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1 Name (print, please) ID Operations Management I 7- Winter 00 Odette School of Business University of Windsor Midterm Exam I Solution Wednesday, ebruary, 0:00 :0 pm Last Name A-S: Odette B0 Last Name T-Z: Odette 09 Instructor: Mohammed azle Baki Aids Permitted: Calculator, straightedge, and a one-sided formula sheet. Time available: hour 0 min Instructions: This exam has 8 pages including this cover page. Please be sure to put your name and student ID number on each page. Show your work. Grading: Question Marks: /0 / / 4 / 5 / 6 / Total: /65

2 Question : (0 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. The nd unit costs $00, and the 8 th unit $64. What is the rate of learning? a. 00% b. 80% c. 64% d. 50% e. None of the above. Economies of scale can be represented as a. a < b. a c. a > f a ( y) ky where, k is a constant and. Best operating level refers to a. the number of units produced in the most recent period b. peak capacity c. design capacity d. average capacity used.4 Aggregate forecasts are less accurate than disaggregate forecasts. a. True b. alse.5 Master production scheduling is done before aggregate planning a. True b. alse.6 In a level strategy a. a constant amount of inventory is maintained b. shortages are not allowed c. both of the above d. none of the above.7 The exponential smoothing method is designed for a. stationary series b. time series with trend c. time series with seasonality d. time series with trend and seasonality

3 b.8 Learning curve is represented as Y ( u) au a. Intercept b. Slope c. Rate of learning d. The time/cost required by the st unit e. ln( L) / ln( ). What is a?.9 Which of the following is an input to the aggregate production planning? a. Current level of resources b. Level of resource required to meet the demand forecast c. Both of the above d. None of the above.0 Which of the following is a smoothing cost? a. The cost of holding inventory b. Backorder cost c. Straight time cost d. Overtime cost e. Cost of hiring workers

4 Question : ( points) Based on past experience, an oil company estimates that the construction cost of new refineries obeys the law f ( y) 0.04y, where y is measured in barrels per day and f ( y) in millions of dollars. Demand is growing at a constant rate of.5 million barrels per year (assume 65 days per year) and the discount rate for future costs is 5 percent. a. ( points) If the size of the refinery is doubled, what is the percentage increase in the construction costs? ( y) ( y) ( y ) ( y) 0.5 f f ( points) Hence, the cost increases by 4.40% ( point) b. ( points) Determine the optimal timing of plant additions. igure -4 is reproduced below. a 0.5 Hence, from igure -4, rx. ( point) rx. x 4.8 years ( points, including point for unit) r 0.5 c. ( points) Determine the optimal size of each plant addition. Size of each plant addition, ( 4.8)(.5) 6 xd million barrels ( points, including point for unit) d. ( points) Determine the optimal cost of each plant addition. Size of each capacity addition 6,000,000 6, 48barrels per day (0.5 point) 65 Hence, cost, f ( y) 0.04y 0.04( 6,48) 6. 7 (.5 points, including 0.5 point for unit) million dollars unction a igure u rx 4

5 Question : ( points) Observed weekly sales of ball peen hammers at the town hardware store over a six-week period have been 5, 8, 0, 7,,. a. ( points) Suppose that three-week moving averages are used to forecast sales. Determine the onestep-ahead forecasts for weeks 4 through 6. D + D + D + D + D + D4 + D D 4 5 D 5 6 ( point) 5( point) 0( point) b. (4 points) Suppose that exponential smoothing is used with a smoothing constant of α 0.5. ind the exponential smoothing forecasts for weeks 5 and 6. (To get the method started, use the same forecast for week 4 as you used in part a.) 4 (rom part a) αd + α ( ) 4 ( 0.5)( 7) + ( 0.5)( ). 5 ( α) ( 0.5)( ) + ( 0.5)(.5) αd5 + 5 ( points) ( points) c. (4 points) Based on the MAD values given by the forecasts of weeks 5 and 6, which method did better? -week moving average: E D E6 6 D6 0 9 E5 + E MAD 8.5(.5 points) Exponential smoothing: E D E6 6 D E5 + E MAD 7.5 (.5 points) Based on MAD values, exponential smoothing is better. ( point) 5

6 Question 4: ( points) Here are the data for the past months of actual sales of a particular product: Month Actual Demand 0 4 a. (7 points) Calculate the double exponential smoothing forecasts 0, and, using S 0 0, G 0, α0.0, and β 0.5. Month t Actual demand 0 S S t G t t-,t αd + ( α)( S0 + G0 ) ( 0.)( 0) ( 0.)( 0 + ) ( points) G + β( S S0 ) ( β) G0 ( 0.5)( 0.8 0) ( 0.5)( ) ( points) 0, S + G ( points) ( point), S + G 0 b. ( points) What is,? S G ( α)( S + ) ( 0.0)( 4) + ( 0.0)( ) αd + G ( S S ) + ( β) ( 0.5)( ) + ( 0.5)( 6.45) β G, S + G ( point) ( point) ( point) c. ( point) What is, 5? ( ) ( ) ,5 S + 5 G ( point) 6

7 Question 5: ( 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 000, 00 and 800, expressed in thousands of cookies. During a 40-day period when there were 0 workers, the company produced.9 million cookies. Assume that the numbers of workdays over the three months are respectively 4, and 0. There are currently 80 workers employed, and there is no starting inventory of cookies. a. (6 points) What is the minimum constant workforce (level strategy) required to meet demand (shortages not allowed) over the next three months? b. (5 points) Assume that the inventory holding cost is 0 cents per cookie per month, hiring cost is $00 per worker, and firing cost is $00 per worker. Evaluate the cost of the plan derived in a. 7

8 Question 6: ( points) You ve recorded production time of a major product and found the processing time for each unit as follows: Unit Number, u Time (Hours), Y(u) a. ( points) Compute the logarithms of the numbers in each column (use natural logs). b. (6 points) Using the linear regression method on ln(u) and ln(y(u)) values, derive the slope and intercept of the regression line. ( 4)( 4.676)(.685) ( 4)( 4.676) xy nxy 5.48 Slope x nx x ( x) ( 4)( 5.48) ( )( 6.479) ( 4)( 79.55) ( ) n xy y Slope n x ( 0.)( 4.676). 988 Intercept y bx.685 ( point) -0. or, using another formula 0. ( point) c. ( points) Estimate the learning curve parameters. What is the time required to produce the first unit? What is the rate of learning? The time required to produce the st Intercept.988 unit, a e e hours ( point) b slope ( ) The rate of learning, L e slope ( ln( ) ) e 0.ln() e e 0.5 d. ( point) How much time will it be required to produce the,000 th unit? b 0. Y u au hours ( point) ( ) ( ) % ( point) 8