Production Management Winter 2002 Odette School of Business University of Windsor. Midterm Exam 2 Solution Tuesday, March 26, 7:00 9:00 pm

Transcription

1 Name (print, please) ID Production Management Winter 00 Odette School of Business University of Windsor Midterm Exam Solution Tuesday, March 6, 7:00 9:00 pm Instructor: Mohammed Fazle Baki Aids Permitted: Calculator, straightedge, and a two-sided formula sheet. Time available: hours Instructions: This exam has 1 pages including this cover page and one page of table Please be sure to put your name and student ID number on each page. Show your work. Grading: Question Marks: 1 /10 /7 /6 4 /4 5 /8 6 /5 7 /9 8 /6 9 /10 Total: /65

2 Question 1: (10 points) Multiple Choice Questions 1.1 Suppose that we want to set up a kanban control system and want to determine the number of kanban card sets needed. If the expected demand during the lead time is 0 per hour, the safety stock is 0% of the demand during lead time, the container size is 10, and the lead time to replenish an order is 5 hours, what is the number of kanban sets? a. About b. About 4 c. About 18 d. About 0 e. About 6 1. Which of the following are related to JIT? a. A philosophy of waste reduction b. Pull production c. Multi-skilled workers d. Strong supplier relations e. All of the above 1. The costs of quality include which of the following? a. Appraisal costs b. Prevention costs c. Internal failure costs d. External failure costs e. All of the above 1.4 Lot for lot minimizes a. carrying cost b. ordering cost

3 1.5 Which of the following is the ISO 9000 form of certification that requires that a qualified national or international standards or certifying agency serve as an auditor? a. First party b. Second party c. Third party d. All of the above e. None of the above 1.6 Silver-Meal heuristic and least unit cost heuristic perform better if the costs a. change over time b. do not change over time 1.7 reduce setup time a. Cellular layouts b. Poka-yoke 1.8 The fact that the EOQ cost curve is flat near the optimal order quantity implies that a. if there are some managerial reasons to order Q units such that Q EOQ, but Qis near EOQ, then one may order Q units without causing a large increase in inventory cost b. inventory cost is not sensitive to the cost of buying items 1.9 Reduced material handling cost and setup time are advantages of a. cellular layouts b. job shops 1.10 Following charts are suitable for variable data: a. X and R charts b. p and c charts

4 Question : (7 points) Three jobs must be processed on a single machine that starts at 8:0 am. The processing times and due dates are given below: Job Processing Time (Hours) Due Date J1 11:0 am J 1:0 pm J 1 :0 pm Assuming that the jobs are processed in the sequence J1, J, J, compute makespan, total completion time, maximum lateness, and average tardiness. Job Start Time Processing Time Completion Time Due Date Lateness Tardiness J J J Makespan = 6 hours Total completion time = +5+6 = 1 hours Maximum lateness = max(-1,1,-1) = 1 hour Average tardiness = (0+1+0)/ = 1/ hour 4

5 Question : (6 points) Three jobs are to be scheduled on two machines M1 and M. Assume that every job is first processed on M1 and then on M. The processing times are as follows: Job M1 M J1 7 9 J 8 4 J 5 6 a. ( points) Using Johnson s algorithm for two-machine flow-shop, find a sequence of jobs in order to minimize makespan. In each iteration, show the job you assign and position to which the job is assigned. Iteration 1: J has min processing time, 4 on M. Assign J in the end, Position. Delete J. Positions 1 J Iteration : J has min processing time, 5 on M1. Assign J in the beginning, Position 1. Delete J. Positions 1 J J Iteration : Assign J1 in the remaining position. Positions 1 J J1 J b. ( points) Compute makespan given by the sequence obtained in part a. Job M1 M Start Process Finish Start Process Finish J J J Makespan = 5 5

6 Question 4: (4 points) Jumbo s restaurant is trying to create a consecutive days off schedule that uses the fewest workers. Use the following information to create a consecutive days off schedule: Day M Tu W Th F S Su Requirements 4 4 Days off for worker 1: Su, M M Tu W Th F S Su Worker Days off for worker : Tu, W M Tu W Th F S Su Worker 1 Days off for worker : W, Th M Tu W Th F S Su Worker Days off for worker 4: Su, M M Tu W Th F S Su Worker Hence, the solution is as follows: Two workers get days off on Su and M One worker gets days off on Tu and W One worker gets days off on W and Th 6

