Question

Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,300; winter, 7,600; spring, 6,600; summer, 12,300. Inventory at the beginning of fall is 515 units. At the beginning of fall you currently have 35 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, $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. 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	10,300	7,600	6,600	12,300
Beginning inventory	515	-1,385	0	1,800
Production required	9,785	8,985	6,600	10,500
Production hours required	19,570	17,970	13,200	21,000
Production hours available1	16,800	16,800	16,800	16,800
Overtime hours	0	1,170	0	0
Temp workers2	0	0	0	12
Temp worker hours available	0	0	0	5,760
Total hours available	16,800	17,970	16,800	22,560
Actual production	8,400	8,985	8,400	11,280
Ending inventory	-1,385	0	1,800	780
Workers hired	0	0	0	12
Workers laid off	0	0	0	12
	Fall	Winter	Spring	Summer
Straight time	$84,000	$84,000	$84,000	$112,800
Overtime	$0	$9,360	$0	$0
Inventory	$0	$0	$9,000	$3,900
Backorder	$13,850	$0	$0	$0
Hiring	$0	$0	$0	$1,200
Layoff	$0	$0	$0	$2,400
Total	$97,850	$93,360	$93,000	$120,300
Annual cost				$404,510

Calculations:

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