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 currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. 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, $110 for each temp; layoff, $220 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. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.)

Answer 1

	Fall	Winter	Spring	Summer
Forecast	10,000	8,000	7,000	12,000
Beginning inventory	500	-2,300	0	200
Production required	9,500	10,300	7,000	11,800
Production hours required	19,000	20,600	14,000	23,600
Production hours available1	14,400	14,400	14,400	14,400
Overtime hours	0	6,200	0	0
Temp workers2	0	0	0	20
Temp worker hours available	0	0	0	9,600
Total hours available	14,400	20,600	14,400	24,000
Actual production	7,200	10,300	7,200	12,000
Ending inventory	-2,300	0	200	200
Workers hired	0	0	0	20
Workers laid off	0	0	0	20
	Fall	Winter	Spring	Summer
Straight time	$72,000	$72,000	$72,000	$120,000
Overtime	$0	$49,600	$0	$0
Inventory	$0	$0	$1,000	$1,000
Backorder	$23,000	$0	$0	$0
Hiring	$0	$0	$0	$2,200
Layoff	$0	$0	$0	$4,400
Total	$95,000	$121,600	$73,000	$127,600
Annual cost				$417,200

Calculations:

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