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4 DP-Prod Levels - 1 Changing Production Levels Consider a...

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1 Changing Production Levels Consider a production planning problem where demands in each period do not have to be met and excess production can not be carried over into the next period. This problem is one of changing the production levels over a planning horizon so as to minimize the sum of the costs of production level changes and the costs associated with being under or over the product demand each period. The cost of not meeting demand is assumed to be $3 times the under-run quantity squared. The cost of over production is $5 per unused unit, and there is no carry over of these units to future periods. Changing production levels is an expensive proposition and for a production level change of p the cost is estimated to be $10| p | + 2 p 2 . Starting with an existing production level of 30 units, we want to minimize the cost for three time periods with demands (40, 20, 30). In addition, production level changes are restricted to 5 unit increments or decrements. (This restriction is added merely to reduce the computational effort of the example problem and in particular the display requirements.) Let p t
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