protection level for the high fare. What is the optimal protection level for the high fare?
Answer: 136 Seats
Explanation:
Cost of underage Cu is 800 - 300 = 500.
Cost of overage Co is 300.
The critical ratio is 500/(300 + 500) = 0.625.
Look up the z-statistic in the Standard Normal Distribution Function Table that
corresponds to the critical ratio: z = 0.32.
Q = 120 + 0.32 * 50 = 136 seats
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
24) Suppose a protection level of 150 is chosen. What is the expected revenue from high
fare passengers?
Answer: $89,252
Explanation: Q = 150, Solving for z is (Q - μ )/σ = (150 - 120))/50 = 30/50 = 0.6
Then, from the Normal Loss Function table, L(0.6) = 0.1687.
Expected sales = Expected high fare demand - Expected lost sales
120 - σ * L(z) = 120 - 50 * 0.1687 = 111.6
Expected revenue = Expected sales * $800
111.6 * $800 = $89,252
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
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25) NE Airways has noticed no-shows on the flight. Therefore, it has decided to
implement a policy of overbooking. The amount of no-shows is distributed Poisson with
a mean of 5.25. However, overbooking may require bumping passengers off the flight,
which has a net cost estimated at $1000 per bumped passenger. What is the optimal
maximum number of reservations to accept on the flight?
Answer: 303
Explanation:
Cost of underage Cu is 300.
Cost of overage Co is 1000.
The critical ratio is 300/(300 + 1000) = 0.2308.
Look up the protection level in the Poisson Distribution Table in the column
corresponding to the mean of 5.25. Find that when Y = 3, the value in the table is 0.2317.
The maximum number of reservations to accept is 300 + 3 = 303.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
26) If NE Airways overbooked flights by 20 seats and the protection level were set to 150
seats, what would be the booking limit for the low fare tickets?
Answer: 170 seats
Explanation: If 20 seats are overbooked, a total of 320 seats are offered for sale.
Furthermore, 150 seats are protected for high-fare customers, so then the booking limit
for the low-fare customers is 320 - 150 = 170 seats.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
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[The following information applies to questions 27-29.]
JetAirways flight from Philadelphia to Boston has 350 seats. The high-fare on the flight
is $780, and the restricted/low fare is $500. There is ample demand for the low-fare class,
but high-fare demand is uncertain. Demand for the high fare is normally distributed with
mean 150 and standard deviation of 45. Further, the customers buy low fare tickets well
in advance of high fare customers.
27) What is the optimal protection level for the high fare tickets?
Answer: 133.8
Explanation: Cu/(Cu + Co) = (rh - rl )/rh = (780 - 500)/780 = 0.3589 and z = -0.36 (from
the Normal distribution table). Q = 150 - 0.36 * 45 = 133.8.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
28) What is the expected revenue from high-fare passengers when a booking limit of 200
is selected for the low-fare tickets? (Note: Input your answer in thousands).
Answer: $102,960
Explanation: Protection Level is 350 - Booking Limit = 150.
z = (150 - 150)/45 = 0 so that L(z) = 0.3989 (from the Standard Normal Loss Function
Table).
The Expected Lost Sales = L(z) = 45 * 0.3989 = 1 7.9505, and hence,
Expected Sales = 150 - 17.95 = 132.
Expected Revenue = 780 * 132 = 102,960.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Knowledge Application
Blooms: Apply
29) The JetAirways Customers' Bill of Rights states that "Customers who are
involuntarily denied boarding shall receive $1,200 in addition to a ticket refund." The
RM department notices that the number of no-shows is Poisson distributed with a mean
of 7.5. What is the maximum number of reservations in excess of plane capacity that the
airline should accept?
Answer: 6
Explanation: Cu/(Cu+Co) = 500/(1200 + 500) = 0.2941. From the Poisson Distribution
Function Table with mean 7.5, Y = 6.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Knowledge Application
Blooms: Apply
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30) DreamOn Airlines is a startup that emphasizes low prices. They charge a single price
for a seat on a flight, and then customers must purchase "DO bucks" for "amenities." For
example, your first carry-on bag is 5 DO bucks, while your first check-in bag is 50 DO
bucks. Remarkably, even use of the in-flight restroom requires 2 DO bucks. Consistent
with this theme, DreamOn does not offer refunds on tickets. For example, if you miss
your flight, then you need to purchase another ticket on another flight. Given that
DreamOn does not offer refunds, should they overbook their flights? Choose the best
answer.
