Name (print, please) _______________________________________________ ID ___________________________
Operations Management I 73-331 Fall 2001
Odette School of Business
University of Windsor
Final Exam Solution
Saturday, December 15, 7:00 – 10:00 p.m.
CAW Centre Ambassador Auditorium Rows A-C
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a both-sided formula sheet.
Time available: 3 hours
Instructions:
 This solution has 13 pages including this cover page
 It’s not necessary to return the unused blank pages and tables
 Please be sure to put your name and student ID number on each page
 Show your work
Grading:
Question
Score
Question
Score
1
/15
2
/3
3
/6
4
/8
5
/8
6
/6
7
/6
8
/8
9
/8
10
/8
11
/8
12
/8
13
/8
Total
/100
Name:_________________________________________________
ID:_________________________
Question 1: (15 points)
1.1 The MRP report is sent to the following departments:
a. production and finance
b. production and purchasing
1.2 Lot for lot minimizes
a. carrying cost
b. ordering cost
1.3 Silver-Meal heuristic and least unit cost heuristic perform better if the costs
a. change over time
b. do not change over time
1.4 ______________ reduce setup time
a. Cellular layouts
b. Poka-yoke
1.5 Cellular layouts
a. distribute work-load evenly
b. often yield poorly balanced cells
1.6 Following is a trend in supplier policies:
a. Identify suppliers who may supply in large volumes and minimize number of orders
b. Identify suppliers near to the customer
1.7 The fact that the EOQ cost curve is flat near the optimal order quantity implies that
a. if there are some managerial reasons to order Q units such that Q  EOQ, but Q is near
EOQ, then one may order Q units without causing a large increase in inventory cost
b. inventory cost is not sensitive to the cost of buying items
1.8 Which of the following is an input to the aggregate production planning?
a. Level of resources needed
b. Level of resources available
1.9 Which of the following is a shortage cost?
a. The cost of hiring workers to avoid shortages
b. The loss of profit due to shortages
1.10 What of the following is a level strategy?
a. Keeping a constant level of inventory
b. Keeping a constant level of workforce
1.11 Forecasts are always
a. long-term
b. wrong
2
Name:_________________________________________________
ID:_________________________
1.12 Exponential smoothing is designed for
a. stationary series
b. series with trend
1.13 Which of the following uses less memory?
a. Moving average
b. Exponential smoothing
1.14 Moving average and exponential smoothing lag behind a trend, if one exists.
a. True
b. False
1.15 Linear regression is always applied
a. on log(x) and log(y)
b. to explain how one variable changes due to the change of some other variable(s)
Question 2: (3 points)
A supplier of instrument gauge clusters uses a kanban system to control material flow. The gauge
cluster housings are transported five at a time. A fabrication centre produces approximately 16
gauges per hour. It takes approximately two hours for the housing to be replenished. Due to
variations in processing times, management has decided to keep 25 percent of the needed inventory
as safety stock. How many kanban card sets are needed?
Kanban card sets needed 
DL  w 16  2  0.25  16  2 

8
a
5
Question 3: (6 points)
One unit of A is made of one unit of B, and one unit of C. B is made of two units of C.
a. (3 points) Construct a product structure tree.
3
Name:_________________________________________________
ID:_________________________
b. (3 points) Suppose that the gross requirement of A is 100 units. Items A, B and C have on-hand
inventories of 20, 30 and 70 units respectively. Find the net requirement of C.
Gross requirement, A
100
Less item A in inventory
20
Net requirement, A, 100-20 =
80
Gross requirement, B
80
Less item B in inventory
30
Net requirement, B, 80-30 =
50
Gross requirement, C: 80+50(2) =
180
Less item C in inventory
70
Net requirement, C, 180-70
110
Question 4: (8 points)
The MRP gross requirements for Item X are shown here for 4 weeks. Lead time for A is one week,
and setup cost is $8. There is a carrying cost of $0.30 per unit per week. Beginning inventory is 30
units in Week 1.
Week
Gross
requirements
1
2
3
4
30
20
30
40
a. (3 points) Use the EOQ method to determine when and for what quantity the first order should be
released.
K  $8
30  20  30  40
52  1560 units/year
4
h  0.30  52  $15.60 /unit/year

