Name (print, please) _______________________________________________ ID ___________________________
Production Management 73-604 Fall 2007
Odette School of Business
University of Windsor
Midterm Exam 1 Solution
Thursday, October 11, 5:30 pm – 6:50 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 1 hour 20 minutes
Instructions:
 This exam has 12 ages including this cover page.
 Please be sure to put your name and student ID number on each page.
 Show your work.
Grading:
Question
Marks:
1
/10
2
/7
3
/8
4
/10
5
/15
6
/15
Total:
/65
Name:_________________________________________________
ID:_________________________
Question 1: (10 points) Multiple choice questions: circle the most appropriate answer
1.1 In working to a solution to a Decision Tree problem, we start at the ________ of the tree and
calculate ________.
a. start, forward
b. start, backwards
c. end, forward
d. end, backwards
1.2 Chance nodes in a Decision Tree is
a. rectangular
b. square
c. circular
d. triangular
1.3 (i) Capacity can be defined as the ability to hold, receive, store, or accommodate. (ii) The capacity
utilization rate is found by dividing Best Operating Level by Capacity used.
a. (i) true, (ii) false
b. (i) false, (ii) true
c. Both true
d. Both false
1.4 If the payoff of selecting Machine A is $46,000 with a probability of 90% and the payoff of
selecting Machine B is $80,000 with a probability of 50%, which machine would you select if
maximizing payoff is your objective?
a. Machine A
b. Machine B
c. Both
d. None
1.5 We should match ________ products with a ________ supply-chain.
a. functional, responsive
b. functional, efficient
c. innovative, effective
d. innovative, efficient
1.6 Demand for products or services can be broken down into which of the following components of
demand?
a. Random variation
b. Autocorrelation
c. A trend
d. All of the above
1.7 (i) RSFE stands for Readable Safety Function for Error detection. (ii) MAD statistics can be used
to generate Tracking Signals.
a. (i) true, (ii) false
b. (i) false, (ii) true
c. Both true
d. Both false
2
Name:_________________________________________________
ID:_________________________
1.8 Maintaining a stable workforce working at a constant output rate while shortages and surpluses
are absorbed by fluctuating inventory levels, order backlogs and allowing lost sales is which of the
following Production Planning Strategies?
a. Stable workforce, variable work hours
b. Chase
c. Level
d. All of the above
1.9 Linear Programming (LP) is appropriate to Aggregate Planning if the cost and variable
relationships are ________ and demand can be treated as ________.
a. linear, stochastic
b. non-linear, deterministic
c. linear, deterministic
d. non-linear, stochastic
1.10 An Exponential Smoothing method requires which of the following pieces of data to forecast
the future?
a. The most recent forecast
b. The actual demand that occurred for a forecasted future period
c. The value of the smoothing constant Alpha
d. All of the above
Question 2: (7 points)
Alpha Computer Products competed for and won a contract to produce two prototype units of a new
type of computer that is based on laser optics rather than on electronic binary bits. The first unit
produced by Alpha took 6,000 hours to produce and required $200,000 worth of materials,
equipment usage, and supplies. The second unit took 5,400 hours and used $160,000 worth of
materials, equipment usage, and supplies. Labor is $30 per hour. Alpha was asked to present a bid
for 3 additional units as soon as the second unit was completed. Production would start immediately.
What would this bid be? The following table reproduces some parts of Exhibits 2.5 and 2.6.
Unit
1
2
3
4
5
6
7
8
Unit Improvement Factor
80%
85%
90%
95%
1.0000 1.0000 1.0000 1.0000
0.8000 0.8500 0.9000 0.9500
0.7021 0.7729 0.8462 0.9219
0.6400 0.7225 0.8100 0.9025
0.5956 0.6857 0.7830 0.8877
0.5617 0.6570 0.7616 0.8758
0.5345 0.6337 0.7439 0.8659
0.5120 0.6141 0.7290 0.8574
Rate of learning for labor hour =
Cumulative Improvement Factor
80%
85%
90%
95%
1.0000 1.0000 1.0000 1.0000
1.8000 1.8500 1.9000 1.9500
2.5021 2.6229 2.7462 2.8719
3.1421 3.3454 3.5562 3.7744
3.7377 4.0311 4.3392 4.6621
4.2994 4.6881 5.1008 5.5380
4.8339 5.3217 5.8447 6.4039
5.3459 5.9358 6.5737 7.2612
5,400
 90% (1 point)
6,000
Rate of learning for materials, equipment usage and supplies =
3
160,000
 80% (1 point)
200,000
Name:_________________________________________________
Unit
3
4
5
Total
(1 point)
ID:_________________________
Labour hour
Materials, equipment usage and
(1 point)
supplies (1 point)
$5,077.2 200,000  0.7021 =
$140,420
6,000  0.8462 =
4,860.0 200,000  0.6400 =
128,000
6,000  0.8100 =
4,698.0
119,120
6,000  0.7830 =
200,000  0.5956 =
14,635.2
387,540
The total labor cost = 14,635.2  30 =
$439,056.0 (1 point)
Materials, equipment usage and supplies are 387,540.0
Hence, the total cost =
$826,596.0 (1 point)
Alternate solution
Labour hour = 6,000(4.3392-1.9000) = 14,635.2
Materials, equipment usage and supplies = 200,000(3.7377-1.8000) = $387,540.
Question 3: (8 points)
Observed weekly sales of ball peen hammers at the town hardware store over a five-week period
have been 16, 12, 28, 24, 32.
a. (3 points) Suppose that three-week moving averages are used to forecast sales, Determine the
one-step-ahead forecasts for weeks 4 and 5.
