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 90 workers on January 31. You are given the following demand forecast: February, 80,640; March, 60,480; April, 100,160; May, 40,160. Productivity is four units per worker hour, eight hours per day, 21 days per month. Assume zero inventory on February 1. Costs are hiring, $52 per new worker; layoff, $72 per worker laid off; inventory holding, $8 per unit-month; straight-time labor, $8 per hour; overtime, $12 per hour; backorder, $16 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	60,480	100,160	40,160
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

For February and March we have to used exact demand production (chase strategy)

For April and May we have to maintain the workforce and go with overtime (with a maximum cap of 5000 hours overtime)

Beginning inventory for February = 0

Workforce in January = 90

Productivity = 4 units per worker hour

Eight hours a day and 21 days per month

Hiring cost = $52 per new worker

Layoff cost = $72 per worker

Inventory holding = $8 per unit per month

Straight time labor = $8 per hour

Overtime = $12 per hour

Backorder = $16 per unit

Concepts uses:

Production required = forecast + previous month back order (if any) – beginning inventory (if any)

Production hours required = production required/4

Regular production = regular workforce * 4 (for productivity) * 8 (daily work hours) * 21 (days in a month)

Overtime hours = minimum between (5000, (required production – regular production)/4)

Overtime production = overtime hours * 4

Total production = regular production + overtime production

Ending Inventory = Maximum between (0, total production – production required)

Ending Backorders = Maximum between (0, production required – total production)

	February	March	April	May
Forecast	80640	60480	100160	40160
Beginning Inventory	0	0	0	0
Production Required	80640	60480	100160	59840 (forecast + previous backorder)
Production hours Required	20160	15120	25040	14960
Regular workforce	120	90	90	90
Regular production	80640	60480	60480	60480
Overtime hours	0	0	5000	0
Overtime Production	0	0	20000	0
Total Production	80640	60480	80480	60480
Ending Inventory	0	0	0	640
Ending Backorders	0	0	19680	0
Workers Hired	30	0	0	0
Workers Laid off	0	30	0	0

Cost table:

Straight time = regular workforce * 8 (hours a day) * 21 (days a month) * 8 (straight production cost)

Overtime = overtime hours * 12 (overtime cost)

Inventory = ending inventory * 8 (inventory holding cost)

Backorder = ending backorder * 16 (per unit back order cost)

	February	March	April	May
Straight time	$161280	$120960	$120960	$120960
Overtime	0	0	$60000	0
Inventory	0	0	0	$5120
Backorder	0	0	$314880	0
Hiring	$1560	0	0	0
Layoff	0	$2160	0	0
Total	$162840	$123120	$495840	$126080
Total cost				$907880

.

IF YOU HAVE ANY DOUBT, KINDLY COMMENT. I WOULD LOVE TO HELP YOU!!!

IF YOU LIKE THE ANSWER, PLEASE GIVE AN UP-VOTE OR THUMB UP. THIS WILL ENCOURAGE ME TO ANSWER MORE!!