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Optimality of Myopic Policies for Dynamic Lot-Sizing Problems in Serial Production Lines with Random Yields and Autoregressive Demand

Operations Research, Forthcoming

35 Pages Posted: 4 Sep 2011 Last revised: 15 Nov 2012

Matthew J. Sobel

Case Western Reserve University - Department of Operations

Volodymyr Babich

Georgetown University

Date Written: September 9, 2012

Abstract

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).

Keywords: multi-echelon, inventory, supply risk, MDP, myopic policies, Perishable/aging items

JEL Classification: C61

Suggested Citation

Sobel, Matthew J. and Babich, Volodymyr, Optimality of Myopic Policies for Dynamic Lot-Sizing Problems in Serial Production Lines with Random Yields and Autoregressive Demand (September 9, 2012). Operations Research, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1921909 or http://dx.doi.org/10.2139/ssrn.1921909

Matthew J. Sobel

Case Western Reserve University - Department of Operations ( email )

10900 Euclid Ave.
Cleveland, OH 44106-7235
United States

Volodymyr Babich (Contact Author)

Georgetown University ( email )

37th and O St NW
McDonough School of Business
Washington, DC 20057
United States

HOME PAGE: http://explore.georgetown.edu/people/vob2/

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