A) No. Since they don't offer refunds, all customers who purchase tickets will show up
for their flight.
B) No. Since they charge extra for amenities, there is no need to overbook.
C) No. Since their demand will be too low to justify overbooking.
D) No. Since they have a single price for their seats, there is no need to do revenue
management.
E) Yes. Since they have a single price for their seats, they need to maximize revenue.
F) Yes. Even without a refund, there could be some empty seats that could be filled with
overbooking.
G) Yes. Since overbooking is necessary when a firm implements booking limits.
Answer: F
Explanation: The first two options are irrelevant. It is not clear if the demand is low;
nevertheless, they can still overbook, so the third option is false. Overbooking is done
regardless if there is a single class or multiple classes, so the fourth option is false. They
need to maximize revenue even if there were multiple prices, so the fifth option is false.
Overbooking is useful as long as there are no shows, regardless of the booking limits, so
the seventh option is false.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Analytical Thinking
Blooms: Analyze
31) The night before a flight departs, Southeast Airlines reports on their website that
there are no seats available. The next day, however, the flight departs with some empty
seats. Which of the following can be deduced from this observation regarding this flight?
A) The airline must not have charged multiple fares for the flight.
B) The airline must not have overbooked the flight.
C) The airline must have had a very low protection level for its highest fare on this flight.
D) The airline must not have reached the booking limit for its lowest fare on this flight.
E) None of the above.
Answer: E
Explanation: This situation happens when the number of overbooked seats is smaller
than that of no-shows. Multiple fares, protection levels, or booking limit have nothing to
do with the described situation, thus, the first, third and fourth options are wrong. The
second option is wrong because the airline might have overbooked, but have not
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overbooked enough seats.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Analytical Thinking
Blooms: Analyze
32) Suppose that the Inn at Penn uses the news vendor model to set the protection level
optimally. Which of the following changes in the environment would be the best
argument for lowering protection levels?
A) Low fare demand is normally distributed with mean 1000 and standard deviation 50
(rather than unlimited).
B) The high-fare price for the room has gone down to $600 from $700 (but the
distribution of demand remains unchanged).
C) The hotel capacity has gone up from 200 to 300 rooms.
D) All low-fare demand customers stay for one day, while most high-fare customers stay
for two nights.
E) None of the above.
Answer: B
Explanation: High fare decrease would lead to decreasing the protection level. The first
option is incorrect because, for all practical purposes, low-fare demand is still infinite
(relative to capacity). The third option is incorrect because protection levels do not
depend on hotel capacity. The fourth option is incorrect because it implies that the value
of high-fare customers is even higher than $800, so the protection level should be higher.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Analytical Thinking
Blooms: Analyze
33) Suppose that high-fare customers at a Sheraton hotel generally make reservations
very close to the day of their arrival. Which of the following statements indicates the
need for setting the protection level for high-fare demand in a hotel with 100 rooms?
Choose the best answer.
A) The hotel usually conducts last-minute sales of deeply discounted rooms.
B) The low-fare demand is highly uncertain but very small on average.
C) The high-fare demand is Poisson-distributed with mean 20.
D) The low-fare demand can be very large while high-fare demand is limited.
E) The rooms protected for low-fare demand are smaller and have fewer amenities.
F) There are many no-shows so that the hotel overbooks 10 rooms or more.
Answer: D
Explanation: When low-fare demand is infinite, there is a need to protect high-fare
rooms. The first option is incorrect because offering rooms at a discount is the opposite of
protecting them for high-fare travelers. The second option is incorrect because, even
though demand for low-fare rooms can be uncertain, the real need to protect rooms only
arises if low-fare travelers would otherwise take these rooms, but demand from them is
small. The third option indicates that demand for high-fare rooms is low, but by itself, it
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does not indicate the need to establish protection levels since we know nothing about
low-fare demand. The fifth and sixth options are irrelevant to this situation.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Analytical Thinking
Blooms: Analyze
34) JetAirways flies non-stop from Philadelphia to Atlanta. The airline established the
following nested booking limits for its three fare classes:
Which of the following statements is certainly true?
A) The flight has 100 seats in total.
B) The demand distribution for the lowest fare class Q is Poisson.
C) The protection level for the high fare class Y is smaller than for the medium fare class
M.
