EOQ_homework_solutionsE10

EOQ_homework_solutionsE10 - E10 IEOR Module Fall 2010 Prof....

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1 E10 IEOR Module Fall 2010 Prof. Leachman Solutions to Module Homework Assignment #1 Due at start of class Monday Feb. 8 1. Consider a simple inventory system with the following characteristics: Constant demand rate D , finite replenishment rate P > D , ordering (setup) cost A , inventory holding cost h per unit per unit time. The setup time (duration from when replenishment is requested until replenishment begins) is L . Sketch a graph of inventory versus time for this case. Develop the total cost rate function and determine the optimal order size. Figure 3. Inventory Level vs. Time - EMQ Problem 0 20 40 60 80 100 120 140 160 180 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time Inventory Level If we replenish a quantity Q, the duration of the replenishment is Q/P and the height of the inventory at the completion of the replenishment is therefore [ Q/P ]( P D ) = Q (1 – D/P ). The average inventory level is half of this height. The ordering cost rate is AD / Q . We ignore the constant purchase cost rate cD . Considering the relevant costs, the total cost rate is therefore expressed as . 1 2 1 ) ( P D hQ Q D A Q TRC Taking a derivative and solving for Q , we find
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EOQ_homework_solutionsE10 - E10 IEOR Module Fall 2010 Prof....

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