Name:______ID:______
Operations Management I 73-331 Fall 2004
Odette School of Business
University of Windsor
Final Exam Solution
Wednesday, December 15, 12:00 noon – 3:00 p.m.
Ambassador Auditorium: Areas C,D,E,F,G
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and 3 one-sided formula sheets.
Time available: 3 hours
Instructions:
· This exam has 32 pages including this cover page, 1 blank page and 8 pages of Table
· It’s not necessary to return tables and formula sheets
· Please be sure to put your name and student ID number on each odd numbered pages
· Show your results up to four decimal places
· Show your work
Grading:
Question / Score / Question / Score1 / /15 / 2 / /12
3 / /12 / 4 / /12
5 / /12 / 6 / /13
7 / /10 / 8 / /5
9 / /9 / Total / /100
Question 1: (15 points) Circle the most appropriate answer
1.1 Forecasting is used in the context of
a. make-to-order production system
b. assemble-to-order production system
c. make-to-stock production system
d. all of the above
1.2 MRP is used in the context of
a. make-to-order production system
b. assemble-to-order production system
c. make-to-stock production system
d. all of the above
1.3 L4L performs best if
a. holding cost is low
b. ordering cost is low
c. the costs change over time
d. the costs do not change over time
1.4 “Make sure you run out of inventory before you produce new components,” is a condition necessary to minimize cost in the context of
a. MRP with capacity constraints
b. MRP with no capacity constraints
c. both
d. none
1.5 The essence of JIT is the willingness of the worker to
a. produce as much as possible without halting the production at all
b. specialize in a single function
c. maximize the length of the time between maintenance
d. none of the above
1.6 If the rate of learning, is high, the learning is
a. faster and the learning curve flatter
b. faster and the learning curve steeper
c. slower and the learning curve flatter
d. slower and the learning curve steeper
1.7 The following method is used for forecasting a stationary series
a. Exponential smoothing
b. Holt’s method
c. Linear regression
d. a and b
1.8 Which of the following forecast series is expected to be the smoothest?
a. A 4-period simple moving average
b. A 8-period simple moving average
c. An exponential smoothing method with
d. An exponential smoothing method with
1.9 Which of the following is not a part of the cost of hiring?
a. Severance pay
b. Cost of training
c. Cost of advertising
d. b and c
1.10 In a level strategy, cumulative production
a. equals cumulative demand
b. is more than cumulative demand
c. is less than cumulative demand
d. none of the above
1.11 Lead time is the amount of time between
a. two successive order placement
b. two successive updating of inventory on hand
c. placing order and receiving delivery
d. two successive capacity additions
1.12 The motivation for holding inventory includes
a. continuous improvement
b. economies of scale
c. better quality
d. less capital required
1.13 If three products A, B, C are produced in a rotation cycle policy, the following is a possible sequence
a. A, B, C, B, C, A, C, A, B
b. A, C, B, A, C, B, A, C, B
c. A, B, C, A, B, C, B, B, B
d. A, B, A, B, C, A, B, A, B
1.14 The best inventory policy satisfying the Type 1 service objective
a. is easier to compute than the best inventory policy satisfying the Type 2 service
b. can accurately approximate a Type 2 service
c. should be used in place of the best inventory policy satisfying the Type 2 service
d. all of the above
1.15 Which of the following is an overage cost?
a. The cost per unit of positive inventory remaining at the end of the period
b. The cost per unit of the unsatisfied demand
c. The profit margin
d. Depends whether backorder is allowed or not
Question 2: (12 points)
A major oil company is considering the optimal timing for the construction of new refineries. From past experience, each doubling of the size of a refinery at a single location results in an increase in the construction costs of about 75 percent. Furthermore, a plant of size 6,000 barrels per day costs $25 million. Assume that the annual demand for the oil is increasing at a constant rate of 1.5 million barrels yearly and the discount rate for future costs is 20 percent.
a. (4 points) Find the values of and assuming a relationship of the form Assume that is in units of barrels per day.
