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, 81,984; March, 67,200; April, 100,320; May, 40,320. 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 81,984 67,200 100,320 40,320 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

	February March April May Straight time Overtime Inventory Backorder Hiring Layoff Total Total cost

Answer 1

Aggregate Plan:

Particulars	February	March	April	May	Total
Forecast	81,984	67,200	100,320	40,320
Beginning inventory	0	0	0	0
Production required	81,984	67,200	100,320	40,320
Production hours Required (Production Requirement x 1 / 4 hrs. / unit)	20,496	16,800	25,080	10,080
Working days per month	21	21	21	21
Hours per month per Worker (Working Days x 8 hrs. / day)	168	168	168	168
Workers required (Production Hours Required / Hours per month per Worker)	122	100	150	60
Regular workforce	100	122	100	100
Regular production	81,984	67,200	67,200	67,200
Overtime hours [(Production required -Regular production) x (1 / 4) hrs. / unit]	0	0	5,000	0
Overtime production (Overtime hours x 4 units / hr.)	0	0	20,000	0
Total production	81,984	67,200	87,200	67,200
Ending inventory (Total production – Production required)	0	0	0	26,880
Ending backorders (Production required – Total production)	0	0	13,120	0
Workers hired	22	0	0	0
Workers laid off	0	22	0	0
Straight Time Cost (Production Hours x $ 12) (in $)	245,952	201,600	201,600	201,600	850,752
Overtime cost (Overtime production x $ 18) (in $)	0	0	360,000	0	360,000
Inventory cost (Ending inventory x $ 11) (in $)	0	0	0	295,680	295,680
Backorder cost (Ending backorders x $ 22) (in $)	0	0	288,640	0	288,640
Hiring cost (Workers hired x $ 50) (in $)	1,100	0	0	0	1,100
Layoff cost (Workers laid off x $ 70) (in $)	0	1,540	0	0	1,540
Total Cost					$ 1,797,712

Total Cost of the Production Plan = $ 1,797,712.