16  12  28
 18.67
3
12  28  24
F5 
 21.33
3
F4 
b. (3 points) Suppose that exponential smoothing is used to with a smoothing constant of   0.20.
Find the exponential smoothing forecasts for weeks 4 and 5. (To get the method started, use the
same forecast for week 4 as you used in part a.)
F4  18.67
F5  18.67  0.2024  18.67  19.736
c. (2 points) Based on the MAD, which method did better?
MAD MA 
MAD ES 
24  18.67  32  21.33
2
24  18.67  32  19.736
2
Thus, moving average is better.
8
 8.797
4
Name:_________________________________________________
ID:_________________________
Question 4: (10 points)
Lakeroad, a manufacturer of hard disks for personal computers, was founded in 2005 and has sold
the following number of disks:
Year
Numbers Sold (in 000s)
2005
24
2006
35
2007
47
a. (7 points) Calculate the exponential smoothing with trend component forecast for years 2006 and
2007 using an initial trend forecast (T1) of 12, an initial exponential smoothing forecast (F1) of 13,
an  of 0.20, and a  of 0.20.
Year
t
2005
Actual
At
24
Ft
Tt
FITt
13
12
13+12
= 25.00
24.80+11.96
= 36.76
(2 points)
36.408+11.89
= 48.298
(1 point)
2006
35
0.20(24)+0.80(25) = 24.80
(2 points)
0.20(24.80-13)+0.80(12) = 11.96
(2 points)
2007
47
0.20(35)+0.80(36.76)
= 36.408
0.20(36.408-24.80)+0.80(11.96)
= 11.89
b. (3 points) What is the sales forecast for the year 2009 made at the end of 2007?
F2008  0.2047   0.8048.298   48.0384
T2008  0.2048.0384  36.408   0.811.89   11.89408
FIT2008 , 2009  48.0384  2  11.89408  71.8266
Question 5: (15 points)
Use regression analysis on deseasonalized demand to forecast demand in Fall 2007, given the
following historical demand data:
Year
Season
2005
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall
2006
Actual
Demand
61
77
79
64
69
86
90
76
5
Name:_________________________________________________
ID:_________________________
Quarterly average demand = (61+77+79+64+69+86+90+76)/8 = 75.25
Season
Average demand
Winter
(61+69)/2 = 65.0
Spring
(77+86)/2 = 81.5
Summer
(79+90)/2 = 84.5
Fall
(64+76)/2 = 70.0
Period
x
Demand
1
2
3
4
5
6
7
8
 x =36
61
77
79
64
69
86
90
76
Deseasonalized
Demand
y
70.6
71.1
70.4
68.8
79.9
79.4
80.1
81.7
 y =602.0
X =4.5
b
Seasonal Index
65.0/75.25 = 0.8640
81.5/75.25 = 1.0830
84.5/75.25 = 1.1230
70.0/75.25 = 0.9300
4.0000
xy
y2
70.6
142.2
211.1
275.2
399.4
476.4
561.0
653.6
 xy =2789.5344
1
4
9
16
25
36
49
64
 y 2 =204
Y =75.25
n xy   x y
n x 2   x 
2

82,789.5344   36602.0
8204   36 
2

644.2752
 1.9175
336.0
a  Y  b X  75.25  1.9175 4.5  66.6213
FFall,07  y12  a  b12   66.6213  1.9175 12   89.6313
Forecast, fall 2007, reseasonalized = 89.6313(0.9300) = 83.3571
Question 6 (15 points)
Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion,
Michigan. Based on orders received and forecasts of buying habits, it is assumed that the demand
for the next three months is 1100, 1300 and 1000, expressed in thousands of cookies. During a 50day period when there were 150 workers, the company produced 2.5 million cookies. Assume that
the numbers of workdays over the three months are respectively 25, 20 and 21. There are currently
70 workers employed. Beginning inventory is 100 thousand and it is required that there be at least
200 thousand units in the inventory at the end of three months.
a. (9 points) What is the minimum constant workforce required to meet demand (i.e., shortages not
allowed) over the next three months?
Productivity = 2.5  10 6 /50/150 = 333.33 cookies/worker/day
6
Name:_________________________________________________
Month
Net
Production
Required
(000)
1
1100-100
=1000
2
3
ID:_________________________
Cumulative
net
production
required
(000)
1000
#Days
Per
Month
Production
Per Worker
Cumulative
Production
Per Worker
# of Workers
Needed
25
8333.33
8333.33
1300
2300
20
6666.67
15000.00
1000+200
=1200
3500
21
7000.00
22000.00
 1000 
 8.333   120
 2,300 
 15   153.33
 3500 
 22   160
160
Maximum
Minimum constant workforce = 160 workers
b. (6 points) Assume that the inventory holding cost is 15 cents per cookie per month, hiring cost is
$200 per worker, and firing cost is $300 per worker. Evaluate the cost of the plan derived in a.
Month
Beginning
Inventory
(000)
Production
Per
Worker
1
2
3
100
333.33
100
8333.33
6666.67
7000.00
Production
by 160
workers
(000)
1333.3333
1066.6667
1120.0000
Demand
(000)
Ending Inventory
(000)
1100
1300
1000
100+1333.33-1100 = 333.33
333.33+1066.66-1300=100
100+1120-1000=220
Total = 653.3333
Number of workers hired = 160-70 = 90 workers
Hiring cost = 90(200) = $18,000
Inventory holding cost = 653.3333(1000)(0.15) = $98,000
Total cost = $18,000+$98,000 = $116,000
7