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AGGREGATE PLANNING
Internet Case Study for Chapter 13: Aggregate Planning Cornwell Glass Cornwell Glass produces replacement automobile glass for all makes of cars. Cornwell has a sophisticated forecasting system that uses data from past years to find seasonal factors and long-term trends. The system uses data from past weeks to find recent trends. The following table presents the forecasted demands for the coming year on a weekly basis. Week April
Demand Week
Demand
15
1,829 November 4
1,864
22
1,820
11
1,989
29
1,887
18
2,098
6
1,958
25
2,244
13
2,011 December 2
2,357
20
2,063
9
2,368
27
2,104
16
2,387
3
2,161
23
2,402
10
2,258
30
2,418
17
2,307 January
6
2,417
24
2,389
13
2,324
1
2,434
20
2,204
8
2,402
27
2,188
15
2,385 February
3
2,168
22
2,330
10
2,086
29
2,323
17
1,954
5
2,317
24
1,877
12
2,222 March
3
1,822
19
2,134
10
1,803
26
2,065
17
1,777
September 2
1,973
24
1,799
9
1,912
31
1,803
16
1,854 April
7
1,805
23
1,763
May
June
July
August
October
30
1,699
7
1,620
14
1,689
21
1,754
28
1,800
Cornwell uses these forecasts for its production planning. It manufactures several types of glass, and demand is aggregated across products and measured in pounds. It is obvious from the demands that there is a great deal of seasonality/cyclicality in the demand pattern. Cornwell will need to take this into account in developing a production plan for the coming year. Cornwell must consider the costs of hiring or firing workers; using overtime; subcontracting; and holding inventory or running out of the product. The holding cost for glass is $.12 per pound per week. The company estimates that the cost of a late order is $20 per pound per week late. Cornwell currently costs out each hire at $5.63 per pound (based on training costs and production rates per worker). It costs out each fire at $15.73 per pound (based on unemployment compensation and loss of good will). The company currently has the capacity to manufacture 1,900 pounds of glass per week. This capacity cannot be exceeded under any plan. At most, 2,000 pounds can be subcontracted in a given week, and overtime is limited to 250 pounds per week. Glass that is manufactured during overtime costs $8 per pound more than glass manufactured during regular time. Glass that is subcontracted costs $2 more per pound than glass that is produced during overtime. The current inventory is 73 units, and currently production is working at full capacity, 1,900 units. Cornwell has not been able to determine whether demands not met in the current month can be met later or whether these orders are lost. DISCUSSION QUESTIONS 1. Find the production schedule Cornwell should follow under the various assumptions and policies, and detail the differences among these schedules.
2. Consider the following aggregate planning problem for one quarter: Regular Time
Overtime
Subcontracting
Production capacity/month
1,000
200
150
Production cost/unit
$5
$7
$8
Assume that there is no initial inventory and a forecasted demand of 1,250 units in each of the 3 months. Carrying cost is $1 per unit per month. Solve this aggregate planning problem using the linear programming transportation method.
3. A Birmingham, Alabama, foundry produces cast-iron ingots according to a 3-month capacity plan. The cost of labor averages $100 per regular shift hour and $140 per overtime (O.T.) hour. Inventory carrying cost is thought to be $4 per labor-hour of inventory carried. There are 50 direct labor-hours of inventory left over from March. For the next 3 months, demand and capacity (in labor-hours) are as follows: Capacity Month
Regular Labor (hours)
O.T. Labor (hours)
Demand
Apr.
2,880
355
3,000
May
2,780
315
2,750
June
2,760
305
2,950
Develop an aggregate plan for the 3-month period using the transportation method. 4. The James Lawson Chemical Supply Company manufactures and packages expensive vials of mercury. Given the following demand, supply, cost, and inventory data, allocate production capacity to meet demand at minimum cost using the transportation method. A constant workforce is expected. Back orders are permitted. Supply Capacity (in units) Period
Regular Time
Overtime
Subcontract
Demand (in units)
1
25
5
6
32
2
28
4
6
32
3
30
8
6
40
4
29
6
7
40
Other Data Initial inventory
4 units
Ending inventory desired
3 units
Regular-time cost per unit
$2,000
Overtime cost per unit
$2,475
Subcontract cost per unit
$3,200
Carrying cost per unit per period
$ 200
Backorder cost per unit per period
$ 600
5. Refrigeration Corp. needs an aggregate plan for January through June for its refrigerator production. The company has developed the following data:
Costs Holding cost
$8/ refrigerator /month
Subcontracting
$80/ refrigerator
Regular-time labor
$12/hour
Overtime labor
$18/hour for hours above 8 hours/worker/day
Hiring cost
$40/ refrigerator
Layoff cost
$80/ refrigerator
Stockout cost
none
Other Data Current workforce (December)
8 people
Labor hours/ refrigerator 4 hours Workdays/month
20 days
Beginning inventory
250
refrigerators Ending inventory
0 refrigerators
Demand
Forecast
Jan.
400
Feb.
500
March
550
April
700
May
800
June
700
What will each of the two following strategies cost? (a) Plan A: Vary the work force so that production meets the forecasted demand. Bell had eight employees on staff in December. (b) Plan B: Vary overtime only and use a constant workforce of ten. (c) Which plan is best and why?