Question

A company produces three different types of cameras. The hours required to produce each model are listed in the following table:

Camera Model	Model A	Model B	Model C
Hours Required	1.6	1.8	2.3

As of January there are 95 permanent workers and 165 production hours available per worker per month. The forecast demand for each model in the first half of next year is shown in the table below:

Model	January	February	March	April	May	June
A	5000	5600	5300	5100	5400	4000
B	3500	4300	4500	4600	4000	4080
C	1000	1200	1250	1430	900	1100

The idle time cost is $7/hr. and the overtime rate is $4/hr. It costs the company $1300 to hire a worker and $1500 to fire a worker. There are currently 1000 units of Model A, 900 units of Model B and 800 units of Model C in the inventory (beginning inventory for January). The inventory cost is $15/unit-month and the shortage cost is $35/unit-month. The company policy is to have a safety stock of 15 % of the monthly forecast of each model and each month’s safety stock for each model become the beginning inventory for the next month.

Prepare an aggregate plan as follow:

1. Varying work force size
2. Maintain constant work force of 95 workers and use overtime and idle time.
3. Maintain constant work force of 95 workers and build inventory or incur stock-out cost.

Answer 1

Ans 1

The workforce needed is 88 workers in January, 118 workers in February,119 workers in March, 118 workers in April, 108 workers in May, and 84 workers in June month.

Ans 2

The workforce of 95 workers and the idle capacity cost is 59584 in January, overtime cost 60548 in February, 61137.6 overtime in March, 60498.4 overtime in April, 31833.6 overtime in May, 90262.9 idle costs in June.

Ans 3

Workers at 95 constant and Inventory holding cost in January 9600, Shortage cost 69709.87 in February, 70388.68 shortage cost March, 69652.76 shortage cost in April, 36650.53 shortage cost in May, 14542.89 inventory holding cost in June.