Name:______ID:______

Operations Management I 73-331 Fall 2001

Odette School of Business

University of Windsor

Final Exam Solution

Saturday, December 15, 7:00 – 10:00 p.m.

CAW Centre Ambassador Auditorium Rows A-C

Instructor: Mohammed Fazle Baki

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

Time available: 3 hours

Instructions:

  • This solution has 13 pages including this cover page
  • It’s not necessary to return the unused blank pages and tables
  • Please be sure to put your name and student ID number on each page
  • Show your work

Grading:

Question / Score / Question / Score
1 / /15 / 2 / /3
3 / /6 / 4 / /8
5 / /8 / 6 / /6
7 / /6 / 8 / /8
9 / /8 / 10 / /8
11 / /8 / 12 / /8
13 / /8 / Total / /100

Question 1: (15 points)

1.1The MRP report is sent to the following departments:

  1. production and finance
  2. production and purchasing

1.2 Lot for lot minimizes

  1. carrying cost
  2. ordering cost

1.3Silver-Meal heuristic and least unit cost heuristic perform better if the costs

  1. change over time
  2. do not change over time

1.4 ______reduce setup time

  1. Cellular layouts
  2. Poka-yoke

1.5Cellular layouts

  1. distribute work-load evenly
  2. often yield poorly balanced cells

1.6Following is a trend in supplier policies:

  1. Identify suppliers who may supply in large volumes and minimize number of orders
  2. Identify suppliers near to the customer

1.7The fact that the EOQ cost curve is flat near the optimal order quantity implies that

  1. if there are some managerial reasons to order units such that EOQ, but is near EOQ, then one may order units without causing a large increase in inventory cost
  2. inventory cost is not sensitive to the cost of buying items

1.8Which of the following is an input to the aggregate production planning?

  1. Level of resources needed
  2. Level of resources available

1.9Which of the following is a shortage cost?

  1. The cost of hiring workers to avoid shortages
  2. The loss of profit due to shortages

1.10What of the following is a level strategy?

  1. Keeping a constant level of inventory
  2. Keeping a constant level of workforce

1.11Forecasts are always

  1. long-term
  2. wrong

1.12Exponential smoothing is designed for

  1. stationary series
  2. series with trend

1.13Which of the following uses less memory?

  1. Moving average
  2. Exponential smoothing

1.14Moving average and exponential smoothing lag behind a trend, if one exists.

  1. True
  2. False

1.15Linear regression is always applied

  1. on log(x) and log(y)
  2. to explain how one variable changes due to the change of some other variable(s)

Question 2: (3 points)

A supplier of instrument gauge clusters uses a kanban system to control material flow. The gauge cluster housings are transported five at a time. A fabrication centre produces approximately 16 gauges per hour. It takes approximately two hours for the housing to be replenished. Due to variations in processing times, management has decided to keep 25 percent of the needed inventory as safety stock. How many kanban card sets are needed?

Kanban card sets needed

Question 3: (6 points)

One unit of A is made of one unit of B, and one unit of C. B is made of two units of C.

  1. (3 points) Construct a product structure tree.
  1. (3 points) Suppose that the gross requirement of A is 100 units. Items A, B and C have on-hand inventories of 20, 30 and 70 units respectively. Find the net requirement of C.

Gross requirement, A / 100
Less item A in inventory / 20
Net requirement, A, 100-20 = / 80
Gross requirement, B / 80
Less item B in inventory / 30
Net requirement, B, 80-30 = / 50
Gross requirement, C: 80+50(2) = / 180
Less item C in inventory / 70
Net requirement, C, 180-70 / 110

Question 4: (8 points)

The MRP gross requirements for Item X are shown here for 4 weeks. Lead time for A is one week, and setup cost is $8. There is a carrying cost of $0.30 per unit per week. Beginning inventory is 30 units in Week 1.

Week
1 / 2 / 3 / 4
Gross requirements / 30 / 20 / 30 / 40
  1. (3 points) Use the EOQ method to determine when and for what quantity the first order should be released.

Order 40 units in Week 1

  1. (5 points) Use the least unit cost heuristic to determine when and for what quantity the first order should be released.

Order for weeks / Order quantity, Q / Inventory after Week 1 / Inventory after Week 2 / Inventory after Week 3 / Holding cost / Ordering cost / Unit cost
2 / 20 / 0 / 0 / 8 / 0.40
2,3 / 50 / 30 / 0 / 9 / 8 / 0.34
2,3,4 / 90 / 70 / 40 / 0 / 33 / 8 / 0.45

Since the unit cost is minimum for an order size of 50 units in Week 1, order 50 units in Week 1.

Question 5: (8 points)

Following are the net requirements, production capacities and production plan of a product:

Month
1 / 2 / 3 / 4
Net requirements (units) / 40 / 30 / 90 / 60
Production capacities (units) / 70 / 70 / 70 / 70
Production plan (units) / 40 / 50 / 70 / 60
  1. (2 points) Is the above production plan feasible? If the production plan is not feasible, what is the first month of shortage?

Month / Production / Requirement / Cumulative production / Cumulative requirement
1 / 40 / 40 / 40 /  / 40
2 / 50 / 30 / 40+50=90 /  / 40+30=70
3 / 70 / 90 / 90+70=160 /  / 70+90=160
4 / 60 / 60 / 160+60=220 /  / 160+60=220

Since in each month cumulative production is larger than the cumulative requirement, the production plan is feasible.

  1. (4 points) Suppose that the setup cost is $250 and holding cost is $2/unit/month. If the above production plan is feasible, can you find an improved production plan? If the above production plan is not feasible, what is the minimum amount by which the monthly production capacity must be increased in order to make the above production plan feasible?

Month / Production / Capacity / Excess capacity
1 / 40 / 70 / 70-40=30
2 / 50 / 70 / 70-50=20
3 / 70 / 70 / 70-70=0
4 / 60 / 70 / 70-60=10

It is not possible to back-shift production of any month to any previous month(s). Hence, no improvement is possible.

  1. (2 points) Suppose that the production capacities change to 60 units per month. If there exists any feasible production plan with these new capacities, then state a feasible production plan. If there does not exist any feasible production plan with these new capacities, then what is the first month of shortage?

Month / Capacity / Requirement / Cumulative capacity / Cumulative requirement
1 / 60 / 40 / 60 /  / 40
2 / 60 / 30 / 60+60=120 /  / 40+30=70
3 / 60 / 90 / 120+60=180 /  / 70+90=160
4 / 60 / 60 / 180+60=240 /  / 160+60=220

Since in each month cumulative capacity is larger than the cumulative requirement, there exists a feasible production plan.

The following production plan is obtained by lot-shifting technique:

Month / Requirement / Capacity / Production
1 / 40 / 60 / 40
2 / 30 / 60 / 30 30+30 = 60
3 / 90 / 60 (shortage 30 units) / 60
4 / 60 / 60 / 60

Hence, produce 40, 60, 60 and 60 units respectively in Months 1, 2, 3 and 4.

Question 6: (6 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. Suppose that the first unit costs $300, and the second unit $240.

  1. (2 points) What is the rate of learning?
  1. (2 points) Compute the cost of producing the 4th unit based on the learning curve.

Unit / Cost
1 / $300
2 / 300(0.80)=$240
4 / 240(0.80)=$192
  1. (2 points) Compute the cost of producing the 17th unit based on the learning curve.

Question 7: (6 points)

Suppose that Item A has a unit cost of $30, an ordering cost of $25, and an annual demand of 300 units. It is estimated that the holding cost is 20 percent per year.

  1. (3 points) Compute EOQ of Item A.
  1. (3 points) Suppose that both Items A and B should be purchased and there is only $2000 available for buying Items A and B. The unit cost of Item B is $5 and the EOQ of Item B is 200 units. What is the optimal order quantity of Item A?

Cost of EOQ units of A, EOQA = 5030 = $1,500

Cost of EOQ units of B, EOQB = 200 5 = $1,000

Fund required = $2,500

Order quantity of A,

Question 8: (8 points)

Suppose that Item A has a production rate of 400 items per year. The cost and demand information of Item A are the same as those stated in Question 7. That is, Item A has a unit cost of $30, an ordering cost of $25, and an annual demand of 300 units. It is estimated that the holding cost is 20 percent per year.

  1. (3 points) Compute EPQ of Item A.

  1. (1 point) What is the cycle time of Item A?

Item C has a production rate of 2000 items per year, a unit cost of $100.00, an ordering cost of $50, and an annual demand of 400 units. Items A and C have the same holding cost i.e. 20 percent per year.

