Review for Midterm 2
OPSM 301
Practice Problems
Problem 1:
A major drug store chain wishes to build a new warehouse to serve the whole
Midwest. At the moment, it is looking at three possible locations. The factors,
weights, and ratings being considered are given below:
Ratings
Factor
Weights Peoria Des Moines Chicago
Nearness to markets
20
4
7
5
Labor cost
5
8
8
4
Taxes
15
8
9
7
Nearness to suppliers
10
10
6
10
Which city should they choose?
Practice Problems
Problem 1:
Based upon the weights and rating,
A major drug store chain
wishes
to build
warehouse to serve the whole
Des
Moines
shoulda new
be chosen.
Midwest. At the moment, it is looking at three possible locations. The factors,
weights, and ratings being considered are given below:
Weighted
Ratings
Ratings
Factor
Weights Peoria Des Moines Chicago
80
140
100
Nearness to markets
20
4
7
5
40
40
20
Labor cost
5
8
8
4
120
135
105
Taxes
15
8
9
7
100
60
100
Nearness to suppliers
10
10
6
10
Total
340
375
325
Which city should they choose?
Practice Problems
Problem 2:
Balfour’s is considering building a plant in one of three possible locations.
They have estimated the following parameters for each location:
Location
Waco, Texas
Tijuana, Mexico
Fayetteville, Arkansas
Fixed Cost
$300,000
$800,000
$100,000
Variable Cost
$5.75
$2.75
$8.00
For what unit sales volume should they choose each location?
Practice Problems
Transition
Problem
2: between Waco and Tijuana
300,000 + 5.75x = 800,000 + 2.75x
Balfour’s is considering building a plant in one of three possible locations.
3x = 500,000
They have estimated the following parameters for each location:
x = 166,000
Location
Waco, Texas
Tijuana, Mexico
Fayetteville, Arkansas
Fixed Cost
Variable Cost
$300,000
$5.75
$800,000
$2.75
$100,000
$8.00
Transition between Waco and Fayetteville
For what unit sales volume should they
choose
each location?
300,000
+ 5.75x
= 100,000 + 8.00x
2.25x = 200,000
x = 88,888
Practice Problems
Transition
Problem
2: between Waco and Tijuana
Transition between Waco and Fayetteville
300,000 + 5.75x
= 800,000
+ 2.75x
Locate
in Fayetteville
Balfour’s is considering building a plant 300,000
in one of+ three
locations.
5.75x possible
= 100,000
+ 8.00x
3x = 500,000
They have estimated the following parameters for each
2.25xlocation:
= 200,000
x = 166,000
x = 88,888
Location
Waco, Texas
Tijuana, Mexico
Fayetteville, Arkansas
Fixed Cost
$300,000
$800,000
$100,000
Variable Cost
$5.75
$2.75
$8.00
For what unit sales volume should they choose each location?
Practice Problems
Problem 3:
Our main distribution center in Phoenix, AZ is due to be replaced with a
much larger, more modern facility that can handle the tremendous needs
that have developed with the city’s growth. Fresh produce travels to the
seven store locations several times a day making site selection critical for
efficient distribution. Using the data in the following table, determine the
map coordinates for the proposed new distribution center.
Practice Problems
Problem 3:
Our main distribution center in Phoenix, AZ is due to be Truck
replaced
withTrips
a
Round
much larger,
modern facility
can handle
needs
Storemore
Locations
Mapthat
Coordinates
(x, the
y) tremendous
per Day
that haveMesa
developed with the city’s growth.
(10, 5)Fresh produce travels
3 to the
seven store locations several times a day making site selection critical for
Glendale
(3, 8)
3
efficient distribution. Using the data in the following table, determine the
Camelback
(4, 7)
2
map coordinates for the proposed new distribution center.
