MGT 3110: Exam 3 Study Guide
Discussion questions
1. What is the purpose of safety stock in the ROP model?
2. Define aggregate production plan? What is the objective and what are the requirements for
developing one?
3. What are demand options for aggregate planning? Give examples and discuss the effects of each.
4. Describe “Chase” strategy for aggregate planning and discuss the advantages and disadvantages this
approach.
5. Describe “Level” strategy for aggregate planning and discuss the advantages and disadvantages this
approach.
6. Describe “Mixed” strategy for aggregate planning and discuss the advantages and disadvantages this
approach.
7. Define independent and dependent demand items.
8. What is Master Production Schedule?
9. What is Bill of Materials?
10. What is Low-Level coding and what how is it used?
11. What are the benefits of MRP?
12. What are the inputs required for MRP?
13. What is “Lot Sizing” in MRP?
14. What are the reasons for using a lot sizing method other than Lot-for-lot?
15. Explain the terms flowtime and lateness.
16.
17.
18.
19.
What are the advantages and disadvantages of shortest processing time (SPT) rule?
What is the Critical Ratio? To what jobs does Critical Ratio give priority to?
What can be said about the jobs if CR < 1, or =1, or > 1?
What is input-output control?
Problems
1.
The Winfield Distributing Company has maintained an 80% service level policy for
inventory of string trimmers. Mean demand during the reorder period is 130 trimmers, and
the standard deviation is 80 trimmers. What is the value of ROP and SS?
2.
The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of
ergonomically correct office chair which costs $300. The annual holding cost rate is 40%,
annual demand is 600, and the order cost is $20 per order. The store is open 300 days per
year and PCE has decided to establish a customer service level of 90%.
a.
Suppose that the lead time is a constant 4 days and the demand is variable with a
standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?
b.
Suppose that the lead time is a variable with an average of 4 days and standard
deviation of 3 days. Further suppose that the demand is constant. What is the safety
stock and reorder point?
c.
Suppose that the lead time is a variable with an average of 4 days and standard
deviation of 3 days. Further suppose that the demand is also variable with a standard
deviation of 2.4 chairs per day. What is the safety stock and reorder point?
3.
A warehouse store sells laser printer cartridges in bulk. The company places restocking
orders 1000 boxes at a time. The annual demand is 7000 boxes. The demand during lead
time is given below. The average demand during lead time is 60 boxes. Assume holding
cost of $5 per box per year and a stock out cost of $50 per box.
Demand during lead time
40
50
60
70
80
90
Probability
0.1
0.2
0.2
0.2
0.2
0.1
Determine the least cost safety stock and the corresponding ROP.
4.
An oyster bar buys fresh oysters for $3 per pound and sells them for $10 per pound. Unsold oyster
at the end of the day is sold to a grocery store for $1.20 per pound. The daily demand is estimated
to be 150 pounds with a standard deviation of 12 pounds. How many pounds of oysters must be
ordered each day?
5.
Leisure Travels, Inc. manufactures and sells Recreation Vehicles. The demand for the next four
quarters is forecasted as 160, 180, 220, and 200. The labor required to produce one unit is 100
hours. Each worker works 8 hours per day for 65 days per quarter. Regular wages is $15 per hour
and O.T. wages is $20 per hour. O.T. is limited to 20% regular hours. Limited subcontracting is
available at the rate of $2500 per unit. Holding cost per unit per quarter is $100. Cost of hiring a
worker is $350 and firing worker will cost $500. The company currently has 30 employees.
a.
b.
c.
d.
e.
f.
6.
Determine the production rate per worker per day and per quarter.
Determine the regular time wage per worker per day and per quarter.
Determine the O.T. cost per unit.
Develop a “Chase” plan and the corresponding cost summary.
Develop a “Level” plan and the corresponding cost summary.
Develop a “Mixed” plan with a constant work force of 31 workers, but produce only
what the net demand is each month, i.e. not accumulate any inventory in excess of the
safety stock. If regular time capacity is not sufficient, use O.T. production first and
use subcontracting only of O.T. capacity is not enough to make up the shortage.