  1. (3 points) What is the cycle time if both Items A and C are produced in a single facility and a rotation cycle policy is used?
  1. (1 point) What is the optimal order quantity of Item A?

Question 9: (8 points)

Historical demand for a product is:

/ Month / Demand
1 / January / 22
2 / February / 23
3 / March / 25
4 / April / 27
  1. (2 points) Using a simple three-month moving average, find the May forecast
  1. (2 points) Using a single exponential smoothing with and an April forecast = 26, find the May forecast
  1. (2 points) Using a double exponential smoothing method with and , find and .
  1. (2 points) Using and found in part , find the May forecast made in January.

Question 10: (8 points)

The J&B Card Shop sells calendars. The once-a-year order for each year’s calendar arrives in September. The calendars cost $13 and J&B sells them for $25 each. At the end of July, J&B reduces the calendar price to $5 and can sell all the surplus calendars at this price. How many calendars should J&B order if the September-to-July demand can be approximated bynormal distribution with and .

  1. (2 points) What is the overage cost?

Purchase price – salvage value = $13-5=$8

  1. (2 points) What is the underage cost?

Selling price – Purchase price = $25-13=$12

  1. (4 points) Compute the optimal order quantity

Find such that

Or,

Or,

Hence, from Table A-1 (the -value for which area = 0.10

Question 11: (8 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 200 radios each year. The annual demand follows a normal distribution with a standard deviation of 50. The store pays $80 for each radio. The holding cost is 20 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. The penalty cost is estimated to be about $60 per stock-out. Replenishment lead time is three months. Find an optimal (Q,R) policy with no service constraint. Use the iterative method and show 2 iterations. Show your computation on the next page and summarize your results in the table below:

Summary of results obtained from Excel (hand computation shown later):


Hand computation for Question 11:

Iteration 1

1-1

1-2

(See Table A-4)

1-3(See Table A-4)

1-4

1-5

(See Table A-4)

Iteration 2

2-3(See Table A-4)

2-4

2-5

(See Table A-4)

Question 12: (8 points)

The Easty Brewing Company produces a popular local beer known as Iron Stomach. Beer sales are somewhat seasonal, and Yeasty is planning its production and manpower levels on March 31 for the next three months. The demand forecasts are

Month / Production days / Forecasted Demand
April / 20 / 8,000
May / 25 / 9,000
June / 24 / 9,600

As of March 31, Yeasty had 30 workers on the payroll. Over a period of 10 working days when there were 100 workers on the payroll, Yeasty produced 10,000 cases of beer. As of March 31, Yeasty expects to have 500 cases of beer in stock. It plans to start July with 600 cases on hand. Based on this information, find the minimum constant workforce plan (level strategy) for Yeasty over the three months.

Productivity units/worker/day

Month
A / Net requirement
B / Cumulative net requirement
C / Units produced per worker
D / Cumulative units produced per worker
E / Number of workers needed
F=
April / 7,500 / 7,500 / 2010=200 / 200 /
May / 9,000 / 7,500+9,000 =16,500 / 2510=250 / 200+250 =450 /
June / 10,200 / 16,500+10,200 =26,700 / 2410=240 / 450+240 =690 /
Maximum

Minimum constant number of workers needed = 39
Question 13: (8 points)

Hy and Murray are planning to set up an ice cream stand in Shoreline Park. After five months of operation, the observed sales of ice cream and the number of park attendees are:

Month
1 / 2 / 3 / 4 / 5
Ice Cream Sales in hundreds, Y / 7 / 4 / 2 / 5 / 6
Park Attendees in hundreds, X / 12 / 11 / 6 / 17 / 21
  1. (6 points) Determine a regression equation treating ice cream sales as the dependent variable (on the vertical axis) and park attendees as independent variable (on the horizontal axis).

12 / 7 / 84 / 144
11 / 4 / 44 / 121
6 / 2 / 12 / 36
17 / 5 / 85 / 289
21 / 6 / 126 / 441
Total / 67 / 24 / 351 / 1031
Average / 13.4 / 4.8

Slope

Intercept

Hence, the regression equation is

  1. (2 points) Forecast the ice cream sales in the next month, if the projected number of park attendees in the next month is 2,400

hundred

Hence, ice cream sales is 713.964 units

1