Name:______ID:______
Production Management 73-604 Fall 2006
Odette School of Business
University of Windsor
Midterm Exam 2 Solution
Thursday, November 23, 5:30 – 6:50 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided one-page formula sheet.
Time available: 1 hour and 20 minutes
Instructions:
· This solution has 8 pages
· Please be sure to put your name and student ID number on each page.
· Show your work.
Grading:
Question Marks:
1 /10
2 /5
3 /10
4 /10
5 /10
6 /10
7 /10
Total: /65
Question 1: (10 points) Circle the most appropriate answer
1.1 Which of the following is false?
a. Inventory is defined in the textbook as the stock of any item or resource used in an organization
b. An inventory system is the set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be.
c. In inventory models, if you have high holding costs the model would tend to favor high inventory levels.
d. If there were no setup costs in an inventory modeling situation where we change from one product to another we would have small lots, reducing inventory levels and costs.
1.2 Which of the following is true?
a. Fixed-time period inventory models generate order quantities that vary from time period to time period, depending on the usage rate.
b. Fixed-order quantity systems assume a discontinuous counting of inventory on hand, with a less than immediate order when a reorder point is reached.
c. The standard fixed-time period model assumes that inventory is never counted but determined by EOQ measures.
d. Safety stock is not necessary in any fixed-time period model.
1.3 All firms keep a supply of inventory for which of the following reasons?
a. To maintain dependence dependence of operations.
b. To meet variation in product demand.
c. To have inflexibility in production scheduling.
d. All of the above.
1.4 A product structure tree can do which of the following?
a. Reduce product scrap.
b. Help to compute component usage.
c. Reduce labor overtime.
d. Reduce regular time labor.
1.5 Which of the following is false?
a. Priority rules are the rules used to obtain a job sequence in production scheduling.
b. The objective of Johnson’s rule for job sequencing is to minimize flow time from the beginning of the first job until finish of the last.
c. Johnson’s rule, a priority rule sued in sequencing production jobs is used only in production situations where we are dealing with one machine or one stage of production activity.
d. All of the above.
1.6 Inventory models designed to consider holding costs might include which of the following cost items?
a. Breakage
b. Order placing
c. Typing up an order
d. All of the above
1.7 Which of the following is false?
a. JIT is an integrated set of activities designed to achieve high-volume production using minimal inventories of raw materials, work in process, and finished goods.
b. A philosophy of operations management that seeks to eliminate waste in all aspects of a firm’s production activities, including human resources, vendor relations, technology, and the management of materials and inventories is often referred to as (Big) JIT.
c. A focused factory tends to be a small plant designed for one purpose.
d. A focused factory network under JIT is a large vertically integrated set of manufacturing facilities.
1.8 Which of the following is false?
a. It is impossible to have a zero-variability in production process.
b. An example of assignable variation in a production system may be caused by workers not being trained the same.
c. Variation that is inherent in a production process itself is called common variation.
d. The capability index is used to index economic changes in service systems.
1.9 You have just used the capability index formulas to compute the two values “min[1.5,1].” Which of the following is the interpretation of these numbers?
a. The true capability index value is 2.5.
b. The mean of the production process has shifted.
c. The mean of the production process has not shifted.
d. None of the above.
1.10 The assignment method is appropriate in solving scheduling problems that have which of the following characteristics?
a. There are “n” things to be distributed to “n” destinations.
b. Each thing must be assigned to one and only one destination.
c. Only one criterion can be used (e.g., minimize cost, maximize profit, etc.)
d. All of the above.
Question 2: (5 points) Three jobs must be processed on a single machine that starts at 8:30 am. The processing times and due dates are given below:
Job / Processing Time (Hours) / Due DateJ1 / 3 / 1:30 pm
J2 / 6 / 3:30 pm
J3 / 2 / 7:30 pm
Assuming that the jobs are processed in the sequence J1, J2, J3, compute makespan, total completion time, maximum lateness, and average tardiness.
Job / Start Time(Hours) / Processing Time
(Hours) / Completion Time
(Hours) / Due Date
(Hours) / Lateness
(Hours) / Tardiness
(Hours)
J1 / 0 / 3 / 3 / 5 / -2 / 0
J2 / 3 / 6 / 9 / 7 / 2 / 2
J3 / 9 / 2 / 11 / 11 / 0 / 0
Makespan = 11 hr.
Total completion time = 3+9+11 = 23 hr.
Maximum lateness = 2 hr.
Average tardiness = 2/3 = 0.6667 hr.