Q
2 K

h
2  8  1560
 40
15.60
Order 40 units in Week 1
4
Name:_________________________________________________
ID:_________________________
b. (5 points) Use the least unit cost heuristic to determine when and for what quantity the first order
should be released.
Order for
weeks
Order
quantity,
Q
Inventory
after
Week 1
Inventory
after
Week 2
2
20
0
2,3
50
30
0
2,3,4
90
70
40
Inventory
after
Week 3
0
Holding
cost
Ordering
cost
Unit cost
0
8
0.40
9
8
0.34
33
8
0.45
Since the unit cost is minimum for an order size of 50 units in Week 1, order 50 units in Week 1.
Question 5: (8 points)
Following are the net requirements, production capacities and production plan of a product:
Month
1
2
3
4
Net requirements
(units)
40
30
90
60
Production
capacities (units)
70
70
70
70
Production plan
(units)
40
50
70
60
a. (2 points) Is the above production plan feasible? If the production plan is not feasible, what is the
first month of shortage?
Month
Production
Requirement
Cumulative production
Cumulative requirement
1
40
40
40

40
2
50
30
40+50=90

40+30=70
3
70
90
90+70=160

70+90=160
4
60
60
160+60=220

160+60=220
Since in each month cumulative production is larger than the cumulative requirement, the production
plan is feasible.
5
Name:_________________________________________________
ID:_________________________
b. (4 points) Suppose that the setup cost is $250 and holding cost is $2/unit/month. If the above
production plan is feasible, can you find an improved production plan? If the above production
plan is not feasible, what is the minimum amount by which the monthly production capacity must
be increased in order to make the above production plan feasible?
Month
Production
Capacity
Excess capacity
1
40
70
70-40=30
2
50
70
70-50=20
3
70
70
70-70=0
4
60
70
70-60=10
It is not possible to back-shift production of any month to any previous month(s). Hence, no
improvement is possible.
c. (2 points) Suppose that the production capacities change to 60 units per month. If there exists
any feasible production plan with these new capacities, then state a feasible production plan. If
there does not exist any feasible production plan with these new capacities, then what is the first
month of shortage?
Month
Capacity
Requirement
Cumulative capacity
Cumulative requirement
1
60
40
60

40
2
60
30
60+60=120

40+30=70
3
60
90
120+60=180

70+90=160
4
60
60
180+60=240

160+60=220
Since in each month cumulative capacity is larger than the cumulative requirement, there exists a
feasible production plan.
The following production plan is obtained by lot-shifting technique:
Month
Requirement
Capacity
Production
1
40
60
40
2
30
60
30 30+30 = 60
3
90
60 (shortage 30 units)
60
4
60
60
60
Hence, produce 40, 60, 60 and 60 units respectively in Months 1, 2, 3 and 4.
6
Name:_________________________________________________
ID:_________________________
Question 6: (6 points)
Suppose that the Travel EZ Corporation believes that a learning curve accurately describes the
evolution of its production costs for a new line of handbags. Suppose that the first unit costs $300,
and the second unit $240.
a. (2 points) What is the rate of learning?
L
240
 0.80  80%
300
b. (2 points) Compute the cost of producing the 4 th unit based on the learning curve.
Unit
Cost
1
$300
2
300(0.80)=$240
4
240(0.80)=$192
c. (2 points) Compute the cost of producing the 17th unit based on the learning curve.
b
ln L
ln 0.80

 0.3219
ln 2
ln 2
Y 17   au b  30017 
 0.3219
 120.5146
Question 7: (6 points)
Suppose that Item A has a unit cost of $30, an ordering cost of $25, and an annual demand of 300
units. It is estimated that the holding cost is 20 percent per year.
a. (3 points) Compute EOQ of Item A.
K  $25
  300 units/year
h  30  0.20  $6 /unit/year
2 K
2  25  300

 50 units
h
6
b. (3 points) Suppose that both Items A and B should be purchased and there is only $2000
available for buying Items A and B. The unit cost of Item B is $5 and the EOQ of Item B is 200
units. What is the optimal order quantity of Item A?
EOQ 
Cost of EOQ units of A, EOQA = 5030 = $1,500
Cost of EOQ units of B, EOQB = 200 5 = $1,000
Fund required = $2,500
Fund available
2,000
m

