Question

The personnel department of the A&M Corporation want how many workers will be needed each month for the next six-month production period. The following is monthly demand forecast for the six-month period.

Month Forecast Demand

July 1250

August 1100

September 950

October 900

November 1000

December 1150

The inventory 0n hand at the end of June was 500 unites. The company wants to maintain a minimum inventory of 300 unites each month and would like to have 400 unites on hand at the end of December. Each unite requires five employee-hours to produce there are 20 working days each month, and each employee workers an eight-hour day. The workforce at the end of June was 35 workers.

a. Determine a minimum inventory production plan(i.e. one that allows arbitrary miring and firing)

b. Determine the production plan that meets demand but does not hire or fire workers during the six-month period.

Answer 1

a. Determine a minimum inventory production plan(i.e. one that allows arbitrary miring and firing)

We will solve this linear programming problem using Excel -> Solver as shown below.

Hence, the optimal number of workers per month is as follows:

						December
						39
						8

b. Determine the production plan that meets demand but does not hire or fire workers during the six-month period.

As per this level production plan, we will keep the same number of workers for 6 months.

Total demand for 6 months = (1250+1100+950+900+1000+1150)/6 = 1058.33

Number of units produced by one worker per month = (20*8)/ 5 = 32 units

In order to produce 1058.33 per month we need 1058.33/ 32 = 33.07 hence we would keep 34 workers per month to cater to demand and minimum inventory requirement

Hence, the optimal solution is

	July	August	September	October	November
Number of workers required	34	34	34	34	34
Number of workers Hired/ Fired	-1	0	0	0	0

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