D) The airline does not overbook.
E) None of the above.
Answer: C
Explanation: Let C be the capacity of the plane. The protection level for the high fare Y
is C-30. If up to 30 seats are available to book the low and medium fares, then the
remaining fares are protected for the high-fare class. The protection level for the medium
fare class M is C - 20. If up to 20 seats are available to book the low fare, then the
remaining fares are available to book the higher fare classes. Thus, the high-fare
protection level is lower (C - 30 < C - 20).
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits; Implementation of Revenue Management
AACSB: Knowledge Application
Blooms: Apply
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35) JetWest Airlines uses the following bid prices over a three-week period:
Week Bid Prices
Week 1
Week 2
Week 3
PHL to STL
250
180
300
STL to LAX
150
180
250
If this bid-price control is implemented, which of the following is definitely true?
A) The highest ticket price sold in Week 3 on the itinerary is $550.
B) Fare class $200 for PHL to STL is closed in the first two weeks.
C) Fare class $375 for PHL-LAX is open during week 1 and 2.
D) Fare class $275 for PHL-LAX is closed during week 1.
E) Fare class $180 for STL-LAX is open during all the weeks.
Answer: D
Explanation: During week 1, to fly from PHL to LAX the ticket price should be higher
than the sum of two bid prices, $250 + $150 = $400.
Difficulty: 3 Hard
Topic: Implementation of Revenue Management
AACSB: Knowledge Application
Blooms: Apply
36) Overbooking will not increase revenue when
A) all customers turn up (there are no no-shows or cancellations).
B) there are only a few fare classes.
C) there are enough seats available to accommodate demand most of the time.
D) protection levels are set optimally.
E) there is no seasonality effect.
F) the airline charges customers for cancellations.
Answer: A
Explanation: If there aren't any no-shows or cancellations, there is no reason to
overbook.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Analytical Thinking
Blooms: Analyze
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37) The use of revenue management with the explicit objective of maximizing revenue
(as opposed to maximizing profit) is most appropriate when
A) The variability in demand is high relative to the mean.
B) The variable cost of serving a customer is negligible.
C) There are only two customer segments.
D) Net profit as a percentage of revenue is low.
E) Capacity is significantly constrained.
Answer: B
Explanation: If the variable cost of serving a customer is not negligible, then the profit
maximization (rather than revenue maximization) becomes appropriate.
Difficulty: 3 Hard
Topic: Implementation of Revenue Management
AACSB: Analytical Thinking
Blooms: Analyze
38) Which of the following statements are true about nested booking limits?
I. If a particular fare class is open, then all higher fare classes are open as well.
II. If a particular fare class is closed, then all lower fare classes are closed as well.
III. If a particular fare class is open, then all higher fare classes are closed.
IV. If a particular fare class is closed, then all lower fare classes are open.
A) I Only
B) II Only
C) III Only
D) IV Only
E) I and II
F) III and IV
G) None are true.
Answer: E
Explanation: Nested means that if a fare class is open, all higher fare classes will be open
as well, which implies I and II. III and IV make little sense.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Analytical Thinking
Blooms: Analyze
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39) What is the relationship between a booking limit and a protection level in a revenue
management system with two fare classes and no overbooking?
A) There is no relationship between the two.
B) The booking limit is always greater than the protection level.
C) The booking limit is always less than the protection level.
D) The ratio of the booking limit to the protection level equals the critical ratio.
E) The sum of the booking limit and the protection level equals the available capacity.
Answer: E
Explanation: The sum of the booking limit and the protection level equals the available
capacity. This is the definition of booking limits and protection levels.
Difficulty: 3 Hard
Topic: Implementation of Revenue Management
AACSB: Analytical Thinking
Blooms: Analyze
40) Which of the following is an example of revenue management with booking limits?
A) A seller of bandwidth offers a low fare for regular speed service and a high fare for
high-speed service.
B) A hotel cuts its discount fare to ensure that more rooms are filled.
C) A hotel cuts its full fare to ensure that more rooms are filled.
D) A utility sells a portion of its capacity with long term contracts and reserves a portion
of its capacity for the spot market, which yields a higher price on average.
E) A university admits more students than its desired class size to ensure that its actual
class size is not too low.