 0.80
Fund needed
2,500
Order quantity of A, QA*  mEOQA  0.80  50  40 units
7
Name:_________________________________________________
ID:_________________________
Question 8: (8 points)
Suppose that Item A has a production rate of 400 items per year. The cost and demand information
of Item A are the same as those stated in Question 7. That is, Item A has a unit cost of $30, an
ordering cost of $25, and an annual demand of 300 units. It is estimated that the holding cost is 20
percent per year.
a. (3 points) Compute EPQ of Item A.
K  $25
  300 units/year
h  30  0.20  $6 /unit/year
 300 
h'  61 
  $1.5/unit/year
 400 
2 K
2 K 
2  25  300


 100
h'
h'
1.5
b. (1 point) What is the cycle time of Item A?
EPQ 
Q 100

 0.3333 year
 300
Item C has a production rate of 2000 items per year, a unit cost of $100.00, an ordering cost of $50,
and an annual demand of 400 units. Items A and C have the same holding cost i.e. 20 percent per
year.
c. (3 points) What is the cycle time if both Items A and C are produced in a single facility and a
rotation cycle policy is used?
2K A  K C 
225  50 
T* 

400 
  
 300 

  
0.20  301 
300  0.20  1001 
400
h A 1  A  A  hC 1  C  C
400
2000




P
P
A 
C 


T
 0.14797 year
d. (1 point) What is the optimal order quantity of Item A?
QA*   AT *  0.14797  300  44.39 units
Question 9: (8 points)
Historical demand for a product is:
Month
t
Demand
1
January
22
2
February
23
3
March
25
4
April
27
a. (2 points) Using a simple three-month moving average, find the May forecast
FMay 
23  25  27
 25 units
3
8
Name:_________________________________________________
ID:_________________________
b. (2 points) Using a single exponential smoothing with   0.2 and an April forecast = 26, find the
May forecast
FMay  D Apr  1   FApr  0.20  27  0.80  26  26.2 units
c. (2 points) Using a double exponential smoothing method with   0.1,   0.1, S 0  20, and
G0  2 , find S1 and G1 .
S1  D1  1   S 0  G0   0.10  22  0.9020  2  22
G1  S1  S 0   1  G0  0.1022  20  0.90  2  2
d. (2 points) Using S1 and G1 found in part (c ) , find the May forecast made in January.
F1,5  S1  4G1  22  4  2  30 units
Question 10: (8 points)
The J&B Card Shop sells calendars. The once-a-year order for each year’s calendar arrives in
September. The calendars cost $13 and J&B sells them for $25 each. At the end of July, J&B
reduces the calendar price to $5 and can sell all the surplus calendars at this price. How many
calendars should J&B order if the September-to-July demand can be approximated by normal
distribution with   200 and   100 .
a. (2 points) What is the overage cost?
C o  Purchase price – salvage value = $13-5=$8
Area=0.60-0.50=0.10
Cu  Selling price – Purchase price = $25-13=$12
c. (4 points) Compute the optimal order quantity
p
Probability
b. (2 points) What is the underage cost?
 100
Cu
12

 0.60
Cu  Co 12  8


  0.60
Find z * such that P    z  z *  0.60

Or, P   z  0  P 0  z  z *

=200 z = 0.25
Demand

Or, P 0  z  z *  0.60  P   z  0  0.60  0.50  0.10
Hence, from Table A-1 z *  0.25 (the z -value for which area = 0.10
Q *    z *  200  0.25  100  225 units
9
Name:_________________________________________________
ID:_________________________
Question 11: (8 points)
The home appliance department of a large department store is planning to use a lot size-reorder
point system to control the replenishment of a particular model of FM table radio. The store sells an
average of 200 radios each year. The annual demand follows a normal distribution with a standard
deviation of 50. The store pays $80 for each radio. The holding cost is 20 percent per year. Fixed
costs of replenishment amount to $100. If a customer demands the radio when it is out of stock, the
customer will generally go elsewhere. The penalty cost is estimated to be about $60 per stock-out.
Replenishment lead time is three months. Find an optimal (Q,R) policy with no service constraint.
Use the iterative method and show 2 iterations. Show your computation on the next page and
summarize your results in the table below:
Summary of results obtained from Excel (hand computation shown later):
Fixed cost (K )
Holding cost (h )
Penalty cost (p )
Mean annual demand ()
Lead time () in years
Lead time demand parameters:


