Analysis and Algorithms for Service Parts Supply Chains by John A. Muckstadt

By John A. Muckstadt

* presents a vast review of modeling ways and answer methodologies for addressing stock difficulties, particularly the administration of excessive fee, low call for fee carrier elements present in multi-echelon settings

* The textual content can be used in a number of classes for first-year graduate scholars or senior undergraduates, or as a reference for researchers and practitioners

* A historical past in stochastic tactics and optimization is assumed

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Extra resources for Analysis and Algorithms for Service Parts Supply Chains (Springer Series in Operations Research and Financial Engineering)

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Prove Theorem 3. 3. 1, we proved the optimality of order-up-to policies for a single location system by employing a “single-unit, single-customer” approach. We assumed that an exogenous finite state, ergodic Markov Chain governs the demand process. Suppose this chain is trivial, that is, it has only a single state s. Determine the states that the system attains in the first five periods given the following information. The maximum lead time is 4 periods. At the beginning of period 1, there are 3 backorders and there is no inventory in the system.

2. An order is placed, which we denote by qn , where qn is a nonnegative integer. All units in locations j = 2, 3, . . , m move to the next location prior to placing the order, that is, location j − 1. 2 Optimality of Order-Up-To Policies in Serial Systems 25 m + 1 to location m. If it has been ordered from the supplier periods ago (1 ≤ < m), it is in location m − . 3. Demand Dn is realized and these new customers arrive and are at distance 1. That is, customers at distances 2, 3, . . , 2 + Dn − 1 all arrive and are, by definition, now at distance 1.

Consider the policy Rn (sn , y) = {Release} if and only if y ≤ y ∗ (n, sn ) . Policy Rn is an optimal policy for every subsystem. The next observation we make is that when policy Rn is used in period n for every subsystem, the resulting policy for the original system S is an order-up-to policy. This can be shown either using an algebraic proof or using a more intuitive argument, which we now provide. Theorem 5. The optimal policy for S is to release as many units as necessary to raise the inventory position to y ∗ (n, sn )−1 in period n when in Markovian state sn and the planning horizon consists of N periods.

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