Consider the following Solver model for an aggregate planning problem givebn in the next page.
a. What is the Solver Target cell?
b. What are the Solver changing cells?
c. What are the Solver constraints?
d. What options of Solver must be checked?
e.
Determine the excel formula for the following cells:
B17
B18
B19
B22
E22
B23
C26
D26
E26
B29
C29
F29
G29
H29
G33
B35
B36
B37
B38
B39
B40
B41
7.
A Bill of Materials is desired for a bracket (A) that is made up of a base (B), two springs (C) and
four clamps (D). The base is assembled from one clamp (D) and two housings (E). Each clamp has
one handle (F) and one casting (G). Each housing has two bearings (H) and one shaft (I).
a. Develop a product structure tree.
b. The lead time for the parts are given below. Develop a time-phased product structure.
c. The available inventory for each part is given in the table below. Determine the net
requirement quantities of all parts required to assemble 50 units of bracket A.
Item
A
B
C
D
E
F
G
H
I
8.
5
5
10
20
50
150
50
5
0
A product (A) consists of a base (B) and a casting (C). The base consists of a plate (P) and three
fasteners (F). The lead time, current on-hand inventory and scheduled receipts are given below. All
components are lot for lot. The MPS requires start of production of 100 units of product A in week
4 and 150 in week 6. Produce the MRP for the upcoming six weeks. Produce a list of all planned
order releases.
Part
B
C
P
F
9.
Available
Lead time
1
2
3
2
1
2
1
1
2
Lead time
1
3
2
4
On-hand
100
30
0
0
Scheduled receipts
50 in week 1
20 in week 1, 30 in week 2
50 in week 1
30 in week 1, 40 in week 3
For the following item the inventory holding cost is $0.80 per week and the setup cost is $300.
Determine the lot sizes and total cost for this item under (i) Lot-for-Lot, (ii) EOQ, and (iii)
PPB methods
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand
100
Net Requirement
Planned receipts
Planned order releases
LT =
1
100
1
2
250
3
200
4
150
5
250
6
200
7
200
8
150
10.
Consider the following planned and actual hours of input and output.
Week ending
Planned input
Actual input
Planned output
Actual output
1
2
3
4
5
6
7
8
500
700
650
600
800
700
650
700
700
700
650
800
600
800
650
700
600
600
650
650
800
500
700
500
700
500
700
600
800
800
700
800
Prepare the Input/Output Control chart for this workstation. Assume an initial actual
backlog of 120 hours and zero for the two cumulative deviations.
11.
The following jobs are waiting to be processed on day 250
Job
A
B
C
D
E
F
Date Job received
215
220
225
240
245
250
Production days needed
30
20
40
50
20
35
Date job due
290
415
375
315
420
380
Sequence the jobs in the order of SPT, EDD, and Critical Ratio, and compute (i) Average flow time, (ii)
Average lateness, (iii) Average no. of jobs in the system, and (iv) Utilization, for each of the three
schedule of jobs.
Answers to discussion questions
1. What is the purpose of safety stock in the ROP model?
The purpose of safety stock is to decrease the probability of stock out during lead time of a
replenishment order, which increases the probability of meeting demand, aka service level.
2. Define aggregate production plan? What is the objective and what are the requirements for
developing one?
Aggregate production plan is a plan of overall production level, prepared over a rolling horizon of 12
to 18 monthly periods, or 4 to 6 quarterly periods.
The objective is to minimize cost by adjusting production rates, labor levels, inventory levels,
overtime work, subcontracting rates.
The requirements for developing an aggregate production plan include:
 a logical overall unit for measuring sales and output
 a forecast of demand for the planning horizon in these aggregate terms
 standard hours to produce one unit of the product in these aggregate term
 cost data such as wages (regular time, overtime, and subcontracting), inventory carrying cost,
and hiring/firing costs
3. What are demand options for aggregate planning? Give examples and discuss the effects of each.
Demand options are techniques used to even out fluctuations in demand. Following are some
examples.
 Back ordering during high- demand periods (Effective if substitute products are not available,


but may result in loss of customer orders to competition and lost customer good will)
Counter-seasonal product mix (effective in reducing huge ups and downs in demand , but
may lead to products or services outside the company’s areas of expertise
Economic incentives such as discounts (loss of profit)
4. Describe “Chase” strategy for aggregate planning and discuss the advantages and disadvantages this
approach.
