Question

A firm must plan production for the next six months. Each unit costs $480 to produce and it has an inventory holding cost of $20 per unit per month based on ending inventory levels. The cost to hire a worker is $330, and the cost to fire a worker is $660 per worker. Each worker produces 10 units per month. There are 25 persons on the payroll at the beginning of the first month. The company currently has 200 units of inventory in stock, and it wants to keep at least this many units as safety stock at the end of every month. Assume hiring and layoff/firing, if necessary, occur at the beginning of the month.

Month	1	2	3	4	5	6
Demand	420	420	420	420	470	550

a. From the information given above, what level production rate will meet demand for the next six months? Using that rate, complete the level plan below. (Leave no cells blank - be certain to enter "0" wherever required.)

Level Plan
Month	Demand	Regular Production	Ending Inventory	Number of Workers	Hire	Fire
1	420
2	420
3	420
4	420
5	420
6	420
Total	2700

b-1. At that production rate, what is the maximum end-of-period inventory experienced at some time during the six months?

Maximum end-of-period inventory

Units

b-2. What would be the cost of a level production plan?

Total Cost

c-1. From the information given above, Develop a chase (Hire and Fire only) Production Plan? (Leave no cells blank - be certain to enter "0" wherever required.)

Level Plan
Month	Demand	Regular Production	Ending Inventory	Number of Workers	Hire	Fire
1	420
2	420
3	420
4	420
5	420
6	420
Total	2700

c-2. What is the total cost of a chase (hire and fire only) production plan?

Total Cost

Answer 1

a.

Level Plan
Month	Demand	Regular	Ending	Number of	Hire	Fire
		Production	Inventory	Workers
1	420	450	230	45	20	0
2	420	450	260	45	0	0
3	420	450	290	45	0	0
4	420	450	320	45	0	0
5	470	450	300	45	0	0
6	550	450	200	45	0	0
Total	2700	2700	1600		20	0

b-1.

Maximum end-of-period inventory = 320 units

b-2.

Total cost = regular production cost + inventory holding cost + hire cost + fire cost

= 2700*480+1600*20+20*330+0*660 = 1334600

c-1.

Hire and Fire
Month	Demand	Regular	Ending	Number of	Hire	Fire
		Production	Inventory	Workers
1	420	420	200	42	17	0
2	420	420	200	42	0	0
3	420	420	200	42	0	0
4	420	420	200	42	0	0
5	470	470	200	47	5	0
6	550	550	200	55	8	0
Total	2700	2700	1200		30	0

C-2
Total cost = regular production cost + inventory holding cost + hire cost + fire cost

= 2700*480+1200*20+30*330+0*660 = 1329900