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

Productivity is 4 unit per worker hour, eight hours per day, 22 days per month
Units produced in 1 hour	4
Monthly productivity /worker = 22*4*8	704
Worker required in Feb = 80256/704	114

1. For Feb, we need 114 workers as shown in the calculation, hence 114-100= 14 are hired and then laid off in March when the requirement is for 100(70400/704). As per rules, the workforce is kept constant till May.
2. We need overtime in April but limited to 5000 hours as required production hours are much more than capacity. This leads to backorders and ending inventory is zero.
3. In May, we do not need overtime, but backorders are fulfilled in the month. Hence , Ending inventory = 50320- (40360+9960) =20080
4. Inventory cost = Ending inventory * Cost of inventory holding
5. Beginning inventory in May is negative due to backorders.

Month	Feb	Mar	Apr	May
Forecast	80,256	70,400	1,00,360	40,360
Beginning inventory	0	0	0	-9,960
Production required	80,256	70,400	1,00,360	50,320
Production hours required (Divide by 4)	20064	17600	25090	12580
Regular workforce (Divide production hours required by 704)	114	100	100	100
Regular production	80256	70400	70400	70400
Regular production hours available (S)	20064	17600	17600	17600
Overtime hours (Production hours required-regular production hours), Limit to 5000 (O)	0	0	5000	0
Overtime production	0	0	20000	0
Total production	80256	70400	90400	70400
Ending inventory (I)	0	0	0	20,080
Ending backorders = (B)	0	0	9,960	0
Workers hired (H)	14	0	0	0
Workers laid off (L)	0	14	0	0
Costs	Feb	Mar	Apr	May
Straight time = S*10	$ 200,640.00	$ 176,000.00	$ 176,000.00	$    176,000.00
Overtime = O* 15	0	0	$    75,000.00	0
Inventory = I *10	0	0	0	$    200,800.00
Backorder = B *20	0	0	$ 199,200.00	0
Hiring = H * 45	$        630.00	0	0	0
Layoff = L*65	0	$        910.00	0	0
Total Costs	$ 201,270.00	$ 176,910.00	$ 450,200.00	$    376,800.00
Total plan costs				$    1205180.00