Chase strategy matches output rates to demand forecast for each period by varying the workforce
levels or vary production rate.
Advantage: Very low inventories
Disadvantage: Requires frequent hiring and firing of workers
5. Describe “Level” strategy for aggregate planning and discuss the advantages and disadvantages this
approach.
Level strategy uses uniform production rate. Fluctuations in demand is managed through
accumulation of inventory during lean demand periods.
Advantage: Stable production leads to better quality and productivity
Disadvantage: High levels of inventory
6. Describe “Mixed” strategy for aggregate planning and discuss the advantages and disadvantages this
approach.
Mixed strategy maintains uniform production rate, but does not build inventory. Overtime and
subcontracting is used to meet demand.
Advantage: Stable production leads to better quality and productivity and low levels of inventory
Disadvantage: Use of overtime and/or subcontracting may increase cost and may lead to quality
related problems
7. Define independent and dependent demand items.
Finished products whose demand is independent of production decisions are called
“Independent demand” items. Items for which demand can be directly calculated from
production decisions are called “Dependent demand” items. These are raw-materials and
parts required for the production of the finished goods.
8. What is Master Production Schedule?
Master Production Schedule specifies production quantities of each Independent Demand
item for a planning horizon of 12 to 15 weeks. Total of MPS quantities must be in
accordance with the aggregate production plan.
9. What is Bill of Materials?
Bill of materials is structured list of components, ingredients, and materials needed to make
an end product. Items needed to produce a given part are called components or “children”.
The part into which the components go us called “Parent”. The BOM also gives the number
of units of a child item needed to produce one unit of the parent item.
10. What is Low-Level coding and what how is it used?
A level code starting from zero at the top of the BOM tree and incremented by 1 going down
each level of the BOM tree is assigned. Then, the lowest level at which an item appears is
called Low-Level code. The MRP computations are processed one level at a time, starting
from level zero.
11. What are the benefits of MRP?
 Better response to customer orders
 Faster response to market changes
 Improved utilization of facilities and labor
 Reduced inventory levels
12. What are the inputs required for MRP?
 Master Production Schedule
 Bill of Materials
 Inventory status
13. What is “Lot Sizing” in MRP?
The process of combining net requirements into production lots is called lot sizing.
14. What are the reasons for using a lot sizing method other than Lot-for-lot?


Lot-for-lot often requires too many lots that may not be economically justifiable
Sometime lot-for-lot generates absurdly small lots
15. Explain the terms flowtime and lateness.
Flow time is the length of time a job is in the system; lateness is completion time minus due
date.
16. What are the advantages and disadvantages of shortest processing time (SPT) rule?
SPT minimizes the average flow time, average lateness, and average number of jobs in the
system. It maximizes the number of jobs completed at any point. The disadvantage is that
long jobs are pushed back in the schedule.
17. What is the Critical Ratio? To what jobs does Critical Ratio give priority to?
The Critical Ratio (CR) is an index number computed by diving the time until due date by
the working time remaining. The CR gives priority to jobs that must be done to keep
shipping on schedule.
18. What can be said about the jobs if CR < 1, or =1, or > 1?
If CR < 1, then the job has fallen behind, the work remaining exceeds the time until due date.
If CR = 1, then the job is on schedule, the work remaining exactly equals the time until due
date. If CR > 1, then there is slack, the time until due date exceeds the work remaining.
19. What is input-output control?
Input/output control keeps track of planned versus actual inputs and outputs, highlighting deviations
and indicating bottlenecks using cumulative backlog.
Answers to problems
1.
2.
Given dL = 130, dLT = 80, and for 80% service level, Z = 0.84
ROP = 130 + 0.84 x 80 = 197.2, or round up to 198 for at least 80% service level
d = D/No. of days per year = 600/300 = 2 per day, Z for 90% service level = 1.285
a.
Given: L = 4 days Constant, d = 2.4 per day, therefore dLT = 2.4 √4 = 4.8
Safety stock = Z dLT = 1.285 x 4.8 = 6.2 or 7 (round up for at least 90% service level)
ROP = dL + SS = (2 chairs/day * 4) + 7 = 15
b.
