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Solved: The manager of a LaMode company has developed a forecast shown in the table for boxes

 Part 3. Multi-Period Problem The manager of a LaMode company has developed a forecast shown in the table for boxes of cloth. The table also shows the production cost per box, the holding cost per box, the production capacity, the inventory capacity. The company now has 30 boxes of cloth as a beginning inventory of the first period. Formulate a linear programming model to minimize the cost. Calculate inventory cost based on amounts of inventory at the end of each period. Period Forecast Production cost Holding cest Production Capacity Inventory capacity 300 16 oss 230 17 0s 15 0.75 270 50 0.9 280 60 18 0.95 270 50 19 1.00 275 60 20 1.10 265 50 0.85

The manager of a LaMode company has developed a forecast shown in the table for boxes of cloth. The table also shows the production cost per box, the holding cost per box, the production capacity, the inventory capacity. The company now has 30 boxes of cloth as a beginning inventory of the first period. Formulate a linear programming model to minimize the cost. Calculate inventory cost based on amounts of inventory at the end of each period.

Expert Answer

Formulation in Excel

Final Result

Period 1 2 3 4 5 6
Forecast 250 300 230 300 280 290
Beginning Inv 30 50 35 60 30 25
Production 270 285 255 270 275 265
Ending Inv 50 35 60 30 25 0

Total cost = 28,504.75

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