Name:______ID:______
Operations Management I 73-331 Fall 2003
Odette School of Business
University of Windsor
Final Exam Solution
Monday, December 15, 8:30 – 11:30 a.m.
Chrysler Hall North G 133
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and 3 one-sided formula sheets.
Time available: 3 hours
Instructions:
· This exam has 34 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 / /10
3 / /6 / 4 / /12
5 / /4 / 6 / /12
7 / /9 / 8 / /8
9 / /10 / 10 / /5
11 / /9 / Total / /100
Question 1: (15 points) Circle the most appropriate answer
1.1 Consider estimating learning curve parameter values using regression on and . What is a best interpretation of intercept, ?
a. The slope is
b. The slope is
c. An estimate of the time required by the first unit is
d. An estimate of the time required by the first unit is
1.2 Consider the EOQ model with price breaks. The optimal solution is
a. the cheapest realizable EOQ
b. one of the EOQs
c. one of the breakpoints
d. the cheapest realizable EOQ or a cheaper breakpoint
1.3 Forecasting error is described by
a. weighted moving average
b. mean absolute deviation
c. both
d. none
1.4 The dynamic capacity addition model assumes all of the following except
a. a constant rate of increase of demand over a finite planning horizon
b. the same capacity addition at an equal interval of time
c. economies of scale
d. continuous compounding
1.5 Which of the following are advantages of the Exponential Smoothing model?
a. Less computation
b. Less memory requirement
c. Both
d. None
1.6 Smoothing cost includes
a. cost to advertise and interview candidates
b. severance pay
c. both
d. none
1.7 Chase strategy attempts to produce
a. a constant amount each period
b. as much as needed
c. both
d. none
1.8 Annual holding cost and is the same as annual ordering/setup cost at
a. EOQ and EPQ
b. EOQ but not EPQ
c. EPQ but not EOQ
d. none of the above
1.9 Which of the following is not a characteristic of the rotation cycle policy?
a. There is only one setup for each product in each cycle
b. The products are produced in the same sequence in each cycle
c. Only one product is produced at any time
d. For each product, the economic production quantity (EPQ) is produced in each cycle
1.10 To find an optimal policy with Type II service, the penalty cost is
a. not estimated
b. estimated from the cost of backorder
c. estimated from the cost of lost sales
d. computed using the standardized loss function
1.11 Which of the following is not an input to the MRP system?
a. The production schedule of the finished products
b. The production schedule of the components/subassemblies
c. Bill of Materials
d. Inventory records
1.12 Which of the following is not an assumption in the space constraint model?
a. A known, fixed and uniform demand rate
b. Known and fixed cost parameters
c. A single product carried in the inventory
d. The same order size every cycle
1.13 Least Unit Cost (LUC) method performs best if
a. the production environment is make-to-order or assemble-to-order
b. the production environment is make-to-stock or assemble-to-stock
c. inventory costs do not change over time
d. inventory costs change over time
1.14 Andon
a. is the authority to stop a production line
b. makes problems visible
c. lights signal quality problems
d. prevents defects
1.15 The policy is used for
a. multi-period component/subassemblies
b. multi-period finished products
c. single-period discrete demand
d. single-period continuous demand
Question 2: (10 points)
A Japanese steel manufacturer is considering expanding operations. From experience, it estimates that new capacity additions obey the law , where the cost, , is measured in millions of dollars and is measured in tons of steel produced. If the demand for steel is assumed to grow at the constant rate of 3,000 tons per year and future costs are discounted using a 16 percent discount rate
a. (2 points) Determine the optimal timing of plant additions.
b. (2 points) Determine the optimal size of each addition.
Optimal size =
c. (2 points) If the size of the refinery is doubled, what is the percentage increase in the construction costs?
d. (2 points) If a plant size of 30,000 tons per year costs 18 million dollars, find .
e. (2 points) Continue from parts a, b and d. What is the present cost of the next 2 additions? The first one is added today and the second one after the number of years obtained in part a.
Present cost
Question 3: (6 points)
The Paris Paint Company is in the process of planning labor force requirements and production levels for the next four quarters. The marketing department has provided production with the following forecasts of demand for Paris Paint over the next year:
Quarter / Demand Forecast(in thousands of gallons)
1 / 450
2 / 800
3 / 750
4 / 200
Assume that there are currently 275 employees with the company. Employees are hired for at least one full quarter. Hiring costs amount to $400 per employee and firing costs are $800 per employee. Inventory costs are $0.25 per gallon per quarter. It is estimated that one worker produces 1,500 gallons of paint each quarter. Assume that Paris currently has 200,000 gallons of paint in inventory and would like to end the year with an inventory of at least 300,000 gallons.
a. (3 points) Determine the minimum constant workforce plan (i.e., level strategy) for Paris Paint. Assume that stock-outs are not allowed.
Quarter / Production Requirement(000 gallons) / Cumulative Production Requirement
(000 gallons) / Units Produced Per Worker
(000 gallons) / Cumulative Units Produced Per Worker
(000 gallons) / Workers Required
1 / 450-200=250 / 250 / 1.5 (given) / 1.5 /
2 / 800 / 250+800=1,050 / 1.5 / 3 / *
3 / 750 / 1,050+750=1,800 / 1.5 / 4.5 /
4 / 200+300=500 / 1,800+500=2,300 / 1.5 / 6 /
Since the maximum workers required is 400, the minimum constant workforce plan must use 400 workers. So, the number of workers to hire = 400 – 275 = 125 workers.
b. (3 points) Determine the hiring, firing, and inventory holding cost of the plan derived in part a.