(2 points)
(2 points) or,
b. (4 points) Determine the optimal timing of plant additions and the optimal size and cost of each plant addition.
From Fig 1-14, locating ,
Optimal timing, years
(2 points)
Optimal size,
(1 point)
Optimal cost,
(1 point)
or
c. (4 points) Suppose that the largest single refinery that can be built with current technology is 7,500 barrels per day. Determine the optimal timing of plant additions and the optimal size and cost of each plant in this case.
Optimal size, (2 point)
Optimal timing, (1 point)
Optimal cost, (1 point)
or,
Question 3: (12 points)
A popular brand of tennis shoe has had the following demand history by quarters over a two-year period.
Quarter2003 / Demand / Quarter
2004 / Demand
1 / 15 / 1 / 20
2 / 25 / 2 / 35
3 / 75 / 3 / 80
4 / 50 / 4 / 60
a. (4 points) Determine the seasonal factors for each quarter by the method of centered moving averages
N = / 4 / The demand is quarterly, there are 4 quarters in each year.Centered / (B/D)
Period / Demand / MA(4) / MA / Ratio
A / B / C / D / E
1 / 15 / 42.8125 / 0.3504
2 / 25 / 42.8125 / 0.5839
3 / 75 / 41.8750 / 1.7910
4 / 50 / 41.25 / 43.7500 / 1.1429
5 / 20 / 42.5 / 45.6250 / 0.4384
6 / 35 / 45 / 47.5000 / 0.7368
7 / 80 / 46.25 / 46.5625 / 1.7181
8 / 60 / 48.75 / 46.5625 / 1.2886
Final
Seasonal / Seasonal
Period / Factors / Factors
1 / 0.3944 / 0.3919
2 / 0.6604 / 0.6563
3 / 1.7546 / 1.7437
4 / 1.2157 / 1.2082
Total / 4.0251 / 4.0000
b. (4 points) Compute the deseasonalized demand series. Using the method of linear regression, determine the slope and intercept of the straight line that best fits the deseasonalized series.
/ DeseasonalizedDemand
/ /
1 / 38.2745 / 38.2745 / 1
2 / 38.0935 / 76.1869 / 4
3 / 43.0130 / 129.0390 / 9
4 / 41.3854 / 165.5417 / 16
5 / 51.0327 / 255.1636 / 25
6 / 53.3309 / 319.9852 / 36
7 / 45.8805 / 321.1637 / 49
8 / 49.6625 / 397.3000 / 64
Sum / 36 / 360.6730 / 1702.6546 / 204
Average / 4.5 / 45.0841
c.
(4 points) Predict the demand of all quarters of 2005. Plot the original demand of 2003-2004 and predicted demand of 2005.
Deseasonalized demand,
First quarter of 2004: ,
To get the predicted demand, reseasonalize,
Second quarter of 2004: ,
To get the predicted demand, reseasonalize,
Third quarter of 2004: ,
To get the predicted demand, reseasonalize,
Fourth quarter of 2004: ,
To get the predicted demand, reseasonalize,
Question 4: (12 points)
A start-up firm has kept careful records of the time required to manufacture its product, a shutoff valve used in gasoline pipelines.
Cumulative Number of Units Produced, / Number of Hours Required for the Next Unit,50 / 4
75 / 3.3
125 / 2.7
350 / 1.75
700 / 1.3
1500 / 0.95
a. (2 points) Compute the logarithms of the numbers in each column. Use natural logs.
3.9120 / 1.38634.3175 / 1.1939
4.8283 / 0.9933
5.8579 / 0.5596
6.5511 / 0.2624
7.3132 / -0.0513
b. (4 points) Graph the ln(hours) against the ln(cumulative units) and eyeball a straightline fit of the data. Using your approximate fit, estimate slope and intercept.
From graph:
Intercept = 3.00
Slope = -0.40
Accept intercept 2.5 to 3.5
Accpet slope -0.3 to -0.5
Precise answers (not required):
Intercept = 3.02
Slope = -0.42
Graph: 2 points, slope 1 point, intercept 1 point
(Continued…)
c. (4 points) Using the results of part (b), estimate the time required to produce the first unit and the appropriate percentage learning curve that fits these data.