7 Question 5: (8 points) The following matrix contains the material handling costs (in thousand dollars) associated with assigning Machines 1, and to Locations A, B and C. Assign machines to locations to minimize material handling costs. State the optimal assignment and the associated cost. Machines Locations A B C 1 $50 $90 $ a. ( points) Show the matrix obtained after row reduction Machines Locations A B C b. ( points) Continue from part a and show the matrix obtained after column reduction Machines Locations A B C c. ( points) Continue from part b, and show the optimal solution Machines Locations A B C Hence, the optimal solution is: Machine 1 is assigned to location A Machine is assigned to location B Machine is assigned to location C d. ( points) What is the cost associated with the optimal assignment obtained in part c? Assignment Cost Machine 1 is assigned to location A $50 Machine is assigned to location B $90 Machine is assigned to location C $50 Total $140 7

8 Question 6: (5 points) Irwin sells a particular model of fan, with most of the sales being made in the summer months. Irwin makes a one-time purchase of the fans prior to each summer season at a cost of $0 each and sells each fan for $55. Any fans unsold at the end of summer season are marked down to $15 and sold in a special fall sale. a. What is the marginal loss per unit? ML = Purchase price salvage value = $0 $15 = $15 b. What is the marginal profit per unit? MP = Selling price purchase price = $55 $0 = $5 c. ( points) If the demand is uniformly distributed between 400 to 1400 units, find the optimal order quantity. ML 15 p = = = 0.75 ML + MP Q = b p b a = = ( ) ( ) 105 8

9 Question 7: (9 points) The annual demand for a product is 7,040 units. The weekly demand is 50 units with a standard deviation of 100 units. The cost to place an order is $50, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $.5 per unit. a. (4 points) Compute the optimal order quantity. Q = DS H = ( 7,040)( 50).50 = 1,040 units b. (5 points) Compute the reorder point necessary to provide a 98 percent service probability. For a 98 percent service probability, the area under the normal distribution curve on the left side of z, F( z ) = Hence, look for area = = 0.48 in the standard normal table From the standard normal table, z =. 055 for area = Hence, R dl + zσ = =, 491units = L 9

10 Question 8: (6 points) Charlie s Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be shipped directly from Italy. An American distributor stops by every five weeks to take orders. Because the orders are shipped directly from Italy, they take four weeks to arrive. Charlie s Pizza uses an average of 00 pounds of pepperoni each week, with a standard deviation of 40 pounds. Charlie s prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 98 percent probability of not stocking out on pepperoni. Assume that the sales representative just walked in the door and there are currently 1000 pounds of pepperoni in the walk-in cooler. How many pounds of pepperoni must be ordered? T = 5 weeks L = 4 weeks For a 98 percent probability of not stocking out, the area under the normal distribution curve on the left side of z, F( z ) = Hence, look for area = = 0.48 in the standard normal table From the standard normal table, z =. 055 for area = ( T + L) + zσ = 00 ( 5 + 4) +.055( 10) 1000 = 1, Q = d + I T L units 10

11 Question 9: (10 points) Comptek Computers wants to reduce a large stock of personal computers it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule if the store will purchase the personal computers in volume, as follows: Quantity Price 1-9 $ The annual inventory holding cost is 5%, the ordering cost is $160, and annual demand for this particular model is estimated to be 15 units. Compute the optimal order size. First, consider the cheapest price level of c = $900 per unit. h = Ic = = $5/unit/year Kλ ( 15)( 160) EOQ = = h 0.5( 900) = 1. units Since the price level of c = $900 is not available for an order quantity Q = EOQ = 1. units, EOQ is infeasible and a candidate for optimal order quantity is Q 50, because 50 is the minimum order quantity for the price level of c = $900. Now, consider the next price level, c = $95 per unit. h = Ic = = Kλ ( 15)( 160) EOQ = = h 0.5( 95) $1.5/unit/year = 1.15 = Since the price level of c = $95 is available for an order quantity Q = EOQ = 1.15 units, EOQ is feasible and a candidate for optimal order quantity is Q = It s not necessary to consider the other price level. Now, compute total cost for each candidate for optimal order quantity: j Q j Holding cost h Q j j Ordering cost Kλ Q j Cost of item λc j Total cost = Holding cost + Ordering cost + Cost of item Q = = 5, = $118,55 = 11,500 Q = = 1, = $118,667 = 115,65 Conclusion: The total cost is minimum, $118,55 for Q 50. Therefore, an optimal order quantity is Q = 50. = 11