Management Science Methods

Operations Management Application- Workforce Assignment

1. Define the Decision Variables

Pi = number of producers in month i (where i = 1, 2, 3 for April, May, June)

Ti = number of trainers in month i (where i = 1, 2 for April, May)

Ai = number of apprentices in month i (where i = 2, 3 for May, June)

Ri = number of recruits in month i (where i = 1, 2 for April, May)

2. Define the Objective Function

Minimize total wage cost for producers, trainers, apprentices, and recruits for April, May, and June:

Min 3000P1 + 3300T1 + 2200R1 + 3000P2 + 3300T2 + 2600A2+2200R2 + 3000P3 + 2600A3

3. Define the Constraints

Total production in Month 1 (April) must equal or exceed contract for Month 1:

(1) .6P1 + .3T1 +.05R1 > 20

Total production in Months 1-2 (April, May) must equal or exceed total contracts for Months 1-2:

(2) .6P1 + .3T1 + .05R1 + .6P2 + .3T2 + .4A2 + .05R2 > 44

Total production in Months 1-3 (April, May, June) must equal or exceed total contracts for Months 1-3:

(3) .6P1+.3T1+.05R1+.6P2+.3T2+.4A2+.05R2+.6P3+.4A3 > 74

In April there are 100 employees that can be producers or trainers:

(4) P1 + T1 = 100

At the end of June, there are to be at least 140 employees:

(5) P3 + A3 > 140

Each trainer can train two recruits:

(6) 2T1 > R1

(7) 2T2 > R2

The number of producers and trainers in a month must equal the number of producers, trainers, and

apprentices in the previous month

(8) P1 + T1 = P2 + T2

(9) P2 + T2 + A2 = P3

The number of apprentices in a month must equal the number of recruits in the previous month:

(10) A2 = R1

(11) A3 = R2

Non-negativity: P1, T1, R1, P2, T2, A2, R2, P3, A3 > 0