Stochastic Multi-Item Inventory Systems with Markov-Modulated Demands and Production Quantity Requirements

Probability in the Engineering and Informational Sciences 26, pp. 263-293, 2012.

31 Pages Posted: 8 Sep 2015 Last revised: 14 Oct 2017

See all articles by Aykut Atali

Aykut Atali

McKinsey & Co. Inc.

Özalp Özer

Jindal School of Management - The University of Texas at Dallas

Date Written: November 1, 2006

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.

Keywords: Inventory/Production: multi-item/echelon/stage; Markov-modulated; postponement; production smoothing; capacity

Suggested Citation

Atali, Aykut and Özer, Özalp, Stochastic Multi-Item Inventory Systems with Markov-Modulated Demands and Production Quantity Requirements (November 1, 2006). Probability in the Engineering and Informational Sciences 26, pp. 263-293, 2012.. Available at SSRN: https://ssrn.com/abstract=2657241

Aykut Atali

McKinsey & Co. Inc. ( email )

Konigsallee 60C
Chicago, IL Quebec 60603
United States

Özalp Özer (Contact Author)

Jindal School of Management - The University of Texas at Dallas ( email )

Jindal School of Management
800 W. Campbell Road
Richardson, TX 75080
United States

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