Question

Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,300; winter, 8,200; spring, 6,800; summer, 12,300. Inventory at the beginning of fall is 515 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $80 for each temp; layoff, $160 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.)

	Fall	Winter	Spring	Summer
Forecast	10,300	8,200	6,800	12,300
Beginning inventory
Production required
Production hours required
Production hours available1
Overtime hours
Temp workers2
Temp worker hours available
Total hours available
Actual production
Ending inventory
Workers hired
Workers laid off

	Fall	Winter	Spring	Summer
Straight time	$	$	$	$
Overtime
Inventory
Backorder
Hiring
Layoff
Total	$	$	$	$
Annual cost				$

Answer 1

Production Plan as per the data provided :

	FALL	WINTER	SPRING	SUMMER
Forecast	10,300	8,200	6,800	12,300
Beginning Inventory	515	-2585	0	400
Production required	9,785	10,785	6,800	11,900
Production hours required	652	720	454	794
Production hours available1	480	480	480	480
Overtime hours	0	240	0	0
Temp workers2	0	0	0	20
Temp worker hours available	0	0	0	314
Total hours available	480	720	480	794
Actual production	7,200	10,785	7,200	11,900
Ending inventory	0	0	400	0
Workers hired	30	30	30	30
Workers laid off	0	0	0	20

	FALL	WINTER	SPRING	SUMMER
Straight time	72,000	72,000	72,000	72,000
Overtime	0	1,920	0	0
Inventory	0	0	2,000	0
Backorder	25,850	0	0	0
Hiring	0	0	0	1,600
Layoff	0	0	0	3,200
Total	97,850	73,920	74,000	76,800
Annual cost				322,570

Note : Amount shown in the above tables are in $.

Working Notes :

Some formulas that are used to calculate the figures in the above tables

1. Production required = forecast - Beginning inventory
2. Production hours required = (Production required / 30)*2 {i.e. for FALL = (9785/30)*2}
3. Production hour available = (No of hours per day * days per season)
4. Ending Inventory = (Production required - Actual production)

?Rest all the calculations are done with the help of data provided in the question (simple Mathematics with the units and rates provided)