Question 3: (10 points) The weekly demand for a product is 600 units with a standard deviation of 120 units. The cost to place an order is $30, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $6 per unit.
a. (5 points) Compute the optimal order quantity.
units
units
b. (5 points) Compute the reorder point necessary to provide a 96 percent service probability.
units,units,
units
Question 4: (10 points) University Drug Pharmaceuticals orders its antibiotics every four weeks (28 days) when a salesperson visits from one of the pharmaceutical companies. Tetracycline is one of the most prescribed antibiotics, with average daily demand of 2,500 capsules. The standard deviation of daily demand was derived from examining prescriptions filled over the past three months and was found to be 600 capsules. It takes three days for the order to arrive. University Drug would like to satisfy 99 percent of the prescriptions. The salesperson just arrived, and there are currently 5,000 capsules in stock. Compute an optimal order size.
units
units
units
units
Question 5: (10 points) The following matrix contains the material handling costs (in thousand dollars) associated with assigning Machines 1, 2 and 3 to Locations A, B and C. Assign machines to locations to minimize material handling costs. State the optimal assignment and the associated cost.
Machines / LocationsA / B / C
1 / $50 / $80 / $75
2 / 90 / 100 / 110
3 / 70 / 50 / 65
a. (3 points) Show the matrix obtained after row reduction
Machines / LocationsA / B / C
1 / 0 / 30 / 25
2 / 0 / 10 / 20
3 / 20 / 0 / 15
b. (3 points) Continue from part a and show the matrix obtained after column reduction
Machines / LocationsA / B / C
1 / 0 / 30 / 10
2 / 0 / 10 / 5
3 / 20 / 0 / 0
c. (2 points) Continue from part b, and show the optimal solution
Machines / LocationsA / B / C
1 / 0 / 25 / 5
2 / 0 / 5 / 0
3 / 25 / 0 / 0
d. (2 points) What is the cost associated with the optimal assignment obtained in part c?
Machine 1 à Location A à Cost $50, Machine 2 à Location C à Cost $110
Machine 3 à Location B à Cost $50, Total cost 50+110+50 = $210.
Question 6: (10 points) Each unit of A is composed of two units of B and three units of C. Items A, B and C have on-hand inventories of 40, 50 and 60 units respectively. Item B has a scheduled receipt of 30 units in period 1. Lot-for-lot (L4L) is used for Item A. Item B is required to be purchased in multiples of 100. Item C requires a minimum lot size of 50 units. Lead times are one period Item A and two periods for each of the Items B and C. The gross requirements for A are 40 in Period 5, 30 in Period 7, and 80 in Period 9. Find the planned order releases for all items to meet the requirements over the next 10 periods.
a. (3 points) Construct a product structure tree.
b. (3 points) Consider Item A. Find the planned order releases and on-hand units in period 10
Period
/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10Item
A
LT= 1
Q= L4L / Gross Requirements / 40 / 30 / 80
Scheduled receipts
On hand from prior period / 40 / 40 / 40 / 40 / 40 / 0 / 0 / 0 / 0 / 0
Net
requirements / 30 / 80
Time-phased Net Requirements / 30 / 80
Planned order releases / 30 / 80
Planned order delivery / 30 / 80
c. (2 points) Consider Item B. Find the planned order releases and on-hand units in period 10.
Period
/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10Item
B
LT= 2
Q = 100 / Gross Requirements / 60 / 160
Scheduled receipts / 30
On hand from prior period / 50 / 80 / 80 / 80 / 80 / 80 / 20 / 20 / 60 / 60
Net
Requirements / 140
Time-phased Net Requirements / 140
Planned order releases / 200
Planned order delivery / 200
d. (2 points) Consider Item C. Find the planned order releases and on-hand units in period 10.
Period
/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10Item
C
LT= 2
Q>=
50 / Gross Requirements / 90 / 240
Scheduled receipts
On hand from prior period / 60 / 60 / 60 / 60 / 60 / 60 / 20 / 20 / 0 / 0
Net
requirements / 30 / 220
Time-phased Net Requirements / 30 / 220
Planned order releases / 50 / 220
Planned order delivery / 50 / 220
Question 7: (10 points) A single inventory item is ordered from an outside supplier. The anticipated demand for this item over the next 7 months is 12, 15, 13, 11, 9, 10, 13. Current inventory of this item is 4, and the ending inventory should be 5. Assume a holding cost of $3 per unit per month and a setup cost of $60. Assume a zero lead time. Determine the order policy for this item over the next 7 months.
Use the Least Total Cost (LTC) heuristic.
Months / Q / I1 / I2 / I3 / I4 / I5 / I6 / I7 / Holding cost / Ordering cost / Difference1-1 / 8 / 0 / 0 / 60 / 60
1-2 / 23 / 15 / 0 / 45 / 60 / 15
1-3 / 36 / 28 / 13 / 0 / 123 / 60 / 63
3-3 / 13 / 0 / 0 / 60 / 60
3-4 / 24 / 11 / 0 / 33 / 60 / 27
3-5 / 33 / 20 / 9 / 0 / 87 / 60 / 27
3-6 / 43 / 30 / 19 / 10 / 0 / 177 / 60 / 117
6-6 / 10 / 0 / 0 / 60 / 60
6-7 / 28 / 18 / 0 / 54 / 60 / 6
Use the table above to show your computation and summarize your order policy below:
Month / Quantity ordered1 / 23
3 / 33
6 / 28
Note: alternate solution is as follows
Month
/ Quantity ordered1 / 23
3 / 24
5 / 19
7 / 18
7