Workload Scheduling

1.

a) Define the decision variables.

Oi = number of one month contract employees hired (where i = 1, 2, 3, 4, 5, 6 for January, February, March, April, May, June)

Wi = number of two month contract employees hired (where i = 1, 2, 3, 4, 5 for January, February, March, April, May)

Hi = number of three month contract employees hired (where i = 1, 2, 3, 4 for January, February, March, April)

b) Define the objective function

Min. total wage costs for contract employees (cost per contract length) x (number of contracts of each length used)

Min. 2,875*Oi + 5,675*Wi + 8,375*Hi

c) Define the constraints

O1 + W1 + H1 >= 10

W1 + H1 + O2 + W2 + H2 >= 23

H1 + W2 + H2 + O3 + W3 + H3 >= 19

H2 + W3 + H3 + O4 + W4 + H4 >= 26

H3 + W4 + H4 + 05 + W5 >= 20

H4 + W5 + O6 >= 14

Oi, Wi, Hi >= 0

Oi, Wi, Hi must be an integer

d) Determine the optimal solutions:

Jan. Feb. Mar. Apr. May. June.

Option 1 0 4 0 0 3 0

Option 2 0 0 0 3 0 0

Option 3 10 9 0 14 0 0

2.

Number Hired Contract Cost Training Cost Total Cost

Option 1 7 $14,000 $6,125 $20,125

Option 2 3 $14,400 $2,625 $17,025

Option 3 33 $247,500 $28,875 $276,375

TOTAL 43 $275,900 $37,625 $313,525

Total Cost = $313,525

3.

a) Schedule for temporary employees and Costs:

Jan. Feb. Mar. Apr. May. June.

Option 1 10 23 19 26 20 14

Option 2 0 0 0 0 0 0

Option 3 0 0 0 0 0 0

Number Hired Contract Cost Training Cost Total Cost

Option 1 112 $224,000 $78,400 $302,400

Option 2 0 $0 $0 $0

Option