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STOCHASTIC MULTI-ITEM INVENTORY SYSTEMS WITH MARKOV-MODULATED DEMANDS AND PRODUCTION QUANTITY REQUIREMENTS

Published online by Cambridge University Press:  27 April 2012

Aykut Atalı  and
Özalp Özer
Aykut Atalı
Affiliation:
McKinsey & Company, Chicago, IL 60603 E-mail: aykut_atali@mckinsey.com
Özalp Özer
Affiliation:
School of Management, The University of Texas at Dallas, 800 W. Campbell Rd, Richardson, TX 75080 E-mail: oozer@utdallas.edu
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Abstract

We study a multi-item two-stage production system subject to Markov-modulated demands and production quantity requirements. The demand distribution for each item in each period is governed by a discrete Markov chain. The products are manufactured in two stages. In the first stage, a common intermediate product is manufactured, followed by product differentiation in the second stage. Lower and upper production limits, also known as production smoothing constraints, are imposed on both stages for all items. We propose a close-to-optimal heuristic to manage this system. To do so, we develop a lower bound problem and show that a state-dependent, modified base-stock policy is optimal. We also show when and why the heuristic works well. In our numerical study, the average optimality gap was 4.34%. We also establish some monotonicity results for policy parameters with respect to the production environment. Using these results and our numerical observations, we investigate the joint effect of (i) the two-stage production process, (ii) the production flexibility, and (iii) the fluctuating demand environment on the system's performance. For example, we quantify the value of flexible production as well as the effect of smoothing constraints on the benefits of postponement. We show that a redesign of the production process to allow for delayed product differentiation is more effective and valuable when it is accompanied by an investment in production flexibility.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 2 , April 2012 , pp. 263 - 293
Copyright
Copyright © Cambridge University Press 2012

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