Time required to produce the first unit, = eintercept = e3.00 = 20.0855 hours
= -slope = 0.40
Rate of learning, = eslope(ln(2)) = e-0.40(0.6931) = 0.75.79
d. (2 points) Consider the learning curve derived in part (c). How much time will be required to produce the 2,000th unit, assuming the learning curve remains accurate.
The time required for the 2,000th unit is hours
Question 5: (12 points)
Green’s Buttons of Rolla, Missouri, supplies all the New Jersey Fabric stores with three different styles of buttons for men’s dress shirts. The plastic injection molding machine can produce only one button style at a time and requires substantial time to reconfigure the machine for different button styles. As Green’s has contracted to supply fixed quantities of buttons for the next four years, its demand can be treated as fixed and known. The relevant data for this problem are:
Button Type / Annual Sales / Production Rate (units/day) / Setup Time (hours) / Variable CostA / 30,000 / 500 / 5 / $0.30
B / 40,000 / 600 / 3 / $0.20
C / 15,000 / 400 / 8 / $0.40
Assume 8 hours in a day and 250 working days per year. Green’s accounting department established a 17 percent annual interest rate for the cost of capital and a 3 percent interest rate to account for storage space. Setup costs are $25 per hour required to reconfigure the equipment for a new style. Suppose that the firm decides to use a rotation cycle policy for production of the buttons.
a. (5 points) What is the optimal rotation cycle time?
Cycle time
Again, cycle time
Hence, cycle time,
b. (2 points) How large should the lots be?
units
units
units
c. (5 points) Compute the annual cost of holding and setups for each button type at the optimal solution. Compute the total annual cost of holding and setups at the optimal solution.
Button Type A:
Annual holding cost =
Annual setup cost =
Annual total cost = 324.2160+263.7130 = $587.9290
Button Type B:
Annual holding cost =
Annual setup cost =
Annual total cost = 277.7640+158.2278 = $435.9918
Button Type C:
Annual holding cost =
Annual setup cost =
Annual total cost = 241.7400+421.9409 = $663.6809
Hence, total annual cost = 587.9290+435.9918+663.6809 = $1,687.6017
Question 6: (13 points)
Bobbi’s Restaurant in Boise, Idaho is a popular place for weekend brunch. The restaurant serves real maple syrup with French toast and pancakes. Bobbi buys the maple syrup from a company in Maine that requires three weeks for delivery. The syrup costs Bobbi $4 a bottle and may be purchased in any quantity. Fixed costs of ordering amount to about $75 for bookkeeping expenses and holding costs are based on a 20 percent annual rate. Bobbi estimates that the loss of customer goodwill for not being able to serve the syrup when requested amounts to $25. Based on past experience, the weekly demand for the syrup is normal with mean 12 and variance 16 bottles. For the purpose of your calculations, you may assume that there are 52 weeks in a year and that all excess demand is backordered.
a. (5 points) How large an order should Bobbi be placing with her supplier for the maple syrup and when should the orders be placed? Find and .
Iteration 1
Step 1: units
Step 2:
(Table A-4)
Step 3: (Table A-4)
Step 4: 344.5292
(near 344.5292, the process may stop after finding )
Step 5:
(Table A-4)
An optimal policy is Q=345, R=51 (rounded to the nearest integer)
b. (1 point) What level of Type 1 service is being provided by the policy you found in part a?
Type 1 service,
c. (1 point) What level of Type 2 service is being provided by the policy you found in part a?
Type 2 service,
d. (2 points) What policy should Bobbi use if the stock-out cost is replaced with a Type 1 service objective of 95 percent?
Step 1: Set
Step 2: so (From Table A-4)
Step 3: units
An optimal policy is Q=342, R=47
e. (2 points) What policy should Bobbi use if the stock-out cost is replaced with a Type 2 service objective of 95 percent? (You may assume an EOQ lot size.)
Step 1: Set
Step 2:
From Table A-4,
for
for