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Unformatted text preview: EOQ extensions – Notes Doug Thomas [email protected] This note provides a few details for two important deterministic inventory extensions: the jointreplenishment problem and the cyclic production scheduling problem. Joint replenishment Suppose we have multiple items and there is a joint order cost K and a peritem order cost k i for item i . Let T be the time between reorders, demand per unit time is μ i , finite production rate per unit time is γ i , holding cost per unit h i . We start with the simple case where all items are ordered together. It is hopefully clear that this is not necessarily optimal. For a given T , it is clear that order quantities must be μ i T , so average inventory is μ i T/ 2, and inventory cost is simply ∑ i h i μ i T/ 2. Cost per order is K + ∑ i k i and ordering cost per unit time is (1/T) times the cost per order. So, we can express cost per unit time as: C ( T ) = ∑ i h i μ i T 2 + K + ∑ i k i T . (1) It may be convenient to rewrite this as C ( T ) = ∑ i h i μ i 2 T + ( K + X i k i ) 1 T , (2) since for a function f ( x ) = ax + b/x , the value of x that satisfies the first order condition is p b/a . In this case, it can be easily verified that this function is concave, so the first order condition defines a unique minimum. This givescondition defines a unique minimum....
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This note was uploaded on 02/23/2011 for the course MATH 444 taught by Professor Dubey during the Spring '11 term at Amity University.
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