Name:______ID:______

Operations Management I 73-331 Winter 2001

Faculty of Business Administration

University of Windsor

Midterm Exam I Solution

Tuesday, February 13, 10:00 – 11:10 am

Instructor: Mohammed Fazle Baki

Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.

Time available: 1 hour 10 min

Instructions:

·  This exam has 8 pages.

·  Please be sure to put your name and student ID number on each page.

·  Show your work.

Grading:

Question Marks:

1  /5

2  /5

3  /8

4  /6

5  /6

6  /10

Total: /40


Question 1: ( 5 points)

An analyst predicts that an 80 percent experience curve should be an accurate predictor of the cost of producing a new product. Suppose that the cost of the first unit is $2,000. What would he predict is the cost of producing 50th unit?

Answer


Question 2: ( 5 points)

An oil company believes that the cost of construction of new refineries obeys a relationship of the type where is measured in units of barrels per day and in millions of dollars. From the past experience, each doubling of the size of a refinery at a single location results in an increase in the construction costs of about 80 percent. Furthermore, a plant size of 20,000 barrels per day costs $10 million. Find the values of k and a.

Answer


Question 3: ( 8 points)

Observations of the demand for a certain part stocked at a part supply depot during the calendar year of 2000 were:

Month / Demand / Month / Demand
January
/ 89 / April / 221
February / 57 / May / 177
March / 144 / June / 280

a.  (3 points) Using a three-month moving average method, determine the forecasts for April through June 2000.

Answer

b.  (3 points) Using an exponential smoothing method with and a March forecast of 150, determine the forecasts for April through June 2000.

Answer

c.  (2 points) For each method in (a) and (b), compute MAD. Based on the MAD values, comment on which method to use.

Answer

(1 point)

Use Exponential smoothing method, which has a MAD 71.15 < 86.67 (1 point)


Question 4: ( 6 points)

Here are the data for the past 4 months of actual sales of a particular product:

Month / Actual Demand
1 / 220
2 / 227
3 / 229
4 / 234

a.  (5 points) Calculate the double exponential smoothing forecasts for months 1-4 using S0=210, G0=10, a=0.10, and b = 0.20.

Answer

Month
t / Actual
demand / St
(2 points) / Gt
(2 points) / Ft-1,t
(1 point)
1 / 220 / 0.1(220)+0.9(220)
=220 / 0.2(220-210) +0.8(10)=10 / 210+10
=220
2 / 227 / 0.1(227)+0.9(230)
=229.7 / 0.2(229.7-220) +0.8(10)=9.94 / 220+10
=230
3 / 229 / 0.1(229)+0.9(239.64)
=238.576 / 0.2(238.576-229.7) +0.8(9.94)=9.7272 / 229.7+9.94
=239.64
4 / 234 / 0.1(234)+0.9(248.3032)
=246.87 / 0.2(246.87-238.576) +0.8(9.7272)=9.4411 / 238.576+9.7272
=248.3032

b.  (1 point) What is F4,6?

Answer

F4,6 = S4 +2G4 =246.87+2(9.4411) = 265.76


Question 5: ( 6 points)

Windsor Swiss Milk Products manufactures and distributes ice cream in Ontario. The company wants to expand operations by locating another plant in northern Sarnia. The size of the new plant will be a function of the expected demand for ice cream within the area served by the plant. A market survey is currently under way to determine that demand. Windsor Swiss wants to estimate the relationship between the manufacturing cost per gallon and the number of gallons sold in a year to determine the demand for ice cream and thus the size of the new plant. The following data have been collected:

Plant / Thousands of Gallons Sold, X / Cost per Thousand Gallons, Y
1 / 416.9 / $1,015
2 / 472.5 / 973
3 / 250.0 / 1,046
4 / 372.1 / 1,006

a.  (5 points) Develop a regression equation to forecast the cost per gallon as a function of the number of gallons produced.


Answer

(3 points)


b.  (1 point) Suppose that the market survey indicates a demand of 325,000 gallons in Sarnia. Estimate the manufacturing cost per gallon for a plant producing 325,000 gallons per year.

Answer


Question 6: ( 10 points)

Windsor Cookie Company makes a variety of chocolate chip cookies. Based on orders received and forecasts of buying habits, it is estimated that the demand for the next three months is 700, 1000, and 900, expressed in thousands of cookies. Historically, each worker produces 250 cookies per working day. Assume that the numbers of workdays over the three months are respectively 25, 20 and 16. There are currently 75 workers employed, and there are 200 thousand cookies in the inventory.

a.  (5 points) What is the minimum constant workforce required to meet demand over the next three months?

Answer

Month / Production
Required / Cumulative Net ProductionRequired
(2 point) / Number of Working Days / Cumulative Number of Working Days / Cumulative Number of Units Produced Per Worker / Number of Workers Needed
(2 points)
1 / 700-200=500 / 500 / 25 / 25 / 25´250=6250 / 500,000/6250
=80
2 / 1000 / 1500 / 20 / 45 / 45´250=11250 / é1,500,000/11250ù
=é133.33ù=134
3 / 900 / 2400 / 16 / 61 / 61´250=15250 / é2,400,000/15250ù
=é157.38ù=158

Minimum number of workers needed to meet the demand = 158 (1 point)

(Continued…)

b.  (5 points) Assume that the inventory holding cost is 20 cents per cookie per month, cost of hiring is $200 per worker hired and cost of firing is $300 per worker fired. Evaluate the cost of the plan derived in (a).

Answer

Number of workers hired = 158-75=83

Hiring cost = 83 ´ 200 = $16,600 (1 point)

Month / Production Required / Beginning Inventory / Actual Production
(1 point) / Ending Inventory
1 / 700,000 / 200,000 / (158)(25)(250)=987,500 / 487,500
2 / 1000,000 / 487,500 / (158)(20)(250)=790,000 / 277,500
3 / 900,000 / 277,500 / (158)(16)(250)=632,000 / 9,500
Total / 774,500

Inventory holding cost = 774,500(0.2)=$154,900 (1 point)

Total cost = $16,600 + $154,900 = $171,500 (2 points)

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