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, 80,256; March, 70,400; April, 100,360; May, 40,360. Productivity is four units per worker hour, eight hours per day, 22 days per month. Assume zero inventory on February 1. Costs are hiring, $45 per new worker; layoff, $65 per worker laid off; inventory holding, $10 per unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 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.)

Answer 1

FOR PLAN PRODUCTION FOR A FOUR MONTH PERIOD

	February	March	April	May
Forecast (a)	80256	70400	100360	40360
Beginning inventory (b)	0	0	0	0
Production required (c = a-b)	80256	70400	100360	40360
Production hours required (d = c/4)	20064	17600	25090	10090
Regular workforce (e )	100	100	100	100
Regular production (f = e*22*8*4)	70400	70400	70400	70400
Overtime hours (g)	0	0	5000	0
Overtime production (h = g* 4)	0	0	20000	0
Total production (i=f+h)	70400	70400	90400	70400
Ending inventory (j = b+i-a (if b+i-a>0,else 0)	0	0	0	10224
Ending backorders (k = a-b-i (if a-b-i>0,else 0)	9856	9856	19816	0
Workers hired (l)	0	0	0	0
Workers laid off (m)	0	0	0	0
	February	March	April	May
Straight time (n = $10 * f/4)	$176,000	$176,000	$176,000	$176,000
Overtime (o = $15 * g)	$0	$0	$75,000	$0
Inventory (p = $10 * j)	$0	$0	$0	$102,240
Backorder (q = $20 * k)	$197,120	$197,120	$396,320	$0
Hiring   (r = $45 * l)	$0	$0	$0	$0
Layoff (s = $65 * m)	$0	$0	$0	$0
Total	$373,120	$373,120	$647,320	$278,240
Total cost				$1,671,800
Overtime Calculation
	February	March	April	May	Total
Demand	80256	70400	100360	40360	291376
Regular Production	70400	70400	70400	70400	281600
Overtime Required	9856	0	29960	-30040	9776
Hence, no overtime in the month of May, due to spare capacity