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; regular 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 the cells blank, whenever zero (0) is required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.)

Answer 1

Production Planning Cost
	February	March	April	May
Demand	80256	70400	100360	40360
New Hiring	82080	0	0	0
Labour Hours	3210240	2816000	3210240	3210240
Layoff	0	2562560	0	0
Overtime	0	0	75000	75000
Backorder	0	0	377080	0
Storage Cost	0	0	0	411400
Total Cost	3292320	5378560	3662320	3696640

Working Notes

	February	March	April	May
Demand	80256	70400	100360	40360
Worker	1824	1600	1824	889
Lay off	0	224	0	0
overtime production	0	0	1250 units	1250 units
BackOrder	0	0	18854 units	0
Extra labour	0	0	0	935
Storage Cost	0	0	0	41140 units

In the month of Feb and March no Overtime is possible
Hence, Layoff will be paid and production need to be exact as per demand , no stoorage cost.
Changes is required in the monthof April / May only.
No. of Worker	80256 /2X22= 1824	70400 /2X22=1600		40360 /2X22 =918
layoff in the month of March = 1824 - 1600 = 224
layoff in the month of May = 1824 - 918 = 906
Possibilites of April
Extra Labour hours		5000 Hours	1250 Units
It is advisable to bear Backorder cost rather involving in Hiring new labour as impact on future cost.
Possibilities of May
Use of Overtime rather than Laying off of worker as layoff cost
is higher than overtime cost as per rate chart.
total Hours to produce demand = 40360 X4 = 161440 hours
Utilising 5000 hours			(5000 hours)
Balance Hours			156440 hours
Standard Hours available		22 days X 8 hours
No of Workers			156440/ 176 = 889 labour
Extra Labours			1824-889 = 935

4 units per hour
8 hours per day
22 days in a month
New Hiring Cost	$45
Layoff Worker	$65
Inventory Holding	$10
Regular Wages	$10
Overtime		$15
Backorer		$20