Develop a production plan and calculate the annual cost for a firm whose demand
ID: 370886 • Letter: D
Question
Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,000; winter, 8,000, spring, 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall, you have 30 workers. It is not possible to hire any additional workers until next Summer, at which time temporary workers will be hired at the beginning of Summer and laid off at the end of Summer Therefore, no hiring or laying off is possible in the Fall, Winter or Spring. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall Relevant costs are hiring, $100 for each temp, layoff, $200 for each worker laid off, inventory holding, $5 per unit-quarter; backorder, $10 per unit, straight time, $5 per hour, overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. (Round up Number of temp workers" to the next whole number and all other answers to the nearest whole number. Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "O" wherever required.) Fall Winter Spring Summer 10,000 500 8,000 7,000 12,000 200 Forecast Beginning inventory Production required Production hours required Production hours available Overtime hours Temp workers Temp worker hours available Total hours available Actual production Ending inventory Workers hired Workers laid off 0 Fall Winter in Summer 7200 11800 Straight time Overtime Inventory Backorder Hiring 7200 7200 800 TotalExplanation / Answer
Table 1.
Table 2
Grand total = $416600
Notes :
Table 1: Production req : Forecast - Beginning inventory/ Backorders.
Production hours required : Production required / 0.5
Production hours available : 30 workers * 8 hours per day * 60 days per season = 14400
Overtime hours = Production hours req - production hours available
Workers can be hired only in summer and hence hiring and layoff costs nil in fall, winter and spring.
Ending inventory : Production required - Actual production
Actual production : Total hours available * 0.5
Number of workers required to be hired in winter : (Production hours required - Production hrs available) / ( 8 *60).
Hence : (23800 - 14400)/ 480 = 19.17 rounded off to 20 workers.
Table 2 :
Straight time = Total hours available * $5
14400* 5 = $72000
Overtime : Overtime hours * $8.
Inventory costs : Ending inventory units * $5.
Backorder costs : Backorder *$10.
Hiring costs : Number of workers hired * 100
Laying costs : Number of workers * $200.
Particulars Fall Winter Spring Summer Forecast 10000 8000 7000 12000 Beginning inventory 500 (2300) 0 200 Prodn required 9500 10300 7000 11800 Prodn hours reqd 19000 20600 14000 23600 Prodn hours available 14400 14400 14400 14400 Overtime hours 0 6200 0 0 Temp workers 0 0 0 20 Temp workers hours available 0 0 0 9600 Total hours available 14400 20600 14400 24000 Actual production 7200 10300 7200 12000 Ending inventory 0 0 200 200 Workers hired 0 0 0 20 Workers laid off 0 0 0 20Related Questions
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