Given: L = 4 days with L = 3 and demand is constant, dLT = 2 (3) = 6
Safety stock = Z dLT = 1.285 x 6 = 7.7 or 8 (round up for at least 90% service level)
ROP = dL + SS = (2 chairs/day * 4) + 8 = 16
c.
Given: L = 4 days with L = 3 , and d = 2.4 per day, therefore dLT = √4(2.4)2 + 22 32 = 7.684
Safety stock = Z dLT = 1.285 x 7.684 = 9.9 or 10 (round up for at least 90% service level)
ROP = dL + SS = (2 chairs/day * 4) + 10 = 18
3. Number of orders per year = 7, H = $5, S = $50
Safety
ROP
stock
Carrying cost
Expected stock out
60
0
0
(10x.2 + 20x.2 + 30x.1) = 9
70
10
10 x $5 = $50 (10x.2 + 20x.1) = 4
80
20
20 x $5 = $100 (10x.1) = 1
90
30
30 x $5 = $150 0
Stock out
cost/order
Stock out
cost/year
Total
cost
9 x $50 = $450
$3,150
$3,150
4 x $50 = $200
$1,400
$1,450
1 x $50 = $50
$350
$450
0
$0
$150
Least cost safety stock = 30, ROP = 90
4.
Cs = Lost profit = Selling price per unit – Cost per unit = 10 – 3 = $7
Co = Cost/unit – salvage value/unit = 3 – 1.20 = $1.80
Optimum service level = 7/(7 + 1.80) = 0.795 = 79.5%
From normal table, for 79.5% service level, Z = 0.83
Order quantity =  + Z  = 150 + 0.825 (12) = 159.9 or 160
5.
Hiring cost/worker =
Firing cost/worker =
RT Wage/hour =
OT wage rate/hour =
Sub-contracting cost/unit =
350
500
15
20
2500
Worker hours/quarter =
Standard hours/unit =
Holding cost =
520
100
100
a. Production rate/worker/day = 8 hours per day/100 hours per unit = 0.08 per worker/day
Production rate/worker/quarter = 0.08/worker/day x 65 days/quarter = 5.2/worker/ quarter
b. Wage rate per worker per day = $15/hour x 8 hours/day = $120
Wage rate per worker per quarter = $15/hour x 8 hours/day x 65 days/quarter = $7800
c. OT cost/unit = $20/hour x 100 hours/unit = $2000
d. Chase plan
Period
Demand
Production
required
Workers
needed
Workers needed
(Rounded)
30
Hired
workers
Fired
workers
1
2
3
4
160
180
220
200
Cost summary
Regular wages
O.T. cost =
S.C. cost
Hiring cost
Firing cost
Carrying cost
Total cost
160–(0–0) =
160
180
220
200
160/5.2=30.77
180/5.2=34.62
220/5.2=42.31
200/5.2=38.46
31
35
43
39
148
148 workers-quarters x $7800 =
1
4
8
0
13
0
0
0
4
4
1,154,400
13 workers x $350 =
4 workers x $500 =
4,550
2,000
$1,160,950
d. Level Plan
Sum of demand = 760
Average demand = 760/4 = 190 i.e. = production per quarter
Period
1
2
3
4
Average demand =
Cost summary
Regular wages
O.T. cost =
S.C. cost
Hiring cost
Firing cost
Carrying cost
Total cost
Demand
RT Production
160
180
220
200
190
Workers needed/quarter =
Workers rounded up =
E.I.
0
30
40
10
0
80
190
190
190
190
760
36.54
37
37 workers x 4 quarters x $7800 =
(37 workers – 30 workers) x $ 350 =
80 x $100 =
1,154,400
2,450
8,000
$1,164,850
f. Mixed plan
Plan C
No. of workers = 31
Production per quarter with 31 workers = 31 x 5.2 = 161.2 or 161
O.T. capacity/quarter = 161 x 20% = 32
Production
Shortage
Period
Demand
capacity RT Production
161
1
160
Min(160,161) =160 160 – 160=0
161
180-161=19
2
180
Min(180,161) =161
161
220-161=59
3
220
Min(220,161) =161
161
200-161=39
4
200
Min(200,161) =161
643
O.T
Capacity
32
32
32
32
O.T.