Answer: D
Explanation: A utility reserves a portion of its capacity thus establishing protection
level/booking limit. The first option is an example of a premium for faster service but
with no capacity controls. The second and third options are examples of adjusting prices
dynamically which has nothing to do with capacity controls. The fifth option is an
example of overbooking, which is a part of revenue management but is different from
capacity controls in the form of booking limit.
Difficulty: 3 Hard
Topic: Implementation of Revenue Management
AACSB: Analytical Thinking
Blooms: Analyze
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41) Virtual nesting is a solution to what challenge with revenue management?
A) Passengers flying a particular segment may have different itineraries with different
values to the airlines.
B) Forecasting demand for each fare class.
C) Establishing effective fences to segment customers.
D) None of the above.
Answer: A
Explanation: This describes the motivation for virtual nesting. With this solution, a
limited number of buckets are created with its own booking limit and set of fare class.
Difficulty: 3 Hard
Topic: Implementation of Revenue Management
AACSB: Reflective Thinking
Blooms: Analyze
42) Consider an airline with the following dynamic bid prices over two weeks for two
different legs.
Week Bid Prices
April 25 (week 1)
May 02 (week 2)
PHL to ORD
200
160
ORD to SFO
150
180
If bid-price control is implemented, which of the following is true?
A) Fare class $175 ORD-SFO is closed in both the weeks.
B) Fare class $360 for PHL-SFO is closed during week 1.
C) Fare class $360 for ORD-SFO is closed during week 2.
D) Fare class $345 for PHL-SFO is closed in week 1 but open in week 2.
Answer: D
Explanation: The first option is false because the fare is available in Week 1. The second
option is false because $360 is open during both weeks. Similarly, $360 for ORD-SFO is
open both weeks, so the third option is false. The fourth option is true since $345 is open
in the second week but not in week 1.
Difficulty: 3 Hard
Topic: Implementation of Revenue Management
AACSB: Knowledge Application
Blooms: Apply
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43) Overbooking is an optimal strategy only when
A) ample capacity is available.
B) protection levels for high fares do not help.
C) seasonality effects are strong.
D) customer no-shows occur.
E) high-fare customers cannot be turned away.
F) high-fare customers reserve before low fare customers.
Answer: D
Explanation: Customer no-shows occur, hence overbooking makes sense. This is
because the Airline/Hotel lose revenue when customers do not show up. By overbooking,
this effect is mitigated.
Difficulty: 3 Hard
Topic: Overbooking
AACSB: Analytical Thinking
Blooms: Analyze
44) Protection levels are not useful when
A) low-fare customers book their tickets before high fare customers.
B) low-fare customers are significantly hard to bump once they hold a reservation.
C) overall demand is much lower than capacity.
D) fare values fluctuate.
E) low fares sell at about 75% of the value of high fares.
Answer: C
Explanation: Protection levels are not useful if demand is less than capacity.
Difficulty: 3 Hard
Topic: Protection Levels and Booking Limits
AACSB: Analytical Thinking
Blooms: Analyze
Matching Supply with Demand: An Introduction to Operations Management, 4e
(Cachon)
Chapter 19 Supply Chain Coordination
1) Dan's Independent Book Store is trying to decide how many copies of a book to
purchase at the start of the upcoming selling season. The book retails at $28.00. The
publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of
the book at 50% off the retail price, at the end of the season. Dan estimates that demand
for this book during the season is normal with a mean of 1000 and a standard deviation of
250.
The publisher is thinking of offering the following scheme to Dan. At the end of the
season, they will buy back unsold copies at a pre-determined price of $17.00. However,
Dan would have to bear the costs of shipping unsold copies back to the publisher at $1.00
per copy. What is the quantity that Dan should order, to maximize his expected profits?
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Answer: 1,110.
Explanation:
The cost of underage is Cu = 28 - 20 = 8.
The cost of overage is Co = 20 - 17 + 1 = 4.
The critical ratio is 8/(8 + 4) = 0.6667.
Look up the z-statistic in the Standard Normal Distribution Function Table that
corresponds to the critical ratio:
Φ(0.44) = 0.6700, so choose z = 0.44.
Q is 1,000 + 0.44 * 250 = 1,110 books.
Difficulty: 3 Hard
Topic: Buy-Back Contracts
AACSB: Knowledge Application
Blooms: Apply
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2) Corleone Inc. sells a set of products (pasta) to a distributor who uses an order-up-to
model to place orders. In particular, if Corleone is unable to fill the distributor's entire
order, the order is back ordered. For example, the distributor may order one truckload of
pasta that includes 20 different kinds of pasta and the truck ships only when the order
quantity in each kind can be satisfied (so that the truck is indeed full when it makes its
delivery). Which of the following influences the average amount of inventory on-order
between Corleone and the distributor?
I) The travel time between Corleone and the distributor
II) Corleone's in-stock probability for each kind of pasta
III) The standard deviation of the distributor's order quantities
A) I only
B) II only
C) III only
D) I and II
E) I and III
F) II and III
G) I, II and III
H) none of the above
Answer: G
Explanation: Little's Law drives On-order inventory: I = R*T, where I is the quantity onorder, R is the rate at which orders are placed (which will equal the demand rate of the
downstream firm), and T is the average time a request spends on-order. If the possibility
of random lead time is ignored, then the answer would be I only. However, if the
upstream firms in-stock is less than 100%, then the lead time between the two levels of
the supply chain will be random, and the expected time, T will increase. Hence,
technically II is true too. If we continue to assume the possibility of random lead time,
then III may also be true.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Analytical Thinking
Blooms: Analyze
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3) Retailers order replenishment inventory from a supplier in full truckload quantities
(i.e., each retailer waits until it has accumulated enough demand to justify ordering a full
truckload). Suppose there is an industry-wide decline in demand (i.e., each retailer
experiences a reduction in its sales). The supplier collects data on the total amount the
retailers order each day. What is likely to happen to the coefficient of variation of the
order quantities due to the shift in aggregate demand? Assume the retailers continue to
order in full truckload quantities.
A) It is unlikely to change because the retailers are continuing to order in full truckload
quantities.
B) It is unlikely to change because the retailers will continue to order as frequently as
they did before.
C) It is likely to decrease because each retailer's average demand decreases.
D) It is likely to increase because each retailer will order less frequently due to the
decline in sales.
E) None of the above is correct.
Answer: D
Explanation: The order quantity remains the same (one truckload) but the frequency of
ordering decreases (because demand drops, and so it takes longer to fill a truck on
average), so order batching will lead to higher variability in orders.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Analytical Thinking
Blooms: Analyze
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4) One warehouse supplies 50 dealers with parts used by the dealers to repair their
customers' heavy equipment. Dealers currently place orders about once a week, because
the ordering process is somewhat cumbersome — it is a paper process that must be filled
out manually and faxed to the warehouse. The firm will implement a new system that will
allow dealers to submit orders electronically. Because this process should be less
cumbersome, it is expected that the dealers will submit orders more frequently, maybe
some of them even daily. The new system is not expected to change customer demands
for parts (i.e., the dealers' demand processes will be unaffected). What change is this
likely to have on the characteristics of the warehouse's total daily demand (i.e., the total
of the dealers' orders on any given day)?
A) Average daily demand should increase as well as the standard deviation.
B) Average daily demand should increase, but the standard deviation should remain the
same.
C) Average daily demand should increase but the standard deviation should decrease.
D) Average daily demand should remain the same, but the standard deviation should
increase.
E) Average daily demand should remain the same as well as the standard deviation.
F) Average daily demand should remain the same, but the standard deviation should
decrease.
Answer: F
Explanation: The average daily demand of the warehouse is the same as the average
daily demand of the end customer. The new system will not change this. However, since
the order is placed more frequently, dealers are more responsive to customer demand, i.e.,
their orders represent more accurately the customer demand. Compared to the old system,
the new system will reduce the variation in the warehouse's demand.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Mitigating Strategies
AACSB: Analytical Thinking
Blooms: Analyze
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5) Suppose a manufacturer sells an outdoor grill to a hardware store. The manufacturer's
current wholesale price of the grill is $185, and the retailer sells the grill for $250. The
manufacturer is considering offering the retailer a buyback contract with which the
retailer can return grills left over at the end of the season to the manufacturer at $138.75
for each grill. The wholesale price at the start of the season will remain at $185. Which of
the following statements is true?
A) The manufacturer's expected profit will decrease because now the manufacturer must
pay to receive returns without any increase in the upfront wholesale price.
B) The manufacturer's expected profit will increase because return policies can increase
the profits of all of the firms in the supply chain.
C) There isn't enough information given to determine whether the manufacturer's
expected profit increases or decreases.
