Question

Plan production for a four-month period: February through May. For February and March, you should produce to exact demand forecast. For April and May, you should use overtime and inventory with a stable workforce; stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May (zero overtime in February and March). If demand exceeds supply, then backorders occur. There are 100 workers on January 31. You are given the following demand forecast: February, 80,640; March, 67,200; April, 100,280; May, 40,280. Productivity is four units per worker hour, eight hours per day, 21 days per month. Assume zero inventory on February 1. Costs are hiring, $50 per new worker; layoff, $70 per worker laid off; inventory holding, $11 per unit-month; straight-time labor, $12 per hour; overtime, $18 per hour; backorder, $22 per unit.

Develop a production plan and calculate the total cost of this plan. Note: Assume any layoffs occur at beginning of next month. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.)

	February March April May Forecast 80,640 67,200 100,280 40,280 Beginning inventory Production required Production hours required Regular workforce Regular production Overtime hours Overtime production Total production Ending inventory Ending backorders Workers hired Workers laid off sheet is drawn here

	February March April May Straight time Overtime Inventory Backorder Hiring Layoff Total Total cost sheet is drawn here

Answer 1

	Feb	Mar	Apr	May
Forecast	80,640	67,200	100,280	40,280
Beginning inventory	0	0	0	-13,080
Production required	80,640	67,200	100,280	53,360
Production hours required	20,160	16,800	25,070	13,340
Regular workforce	120	100	100	100
Regular production	80,640	67,200	67,200	67,200
Overtime hours	0	0	5,000	0
Overtime production	0	0	20,000	0
Total production	80,640	67,200	87,200	67,200
Ending inventory	0	0	0	13,840
Ending backorders	0	0	13,080	0
Workers hired	20	0	0	0
Workers laid off	0	20	0	0
	Feb	Mar	Apr	May
Straight time	241,920	201,600	201,600	201,600
Overtime	0	0	90,000	0
Inventory	0	0	0	152,240
Backorder	0	0	287,760	0
Hiring	1,000	0	0	0
Layoff	0	1,400	0	0
Total	242,920	203,000	579,360	353,840
Total cost				1,379,120

Calculations: