Aggregate Planning-Cases [PDF]

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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?