Step 1
Step 2
Step 3
Step 4
Step 5
Q=
Area on the right=1-F (z)
z=
R=
L (z )=
n=
Modified Q =
Area on the right=1-F (z)
z=
Modified R =
100 Note: K ,h , and p
16
are input data
60
200 input
0.25 input data
EO Q
Q h / p
Table A1/A4
  z
Table A4
 L( z)
2  np  K  / h
Q h / p
Table A1/A4
  z
10
50 <--- computed
25 input data
Iteration 1 Iteration 2
50
0.0267
1.931667
98.29167
0.010177 0.03179
0.254434 0.79464
53.68102 60.7615
0.071575 0.08102
1.464164 1.39828
86.60409 84.9569
Name:_________________________________________________
Hand computation for Question 11:
Iteration 1
1-1 EOQ 
2K
2 100  200

 50 units
h
16
1-2 1  F z  
Qh
50  16

 0.067
p 60  200
z  1.50 (See Table A-4)
R    z  50  1.5  25  87.5
1-3 Lz   0.0293 (See Table A-4)
n  Lz   25  0.0293  0.7325
1-4 Q 
2np  K 
2  2000.7325  60  100

 59.9895
h
16
1-5 1  F z  
Qh 59.9895  16

 0.08
p
60  200
z  1.405 (See Table A-4)
R    z  50  1.405  25  85.125
Iteration 2
2-3 Lz  
0.0367  0.0359
 0.0363 (See Table A-4)
2
n  Lz   25  0.0363  0.9075
2-4 Q 
2np  K 
2  2000.9075  60  100

 62.14
h
16
2-5 1  F z  
Qh 62.14  16

 0.0828
p
60  200
z  1.385 (See Table A-4)
R    z  50  1.385  25  84.63
11
ID:_________________________
Name:_________________________________________________
ID:_________________________
Question 12: (8 points)
The Easty Brewing Company produces a popular local beer known as Iron Stomach. Beer sales are
somewhat seasonal, and Yeasty is planning its production and manpower levels on March 31 for the
next three months. The demand forecasts are
Month
Production days
Forecasted Demand
April
20
8,000
May
25
9,000
June
24
9,600
As of March 31, Yeasty had 30 workers on the payroll. Over a period of 10 working days when there
were 100 workers on the payroll, Yeasty produced 10,000 cases of beer. As of March 31, Yeasty
expects to have 500 cases of beer in stock. It plans to start July with 600 cases on hand. Based on
this information, find the minimum constant workforce plan (level strategy) for Yeasty over the three
months.
Productivity 
Month
A
10,000
 10 units/worker/day
10  100
Net
requirement
Cumulative net
requirement
B
C
Units
produced per
worker
D
Cumulative
units
produced
per worker
Number of workers
needed
F= C  E 
E
April
7,500
7,500
2010=200
200
7,500  200  38
May
9,000
7,500+9,000
=16,500
2510=250
200+250
=450
16,500  450  37
June
10,200
16,500+10,200
=26,700
2410=240
450+240
=690
26,700  690  39
Minimum constant number of workers needed = 39
12
Maximum
Name:_________________________________________________
ID:_________________________
Question 13: (8 points)
Hy and Murray are planning to set up an ice cream stand in Shoreline Park. After five months of
operation, the observed sales of ice cream and the number of park attendees are:
Month
1
2
3
4
5
Ice Cream Sales in hundreds, Y
7
4
2
5
6
Park Attendees in hundreds, X
12
11
6
17
21
a. (6 points) Determine a regression equation treating ice cream sales as the dependent variable
(on the vertical axis) and park attendees as independent variable (on the horizontal axis).
y
xy
x
x2
Total
Average
Slope 
12
7
84
144
11
4
44
121
6
2
12
36
17
5
85
289
21
6
126
441
67
24
351
1031
13.4
4.8
n xy   x y
n x   x 
2
2

5  351  67  24
5  1031  67 
2

147
 0.2207
666

Intercept  y  slope x  4.8  0.220713.4  1.84
Hence, the regression equation is y  1.8423  0.2207 x
b. (2 points) Forecast the ice cream sales in the next month, if the projected number of park
attendees in the next month is 2,400
y  1.8423  0.2207  24  7.13964 hundred
Hence, ice cream sales is 713.964 units
13