Scottsdale
(15, 10)
6
Apache Junction
(13, 3)
5
Sun City
(1, 12)
3
Pima
(5, 5)
10
(10*3) + (3*3) + (4*2) + (15*6) + (13*5) + (1*3) + (5*10)
3 + 3 + 2 + 6 + 5 + 3 + 10
= 32 = 7.97
Cy =
(5*3) + (8*3) + (7*2) + (10*6) + (3*5) + (12*3) + (5*10)
3 + 3 + 2 + 6 + 5 + 3 + 10
= 32 = 6.69
Practice Problems
Problem 3:
255
Cx =
214
Our main distribution center in Phoenix, AZ is due to be Truck
replaced
withTrips
a
Round
much larger,
modern facility
can handle
needs
Storemore
Locations
Mapthat
Coordinates
(x, the
y) tremendous
per Day
that haveMesa
developed with the city’s growth.
(10, 5)Fresh produce travels
3 to the
seven store locations several times a day making site selection critical for
Glendale
(3, 8)
3
efficient distribution. Using the data in the following table, determine the
Camelback
(4, 7)
2
map coordinates for the proposed new distribution center.
Scottsdale
(15, 10)
6
Apache Junction
(13, 3)
5
Sun City
(1, 12)
3
Pima
(5, 5)
10
Problem 4:
Practice Problems
John Galt Shipping wishes to ship a product that is made at two different
factories to three different warehouses. They produce 18 units at Factory A
and 22 units at Factory B. They need 10 units in warehouse #1, 20 units in
warehouse #2, and 10 units in warehouse #3. Per unit transportation costs
are shown in the table below. How many units should be shipped from
each factory to each warehouse?
Plant A
Plant B
Warehouse #1 Warehouse #2 Warehouse #3
$4
$2
$3
$3
$2
$1
Problem 1:
Practice Problems
John Galt Shipping wishes to ship a product that is made at two different
factories to three different warehouses. They produce 18 units at Factory A
and 22 units at Factory B. They need 10 units in warehouse #1, 20 units in
warehouse #2, and 10 units in warehouse #3. Per unit transportation costs
are shown in the table below. How many units should be shipped from
each factory to each warehouse?
Plant A
Plant B
Warehouse #1 Warehouse #2 Warehouse #3
$4
$2
$3
$3
$2
$1
Problem 5:
Practice Problems
Assume that in Problem 1 the demand at each warehouse is increased by
4 units. Now how many units should be shipped from each factory to each
warehouse?
Plant A
Plant B
Warehouse #1 Warehouse #2 Warehouse #3
$4
$2
$3
$3
$2
$1
Problem 2:
Practice Problems
Assume that in Problem 1 the demand at each warehouse is increased by
4 units. Now how many units should be shipped from each factory to each
warehouse?
Plant A
Plant B
Warehouse #1 Warehouse #2 Warehouse #3
$4
$2
$3
$3
$2
$1
Practice Problems
Problem 6:
What are the appropriate ABC
groups of inventory items?
Problem 6:
Practice Problems
ABC Analysis
Stock Number
What are the appropriate ABC
J24
groups of inventory items? R26
L02
M12
P33
T72
S67
Q47
V20
Percent of
Annual $ Volume Annual $ Volume
12,500
46.2
9,000
33.3
3,200
11.8
1,550
5.8
620
2.3
65
0.2
53
0.2
32
0.1
30
0.1
 = 100.0
Problem 1:
Practice Problems
ABC Analysis
Percent of
Stock Number Annual $ Volume Annual $ Volume
What are the appropriate ABC
J24
12,500
46.2
groups of inventory items? R26
9,000
33.3
L02
3,200
11.8
M12
1,550
5.8
ABC Groups
P33
620
2.3
Annual
Percent of
T72
65
0.2
Class
Items
Volume
$ Volume
S67
53
0.2
A
J24, R26
21,500
79.5
Q47
32
0.1
B
L02,
M12
4,750
17.6
V20
30
0.1
C
P33, &72, S67, Q47, V20
800
 =2.9
100.0
 = 100.0
Practice Problems
Problem 7:
Assume you have a product with the following parameters:
Annual Demand = 360 units
Holding cost per year = $1.00 per unit
Order cost = $100 per order
What is the EOQ for this product?
