Homework Answers
LP model is following:
Decision variables:
Hi = number of workers to be Hired at the beginning of month i
Fi = number of workers to be Fired at the beginning of month i
Wi = net available number of workers after hiring and firing at the beginning of month i
Pi = regular production in month i
Oi = overtime production in month i
Vi = Inventory at the end of month i
Objective:
Min 1600*
Hi +
2000*Fi +
1500*Wi +
15*Pi +
(4*13+15)*Oi +
3*Vi
Constraints:
Pi = (160/4)*Wi
Oi <= (20/4)*Wi
W1-H1+F1=100
W2-H2+F2-W1=0
W3-H3+F3-W2=0
W4-H4+F4-W3=0
P1+O1-V1=3000-500
P2+O2-V2+V1=5000
P3+O3-V3+V2=2000
P4+O4-V4+V3=1000
Hi, Fi, Wi, Pi, Oi, Vi >= 0
Spreadsheet model is following:
EXCEL FORMULAS:
| Month | Demand | Regular production (Pi) | Overtime production (Oi) | Overtime Capacity | Workers (Wi) | Hired (Hi) | Fired (Fi) | Inventory (Vi) |
| 0 | 100 | 500 | ||||||
| 1 | 3000 | =F3*160/4 | 0 | =F3*20/4 | =F2+G3-H3 | 0 | 6 | =I2-B3+C3+D3 |
| 2 | 5000 | =F4*160/4 | 20 | =F4*20/4 | =F3+G4-H4 | 0 | 1 | =I3-B4+C4+D4 |
| 3 | 2000 | =F5*160/4 | 0 | =F5*20/4 | =F4+G5-H5 | 0 | 43 | =I4-B5+C5+D5 |
| 4 | 1000 | =F6*160/4 | 0 | =F6*20/4 | =F5+G6-H6 | 0 | 25 | =I5-B6+C6+D6 |
| Total | =SUM(B3:B6) | =SUM(C3:C6) | =SUM(D3:D6) | =SUM(E3:E6) | =SUM(F3:F6) | =SUM(G3:G6) | =SUM(H3:H6) | =SUM(I3:I6) |
| Cost/Category | 15 | =13*4+15 | 1500 | 1600 | 2000 | 3 | ||
| Category cost | =C8*C7 | =D8*D7 | =F8*F7 | =G8*G7 | =H8*H7 | =I8*I7 | ||
| Total Cost = | =SUM(C9:I9) |
Total cost = $ 705,320
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