Rotation_cycles_basic E10

Rotation_cycles_basic E10 - E10 Spring, 2010 Prof. Leachman...

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1 E10 Spring, 2010 Prof. Leachman Notes on Economic Lot Scheduling and Economic Rotation Cycles 1. The Economic Order Quantity (EOQ) . Consider an inventory item in isolation with demand rate D , holding cost h per unit per unit time, and replenishment cost A (independent of quantity replenished). What is the optimal replenishment lot size Q ? Figure 1 plots inventory level vs. time for this problem for the case D = 1,000 and Q is taken to be 200. Note the “sawtooth” pattern, whereby inventory is replenished by the order quantity (200 in this case), and then steadily falls to 0, whereupon the cycle repeats itself. Figure 1. Inventory Level vs. Time - EOQ Problem 0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time Inventory Level We formulate a function expressing the total cost rate as a function of Q. The relevant costs are the inventory holding cost and replenishment cost. Note that replenishment orders will be placed once every Q/D units of time. The inventory level has a maximum of Q and falls linearly to 0; thus the average inventory level is Q /2. The total cost rate is therefore expressed as . 2 / / ) ( hQ Q AD Q TRC We take a derivative to find the best value of Q :
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2 . / 2 2 / / / * 2 h AD Q h Q AD Q TRC The optimal time between replenishments is given by . / 2 / * * hD A D Q T Figure 2 plots TRC ( Q ) vs. Q for the case of h = 0.5, D = 1,000 and A = 10. The best value of Q is where the ordering cost rate and the holding cost rate are equalized; this occurs at Q = 200 in this case. Note that the total cost rate curve is very flat around the best order size. Figure 2. Total Cost Rate vs. Order Quantity 0 50 100 150 200 250 5 0 7 90 11 130 1 170 190 21 230 25 27 290 31 33 3 Order Quantity, Q Total Cost Rate AD/Q hQ/2 TRC(Q) 2. The Economic Manufacturing Quantity (EMQ) . Now suppose that replenishment is not instantaneous but occurs at a finite production rate P > D . Now what is the optimal replenishment quantity Q and optimal time between replenishments T ? While replenishment is underway, we add to inventory at rate
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This note was uploaded on 02/19/2010 for the course ENGINEERIN 72826 taught by Professor Sengupta/leachman/johnson during the Spring '10 term at Berkeley.

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Rotation_cycles_basic E10 - E10 Spring, 2010 Prof. Leachman...

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