Optimality of Myopic Policies for Dynamic Lot-Sizing Problems in Serial Production Lines with Random Yields and Autoregressive Demand
Matthew J. Sobel
Case Western Reserve University - Department of Operations
Georgetown University - McDonough School of Business
September 9, 2012
Operations Research, Forthcoming
We study lot-size policies in a serial, multi-stage, manufacturing/inventory system with two key generalizations, namely (1) random yields at each production stage and (2) an autoregressive demand process. Previous research shows that the optimal policies in models with random yields (even in models with a single installation) lack the familiar order-up-to structure and are not myopic. Thus, dynamic programming algorithms are needed to compute optimal policies and one encounters the “curse of dimensionality;” this is exacerbated here by the need to expand the size and dimension of the state space to accommodate the autoregressive demand feature. Nevertheless, although our model is more complex, we prove that there is an optimal policy with the order-up-to feature and, more importantly, that the optimal policy is myopic. This avoids the computational burden of dynamic programming. Our results depend on two assumptions concerning the stochastic yield, namely that the expected yield at a work station is proportional to the lot size, and the distribution of the deviation of the yield from its mean does not depend on the lot size. We introduce the concept of echelon-like variables to derive the structure of optimal policies; this is a generalization of the echelon variables in Clark and Scarf (1960). Furthermore, we show that the same kind of policy is optimal for several criteria: infinite-horizon discounted cost, infinite-horizon long-run average cost, and finite-horizon discounted cost (with the appropriate choice of the salvage value function).
Number of Pages in PDF File: 35
Keywords: multi-echelon, inventory, supply risk, MDP, myopic policies, Perishable/aging items
JEL Classification: C61
Date posted: September 4, 2011 ; Last revised: November 15, 2012
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