Production
0
Min(19,32)=19
Min(59,32)=32
Min(39,32)=32
83
S.C.
0
0
59-32=27
39-32=7
34
Cost summary
Regular wages
O.T. cost =
S.C. cost
Hiring cost
Firing cost
Carrying cost
Total cost
31 workers x 4 quarters x $7800 =
83 units x $2000
34 units x $2500 =
(31 – 30) x $350 =
967,200
166,000
85,000
350
$1,218,550
6.
B17
B18
B19
B22
E22
B23
C26
D26
E26
B29
C29
B13/B11*B12
B13*B3*B12
B11*B4
E11
B22+C22-D22
E22
SUM(C22:C25)
SUM(D22:D25)
SUM(E22:E25)
E12
E22*$B$17
F29
G29
E4
SUM(B29:E29)-F29
H29
C29*$B$14
G33
SUM(G29:G32)
B35
E26*B18
B36
D33*B19
B37
B38
E33*B5
C26*B7
B39
B40
B41
D26*B8
G33*B6
SUM(B35:B40)
a. B41
b. C22:D25, D29:E32
c. D29:D32 <= H29:H32
G29:G32 >= E13
C22:D25 = Integer (if needed)
D29:E32 = Integer (if needed)
d. Assume linear model
Assume non-negative
7.
A
B
C2
D1
F
D4
E2
G
H2
I
F
G
F
D
G
B
H
E
I
C
A
F
D
G
1
2
3
4
5
Lead time = 7 weeks
Part
A
B
C
D
E
F
G
H
I
Gross
50
1 x A = 45
2 x A = 2 x 45 = 90
4 x A + 1 x B = 4 x 45 + 40 = 220
2 x B = 80
1 x D = 200
1 x D = 200
2 x E = 2 x 30 = 60
1 x E = 30
Available
5
5
10
20
50
150
50
5
0
Net
50 – 5 = 45
45 – 5 = 40
90 – 10 = 80
220 – 20 = 200
80 – 50 = 30
200 – 150 = 50
200 – 50 = 150
60 – 5 = 55
30 – 0 = 30
6
7
8.
1
2
3
MPS start for A
Item B GR =
Lead time =
Week:
Gross requirement
Scheduled receipts
Projected on-hand
100
Net requirement
Planned receipts
Planned order releases
Item C
Week:
Gross requirement
Scheduled receipts
Projected on-hand
30
Net requirement
Planned receipts
Planned order releases
Item P
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net requirement
Planned receipts
Planned order releases
Item F
Week
Gross requirement
Scheduled receipts
Projected on-hand
Net requirement
Planned receipts
Planned order releases
4
100
0
0
5
6
150
1
1
0
50
100
2
0
3
0
4
100
5
0
6
150
150
150
150
50
0
0
0
0
0
0
0
0
0
100
50
100
100
0
4
100
5
0
6
150
0
0
150
80
20
20
0
0
0
0
150
150
0
Lead time =
3
0
4
0
5
100
6
0
50
50
50
0
0
1
0
20
30
2
0
30
50
0
20
0
0
Lead time =
3
0
80
2
0
3
2
1
0
50
0
50
50
50
0
0
0
0
0
50
0
0
0
0
1
0
30
0
Lead time =
2
3
0
0
40
30
30
4
0
5
300
6
0
70
0
0
230
0
0
0
0
70
230
230
0
Planned order releases:
A has releases of 100 in week 4, 150 in week 7
B has a release of 100 in week 5
C has releases of 20 in week 1, 150 in week 3
P has a release of 50 in week 3
F has a release of 230 in week 1
0
0
4
0
0
9. (i) L-4-L
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net Requirement
Planned receipts
Planned order releases
100
No. of setup =
Carrying cost =
Setup cost = 7 x $300 =
Total cost =
LT =
1
100
1
2
250
3
200
4
150
5
250
6
200
7
200
8
150
100
0
0
250
0
250
250
200
0
200
200
150
0
150
150
250
0
250
250
200
0
200
200
200
0
200
200
150
0
150
150
0
5
250
0
150
100
375
0
6
200
0
275
0
0
375
7
200
0
75
125
375
0
8
150
0
250
0
0
0
7
200
0
0
200
350
8
150
0
150
7
0
2100
2100
(ii) EOQ:
Total demand for 8 weeks = 1500, d = 1500/8 = 187.5
H = $0.80/week
S = 300
2(187.5)300
Q= √
0.8
= 375
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net Requirement
Planned receipts
Planned order releases
100
LT =
1
100
0
100
0
0
375
1
2
250
0
0
250
375
375
3
200
0
125
75
375
0
4
150
0
300
0
0
375
Setup cost per week = (d/Q) S = (187.5/375) x 300 =
Holding cost per week = (Q/2)H per week = (375/2) x 0.80 =
Total cost per week= 150 + 150 =
Cost for 8 weeks = Total cost per week x 8 weeks = 300 x 8 =
150
150
300
2400
(iii) PPB
EPP = 300/0.80 = 375
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net Requirement
Planned receipts
100
LT =
1
100
0
100
0
0
1
2
250
0
0
250
600
3
200
0
350
4
150
0
150
5
250
0
0
250
450
6
200
0
200
Planned order releases
Periods
combined
Quantities
combined
600
450
Periods brought
forward for the
last quantity
New Partperiods
350
Total combined partperiods
Lot #1 with planned receipt in week #2
2
250
0
0
2, 3
250 + 200 = 450
1
200x1 = 200
2, 3, 4
450 + 150 = 600
2
150 x 2 = 300
0
200
200 + 300 = 500
(500 is closer to EPP of 375)
Lot #2 with planned receipt in week #5
5
250
0
0
0
5, 6
250 + 200 = 450
1
200 x 1 = 200
200
(200 is closer to EPP of 375)
5, 6, 7
450 + 200 = 650
2
200 x 2 = 400
200 + 400 = 600
Lot #1 with planned receipt in week #2
7
200
0
0
7, 8
200 + 150 = 350
1
1x 150 = 150
0
150
Summary:
Lot #
Planned order release in Week
Weeks covered
Lot size
Lot PP
1
Week 1
2, 3, 4
600
500
2
Week 4
5, 6
450
200
3
Week 6
7, 8
350
150
850
Total cost = 3 Setups x 300 + 850 x 0.8 = $1,580
#10.
Week ending
Planned input
Actual input
Cumulative deviation
Planned output
Actual output
Cumulative deviation
Backlog
120
1
2
3
4
5
6
7
8
500
700
200
650
600
-50
220
800
700
100
650
700
0
220
700
700
100
650
800
150
120
600
800
300
650
700
200
220
600
600
300
650
650
200
170
800
500
0
700
500
0
170
700
500
-200
700
600
-100
70
800
800
-200
700
800
0
70
#11. SPT
Processing
time (Days)
20
20
30
35
40
50
Job
B
E
A
F
C
D
Days till due
date
165
170
40
130
125
65
Completion
time (Flowtime)
20
40
70
105
145
195
Lateness
0
0
30
0
20
130
575
180
195
Average flow time =
Average lateness =
Average WIP =
Utilization =
95.833
30
2.949
0.339
EDD
Job
A
D
C
F
B
E
Processing
time (Days)
30
50
40
35
20
20
195
Days till due
date
40
65
125
130
165
170
Average flow time =
Average lateness =
Average no. of jobs in the system =
Utilization =
Completion
time (Flowtime)
30
80
120
155
175
195
755
Lateness
0
15
0
25
10
25
75
125.83
12.50
3.87
0.26
CR
Job
D
A
C
F
Processing
time (Days)
50
30
40
35
Days till due
date
65
40
125
130
Completion
time (Flowtime)
50
80
120
155
Lateness
0
40
0
25
CR
1.30
1.33
3.13
3.71
B
E
20
20
195
Average flow time =
Average lateness =
Average no. of jobs in the system =
Utilization =
165
170
129.17
16.67
3.97
0.25
175
195
775
10
25
100
8.25
8.50