Answer: C
Explanation: The buyback contract certainly improves the profit of a hardware store, but
it may or may not improve the profit of the manufacturer. On the one hand, the hardware
store will order more, but on the other hand, the manufacturer will now share the risk of
unsold inventory. The answer depends on the demand distribution and the manufacturer's
cost of production. Hence, there is not enough information.
Difficulty: 3 Hard
Topic: Buy-Back Contracts
AACSB: Analytical Thinking
Blooms: Analyze
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6) A retailer operates a distribution center (DC) that serves 250 retail stores. The retail
stores sell individual units but shipments from the DC to the stores are done in case
quantities (i.e., each store orders from the DC an integer number of cases). Orders
submitted to suppliers for delivery to the DC are done in pallet quantities. Each pallet
holds multiple cases, with the actual number of cases depending on the size and weight of
the product. Which of the following statements is true?
A) The bullwhip effect is not likely to be present in this supply chain because the retailer
is consistent in the order multiples used (i.e., always ordering in a case or pallet
quantities).
B) The bullwhip effect is not likely to be present in this supply chain because the same
firm operates both the DC and the retail stores and can, therefore, better coordinate
ordering.
C) The bullwhip effect is likely to be present in this supply chain because there is
evidence of order batching effects.
D) The bullwhip effect is likely to be present in this supply chain because there is
evidence of forward buying.
E) It is not possible to determine with the information given whether the bullwhip effect
will be present in this supply chain or not.
Answer: C
Explanation: Because orders are shipped in cases and pallets, the deliveries will not
reflect the actual number of units needed but will be rounded to the nearest case/pallet.
Hence, there is evidence of order batching.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Analytical Thinking
Blooms: Analyze
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7) Which of the following situations is likely to cause forward buying among retailers?
I. The supplier offers a temporary price discount.
II. The supplier announces that she is about to cut her price permanently.
III. The supplier announces that she is about to raise her price permanently.
A) Only I.
B) Only II.
C) Only III.
D) Only I. and II.
E) Only I. and III.
F) Only II. and III.
G) I., II. and III.
Answer: E
Explanation: If the price is cut permanently, there is no reason for retailers to buy
forward. However, both a temporary price discount and a permanent rise in price will
result in forward buying.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Reflective Thinking
Blooms: Analyze
8) Which of the following situations is certain to present incentives to forward buy?
A) The retailer has a limited amount of warehouse capacity.
B) The supplier is about to permanently adjust prices lower.
C) The supplier is about to permanently adjust prices higher.
D) The retailer's holding cost is reduced.
E) The supplier's lead time to the retailer is reduced.
F) The retailer's target in-stock probability is increased.
Answer: C
Explanation: Choice A limits the ability to forward buy due to the capacity constraint.
Choices B and E lead give the firm an incentive to stock to a lower level. Choices D and
F give incentives to increase inventory, but not to forward buy. Choice C is then the best
choice because it does provide an incentive to purchase a large quantity.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Analytical Thinking
Blooms: Analyze
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9) Phantom ordering is best described as
A) orders that are intended to be used for diversion.
B) irresponsible ordering on the part of downstream buyers.
C) orders submitted electronically.
D) current orders that are likely to be canceled at some future date.
Answer: D
Explanation: Phantom orders are orders that the customer expects to cancel and typically
are used to give the customer access to supplier capacity which is insufficient to meet
market demand.
Difficulty: 2 Medium
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Knowledge Application
Blooms: Understand
10) Which of the following is the least important part of the contract manufacturing
industry's value proposition?
A) Contract manufacturers can quickly establish production capacity for a firm.
B) Contract manufacturers take advantage of scale to procure components cheaply.
C) Contract manufacturers provide lower assembly costs because they can pool capacity
among multiple customers.
D) Contract manufacturers provide legal services because they have significant
experience with multiple suppliers and customers.
Answer: D
Explanation: The other three options are part of the value proposition of a contract
manufacturer, but choice d is not.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Mitigating Strategies
AACSB: Analytical Thinking
Blooms: Analyze
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11) Which of the following is/are part of Barilla's JITD proposal?
I. Barilla controls the distributor's assortment.
II. Barilla decides how much of each SKU to ship to a distributor.
III. Barilla receives sales and inventory data from its distributor.
IV. Barilla receives sales and inventory data from retailers.
A) I only
B) II only
C) I and III
D) II and III
E) II and IV
F) I, II and III
G) I, III and IV
H) II, III and IV
J) I, II, III and IV
Answer: D
Explanation: From the case, Barilla interacts directly only with the distributors, and
decides on the distributors' quantities but not their assortment.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Knowledge Application
Blooms: Apply
12) The hockey stick phenomenon could be caused by
A) a large fraction of downstream retailers placing orders on the same day of the week.