Practice Problems
Problem 7:
Assume you have a product with the following parameters:
Annual Demand = 360 units
Holding cost per year = $1.00 per unit
Order cost = $100 per order
What is the EOQ for this product?
EOQ =
2 * Demand * Order Cost
=
Holding Cost
72000 = 268.33 items
2 * 360 * 100
=
1
Practice Problems
Problem 8:
Given the data from Problem 7, and assuming a 300-day work year, how
many orders should be processed per year? What is the expected time
between orders?
Practice Problems
Problem 8:
Given the data from Problem 3, and assuming a 300-day work year, how
many orders should be processed per year? What is the expected time
between orders?
Demand
360
N=
=
= 1.34 orders per year
Q
268
Working days
300
T=
=
= 224 days between orders
Expected number of orders 1.34
Practice Problems
Problem 9:
What is the total cost for the inventory policy used in Problem 7?
Practice Problems
Problem 9:
What is the total cost for the inventory policy used in Problem 7?
Demand * Order Cost Quantity of Items * Holding Cost
TC =
+
Q
2
360 * 100 268 * 1
=
+
= 134 + 134 = $268
268
2
Practice Problems
Problem 10:
Litely Corp sells 1,350 of its special decorator light switch per year and
places orders for 300 of these switches at a time. Assuming no safety
stocks, Litely estimates a 50% chance of no shortages in each cycle and
the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15
respectively. The carrying cost per unit per year is calculated as $5 and
the stockout cost is estimated at $6 ($3 lost profit per switch and another
$3 loss of goodwill or future sales). What level of safety stock should Litely
use for this product? (Consider safety stock of 0, 5, 10, and 15 units.)
Safety stock = 0 units
Carrying cost = $0
Practice
Safety stock = 5Problems
units
Safety stock = 10 units
Carrying cost = $5/unit * 5 units
Total
Stockout Costs
Problem
10: =
Carrying cost = $5/unit * 10 units
(stockout costs * possible
1350
1350 =
units of shortage * probability S5 = 6 * 5 * .15 * 300 +
S
=
6
*
5
*
.15
*
10
Corp
sellsof1,350 of its special decorator light switch per year300and
ofLitely
shortage
* number
1350
6 * 10switches
* .15 *
places
orders for 300 of these
at =a time. Assuming
orders
per year)
$20.25 no safety
300
stocks, Litely
estimates a 50% chance of no shortages in each cycle and
1350
$60.75
S0the
= 6 probability
* 5 * .2 *
+ shortages of
= Carrying
cost +
of
5, 10, and 15 units asTotal
0.2,cost0.15,
and 0.15
300
Stockout costas
= $5 and
1350carrying
respectively.
The
cost
per
unit
per
year
is
calculated
Total
cost
=
Carrying
cost
+
6 * 10 * .15 *
+
+ $20.25 = $70.25
300
Stockoutatcost
the stockout cost is estimated
$6 =($3 lost profit per$50switch
and another
1350
$25 sales).
+ $60.75What
= $85.75
$3 6loss
goodwill
level ofSafety
safety
stock
* 15 of
* .15
*
=or future
stock
= 15should
units Litely
300
use for this product? (Consider safety stock of 0,Carrying
5, 10, and
units.)
cost =15
$5/unit
* 15 units
$128.25
Stockout cost = $0
Total cost = Carrying cost +
Stockout cost =
$75 + $0 = $75.00
Practice Problems
Problem 11:
Presume that Litely carries a modern white kitchen ceiling lamp that is
quite popular. The anticipated demand during lead-time can be
approximated by a normal curve having a mean of 180 units and a
standard deviation of 40 units. What safety stock should Litely carry to
achieve a 95% service level?
Practice Problems
Problem 11:
Presume that Litely carries a modern white kitchen ceiling lamp that is
quite popular. The anticipated demand during lead-time can be
approximated by a normal curve having a mean of 180 units and a
standard deviation of 40 units. What safety stock should Litely carry to
achieve a 95% service level?