Quarter / Beginning Inventory(000 gallons) / Production
(000 gallons) / Ending Inventory = Production + Beginning Inventory – Demand
(000 gallons)
1 / 200 / 400(1.5)=600 / 600+200-450=350
2 / 350 / 600 / 600+350-800=150
3 / 150 / 600 / 600+150-750=0
4 / 0 / 600 / 600+0-200=400
Total ending inventory = (350+150+0+400) = 900 thousand gallons
Inventory holding cost = 900,000 ´ 0.25 = $225,000
Hiring cost = 125(400) = $50,000
Total cost = 225,000+50,000 = $275,000
Question 4: (12 points)
A popular brand of tennis shoe has had the following demand history by quarters over a two-year period.
Quarter2002 / Demand / Quarter
2003 / Demand
1 / 25 / 1 / 33
2 / 35 / 2 / 47
3 / 45 / 3 / 55
4 / 40 / 4 / 50
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 / 25 / 38.5 / 0.649350649
2 / 35 / 38.5 / 0.909090909
3 / 45 / 37.25 / 1.208053691
4 / 40 / 36.25 / 39.75 / 1.006289308
5 / 33 / 38.25 / 42.5 / 0.776470588
6 / 47 / 41.25 / 45 / 1.044444444
7 / 55 / 43.75 / 43.75 / 1.257142857
8 / 50 / 46.25 / 43.75 / 1.142857143
Final
Seasonal / Seasonal
Period / Factors / Factors
1 / 0.71291062 / 0.7135
2 / 0.97676768 / 0.9775
3 / 1.23259827 / 1.2336
4 / 1.07457323 / 1.0754
Total / 3.9968498 / 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 / 35.03989219 / 35.03989219 / 1
2 / 35.80425166 / 71.60850331 / 4
3 / 36.47949307 / 109.4384792 / 9
4 / 37.1947644 / 148.7790576 / 16
5 / 46.25265769 / 231.2632884 / 25
6 / 48.07999508 / 288.4799705 / 36
7 / 44.58604708 / 312.1023296 / 49
8 / 46.4934555 / 371.947644 / 64
Sum / 36 / 329.9305567 / 1568.659165 / 204
Average / 4.5 / 41.24131958
c. (4 points) Predict the demand of all quarters of 2004. Plot the original demand of 2002-2003 and predicted demand of 2004.
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 5: (4 points)
Green City sells a particular model of lawn mower, with most of the sales being made in the summer months. Green city makes a one-time purchase of the lawn mowers prior to each summer season at a cost of $150 each and sells each lawn mower for $210. The demand is normally distributed with a mean of 1200 and a standard deviation of 80. Find the optimal order quantity if
a. (2 points) any lawn mower unsold at the end of summer season are marked down to $75 and sold in a special fall sale.
Selling price – purchase price = 210-150 = $60/unit
Purchase price – salvage value = 150-75 = $75/unit
For the optimal order quantity , Probability(demand ),
Find the standard normal -value for which cumulative area on the left, .
Using Table A-1
Table A-1 gives the area between and positive -values.
Since the -value is negative and corresponds to area = 0.50-0.4444 = 0.0556
Hence,
Using Table A-4
Since the -value is negative and corresponds to
Hence,
units
b. (2 points) any lawn mower unsold at the end of summer season are marked down to $120 and sold in a special fall sale.
Selling price – purchase price = 210-150 = $60/unit
Purchase price – salvage value = 150-120 = $30/unit
For the optimal order quantity , Probability(demand ),
Find the standard normal -value for which cumulative area on the left, .
Using Table A-1
Table A-1 gives the area between and positive -values.
Since the -value is positive and corresponds to area = 0.6666-0.50 = 0.0166
Hence,
Using Table A-4
Since the -value is positive and corresponds to
Hence,
units
Question 6: (12 points)
Suppose that Item A has a production rate of 1,152 items per year, unit cost of $16.00, a setup cost of $144, and a monthly demand of 48 units. It is estimated that cost of capital is approximately 20 percent per year. Storage cost amounts to 3 percent and breakage to 2 percent of the value of each item.
a. (2 points) Compute EPQ of Item A.
units per year
per unit per year
units per year
EPQ, units
b. (3 points) What are the maximum inventory and cycle time of Item A? What is the percentage of idle time of the facility if the facility is dedicated to produce Item A only?
Maximum inventory, units
Cycle time, year
Uptime, year, Downtime, year
Percentage of downtime in each cycle =
Item B has a production rate of 1500 items per year, a unit cost of $32.00, an ordering cost of
$90.90, and a monthly demand of 30 units. Recall that the cost of capital is approximately 20 percent per year. Storage cost amounts to 3 percent and breakage to 2 percent of the value of each item.
c. (2 points) What is the cycle time if both Items A and B are produced in a single facility? Consider negligible setup times for both Items A and B.
=0.375 years
d. (5 points) Continue from part c. What are the maximum inventory of Items A and B? What is the percentage of idle time of the facility if the facility is used to produce only Items A and B?
units
units
Uptime of A, years
Uptime of B, years
Maximum inventory, units
Maximum inventory, units
Idle time = years in each cycle
Hence, percentage of idle time = 26%
Question 7: (9 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 360 radios each year. The annual demand follows a normal distribution with a standard deviation of 60. The store pays $80 for each radio. The holding cost is 25 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. Replenishment lead-time is three weeks. Assume 48 weeks in a year.