B) diversion by local and small-scale retailers.
C) diversion by large and wholesale retailers.
D) delayed differentiation of the product.
E) inefficient location pooling.
F) everyday low pricing.
Answer: A
Explanation: This option refers to order synchronization which will lead to the bullwhip
effect.
Difficulty: 2 Medium
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Knowledge Application
Blooms: Apply
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13) Suppose a supply chain consisting of a wholesaler and a retailer decides to switch
from a wholesale price contract to a revenue-sharing contract and changes the wholesale
price in the process. Which of the following could occur as a result?
A) An increase in retailer's profit but a decrease in the wholesaler's profit.
B) A decrease in the retailer's profit but an increase in the wholesaler's profit.
C) A decrease in both retailer's and wholesaler's profits.
D) An increase in both retailer's and wholesaler's profits.
E) All of the above.
Answer: E
Explanation: Depending on contract parameters, any relationship between profits is
possible.
Difficulty: 3 Hard
Topic: More Supply Chain Contracts
AACSB: Reflective Thinking
Blooms: Analyze
14) Apple iTunes store songs are sold at 99 cents per download. Apple pays 65 cents on
average to the respective music label company for each download (which is then shared
with artists). The terms of this agreement are closest to
A) news vendor problem with salvage costs.
B) quantity flexibility contract.
C) revenue sharing contract.
D) buy-back contracts.
E) price protection.
Answer: C
Explanation: Note that Apple shares the revenues of 99 cents per download with the
music provider. This is a typical example of a revenue-sharing contract.
Difficulty: 3 Hard
Topic: More Supply Chain Contracts
AACSB: Analytical Thinking
Blooms: Analyze
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15) According to the Barilla case, the following is the strongest evidence that Barilla is
suffering from the bullwhip effect?
A) After JITD introduction, inventory levels initially went up.
B) The service level at the DC decreased notably during the Gulf War.
C) Barilla sells both fresh and dry pasta products through different distribution channels.
D) Inbound shipments to the Cortese DC fluctuate more than outbound shipments from
the Cortese DC.
E) Most retailers only carry a subset of Barilla's product line.
F) Pasta consumption per capita in southern Italy is higher than in northern Italy.
Answer: D
Explanation: The key evidence is in Exhibit 19.1, showing that uncertainty in inbound
shipments to the Cortese DC is higher than uncertainty in outbound shipments from the
Cortese DC.
Difficulty: 3 Hard
Topic: The Bullwhip Effect: Causes and Consequences
AACSB: Reflective Thinking
Blooms: Analyze
16) A supplier sells a seasonal product with uncertain demand to a retailer. Consider two
contracts. With the wholesale price contract, the supplier sells to a retailer with a
wholesale price of $45; the supplier does not accept returns and, as a result, the retailer
salvages leftover inventory at the end of the season for $30. With the buy-back contract
the supplier sells to the retailer with a wholesale price of $45, the supplier buys back
unsold inventory from the retailer for $38 at the end of the season, and the supplier's
salvage value of returned inventory is $30. The retailer pays $0.50 per unit to ship the
product back to the supplier. Which of the following is true?
A) The retailer is better off with the buy-back contract, but the supplier is worse off.
B) The retailer is better off with the buy-back contract, and the supplier is better off too.
C) The retailer is worse off with the buy-back contract, and the supplier is worse off also.
D) The retailer is worse off with the buy-back contract, but the supplier is better off.
E) The retailer is better off with the buy-back contract, but the supplier could be better off
or worse off.
F) The retailer could be better off or worse off with the buy-back contract, but the
supplier is better off.
G) None of the above.
Answer: E
Explanation: The retailer gets the same wholesale price but a higher salvage value, so the
retailer is better off. The supplier needs to buy back inventory, which is an added cost,
but the retailer may order a larger quantity, which is a benefit. Hence, we cannot
determine if the supplier is better or worse off.
Difficulty: 3 Hard
Topic: Buy-Back Contracts
AACSB: Reflective Thinking
Blooms: Analyze
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17) Revenue sharing contracts greatly benefitted Blockbuster in the VHS rental market.