To find the safety stock for a 95% service level it is necessary to
calculate the 95th percentile on the normal curve. Using the standard
Normal table from the text, we find the Z value for 0.95 is 1.65
standard units. The safety stock is then given by:
(1.65 * 40) + 180 = 66 + 180 = 246 Ceiling Lamps
Practice Problems
Problem 12:
A new shopping mall is considering setting up an information desk manned
by one employee. Based upon information obtained from similar information
desks, it is believed that people will arrive at the desk at a rate of 20 per hour.
It takes an average of 2 minutes to answer a question. It is assumed that the
arrivals follow a Poisson distribution and answer times are exponentially
distributed.
Problem 1:
Practice Problems
A new shopping mall is considering setting up an information desk manned
a. Find the probability that the employee is idle.
by one employee. Based upon information obtained from similar information
b. Find the proportion of the time that the employee is
desks, it is believed that people will arrive at the desk at a rate of 20 per hour.
busy.
It takes an average of 2 minutes to answer a question. It is assumed that the
c. Find the average number of people receiving and
arrivals follow a Poisson distribution and answer times are exponentially
waiting to receive some information.
distributed.
d. Find the average number of people waiting in line to
get some information.
e. Find the average time a person seeking information
spends in the system.
f. Find the expected time a person spends just waiting
in line to have a question answered (time in the
queue).
Practice Problems
Problem 12:
A new shopping mall is considering setting up an information desk manned
a. Find the probability that the employee is idle.
by one employee. Based upon information obtained from similar information
b. Find the proportion of the time that the employee is
desks, it is believed that people will arrive at the desk at a rate of 20 per hour.
busy.
It takes an average of 2 minutes to answer a question. It is assumed that the
c. Find the average number of people receiving and
arrivals follow a Poisson
times
are exponentially
a. Pdistribution
= 1receive
–  / and
= 1answer
–information.
20 / 30
= 0.33
 33%
0 to
waiting
some
distributed.
b. the
p = average
 /  = 0.66
 66%
d. Find
number
of people waiting in line to
get
c. some
Ls = information.
/ ( – ) = 20 / (30 – 20) = 2 people
e. Find
seeking
information
d. the
Lq =average
2 / (time
– )a=person
202 / 30(30
– 20)
= 1.33 people
spends in the system.
e. Ws = 1 / ( – ) = 1 / (30 – 20) = 0.10 hours
f. Find the expected time a person spends just waiting
 / a(
– ) = 20
/ 30(30(time
– 20)in= the
0.0667hours
inf.lineWtoq =have
question
answered
queue).
Practice Problems
Problem 13:
Assume that the information desk employee in Problem 12 earns $5 per
hour. The cost of waiting time, in terms of customer unhappiness with the
mall, is $12 per hour of time spent waiting in line. Find the total expected
costs over an 8-hour day.
Problem 2:
Practice Problems
From the solution to Problem 12:
Assume that the information desk employee in Problem 1 earns $5 per hour.
The average person waits 0.0667 hours and there are
The cost of waiting time, in terms of customer unhappiness with the mall, is
160 (20 arrivals * 8 hours) arrivals per day.
$12 per hour of time spent waiting in line. Find the total expected costs over
an 8-hour day.
Therefore: Total waiting time = 160 x 0.0667 = 10.67 hours
Total cost for waiting = Total waiting time * Cost per hour =
10.67 * $12 = $128 per day.
Salary cost = 8 hours * $5 = $40
Total cost = Salary cost + Waiting cost = $40 + $128 =
$168 per day.
Practice Problems
Problem 14:
Three students arrive per minute at a coffee machine that dispenses exactly
four cups per minute at a constant rate. Describe the system parameters.
Practice Problems
Problem 14:
Three students arrive per minute at a coffee machine that dispenses exactly
four cups per minute at a constant rate. Describe the system parameters.
2
Lq =
= 1.125 people in the queue on average
2( – )

Wq =
= 0.375 minutes in the queue waiting
2( – )

Ls = Lq +
= 1.87 people in the system

Ws = Wq +
1

= 0.625 minutes in the system