The Wingtip shoe company forecasts the following demands during the next six mon

Question

The Wingtip shoe company forecasts the following demands during the next six months:

month 1, 200

month 2, 260

month 3, 240

month 4, 340

month 5, 190

it costs $7 to produce a pair of shoes with regular-time labor (RT) and $11 with overtime labor (OT)

During each month regular time production is limited to 200 pairs of shoes, and overtime production is limited to 100 pairs. It costs $1 per month to hold a pair of shoes in inventory.

Determine how Wingtip can minimized the total cost of meeting the next six month's demand on time.

Explanation / Answer

Mathematical Model Decision Variables RTx= # of shoes produced using regular hours in month x, x=1,-,6 OTx= # of shoes produced using overtime hours in month x, x=1,-,6 Convenience Variables- EIx= # of shoes in ending inventory in month x, x=1,-,6 Auxiliary Calculations Production cost = 7(RT1+RT2+RT3+RT4+RT5+RT6)+11(OT1+OT2+OT3+OT4+OT5+OT6) Holding cost= 1(EI1+EI2+EI3+EI4+EI5+EI6) Objective Minimize Cost= Production Cost + Holding Cost ST EI0=0 EIx= (RTx+OTx+EIx-1)-Dx D1 = 200 D2 = 260 D3 = 240 D4 = 340 D5= 190 D6 = 150 EIx >= 0 RTx

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