Suppose that now Blockbuster is considering similar contracts for DVDs. However,
revenue sharing contracts for DVDs would not be as beneficial for Blockbuster as for
VHS tapes because
A) Netflix dominates the rental market for DVDs.
B) due to the increased number of movies produced, the rentals from any single DVD are
small.
C) using technology and advanced statistics, the studios can predict the demand for
rentals for a particular DVD with greater accuracy.
D) uncertainty in demand for DVDs is much greater than uncertainty in demand for VHS
tapes.
E) the production cost and the wholesale price of each DVD are small relative to those of
a VHS tape so that inefficiency in the supply chain under the wholesale price contract is
minimal.
Answer: E
Explanation: Answers a through d may be true in principle, but they do not necessarily
have anything to do with supply chain inefficiencies, which exist with wholesale price
contracts. Even when demand is highly uncertain, or small, or the other way around, the
supply chain can still be inefficient.
Difficulty: 3 Hard
Topic: More Supply Chain Contracts
AACSB: Analytical Thinking
Blooms: Analyze
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18) Furniture Brands Inc. (FBI) is the sole supplier to a large number of independent and
similarly sized retail furniture outlets. These retailers placed orders weekly, and on each
day of the week, nearly the same number of retailers submitted orders. To improve
supply chain performance, FBI managed to convince 95% of retailers to submit orders on
Monday and the remaining retailers ordered on the other days of the week. Which of the
following statements regarding the mean and standard deviation of the retailers' total
daily orders (i.e., FBI's demand) remains true after the performance improvement effort?
A) The mean and the standard deviation of the orders received have increased.
B) The mean and the standard deviation of the orders have now decreased because nearly
all of the orders are now submitted on Mondays.
C) The mean of the orders is lower, but the standard deviation of the orders has increased.
D) Only the timing of orders has changed; therefore, the mean and the standard deviation
of the orders continue to remain the same.
E) The mean remains the same, but the standard deviation of the orders has increased.
F) The mean remains the same, but the standard deviation of the orders has decreased
because of better supply chain coordination.
Answer: E
Explanation: The retailer's orders become more synchronized, so the standard deviation
increases. The mean remains the same because there is nothing to indicate that their
average order quantity changes.
Difficulty: 3 Hard
Topic: More Supply Chain Contracts
AACSB: Analytical Thinking
Blooms: Analyze
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19) By selecting the parameters of a revenue-sharing contract appropriately, it is possible
to
A. achieve the maximum possible profit in the supply chain by coordinating the actions
of the supplier and the retailer.
B. have the supplier's profit equal to twice the retailer's profit.
C. ensure that the retailer orders the same amount of inventory as he would under any
wholesale price contract.
A) A only
B) B only
C) C only
D) A and B
E) B and C
F) A and C
G) A, B, and C
H) None of the above
Answer: G
Explanation: When structured correctly, the revenue sharing contract allows to
coordinate actions in the supply chain (A), allocate profits in an arbitrary way (B) and
ensure that the retailer orders the same amount of inventory as under any wholesale price
contract (C).
Difficulty: 3 Hard
Topic: More Supply Chain Contracts
AACSB: Analytical Thinking
Blooms: Analyze
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20) Eddie's bookstore currently buys books from the wholesaler using a simple wholesale
price contract. Following the shift in industry practices, the wholesaler starts offering the
bookstore an option to return books at a partial refund (70% of the wholesale price, which
is higher than retailer's current salvage value) while keeping the wholesale price the
same. Suppose shipping costs are negligible. What effect will this new contract have?
I. The bookstore's order quantity will increase.
II. The bookstore's profit will increase.
III. The wholesaler's profit will increase.
A) I only.
B) II only.
C) III only.
D) I and II only.
E) I and III only.
F) II and III only.
G) I, II and III.
H) None of I, II and III.
Answer: D
Explanation: Certainly, the order quantity by the bookstore will increase since the
overage cost has been lowered. Further, the bookstore's profit will increase since it now
gets additional money for returning books. However, it is unclear what happens with the
wholesaler's profit. Although the retailer orders more, now the wholesaler has to accept
the risk of returned books. So, we cannot say that the wholesaler's profit will definitely
increase.
Difficulty: 3 Hard
Topic: Buy-Back Contracts
AACSB: Reflective Thinking
Blooms: Analyze
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