The Stability of a Capacitated, Multi-Echelon Production-Inventory System Under a Base-Stock Policy

Paul Glasserman and Sridhar Tayur
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Paul Glasserman: Columbia University, New York, New York
Sridhar Tayur: Carnegie Mellon University, Pittsburgh, Pennsylvania

Operations Research, 1994, vol. 42, issue 5, 913-925

Abstract: Most models of multilevel production and distribution systems assume unlimited production capacity at each site. When capacity limits are introduced, an ineffective policy may lead to increasingly large order backlogs: The stability of the system becomes an issue. In this paper, we examine the stability of a multi-echelon system in which each node has limited production capacity and operates under a base-stock policy. We show that if the mean demand per period is smaller than the capacity at every node, then inventories and backlogs are stable, having a unique stationary distribution to which they converge from all initial states. Under i.i.d. demands we show that the system is a Harris ergodic Markov chain and is thus wide-sense regenerative. Under a slightly stronger condition, inventories return to their target levels infinitely often, with probability one. We discuss cost implications of these results, and give extensions to systems with random lead times and periodic demands.

Keywords: inventory/production; multistage: stability under base-stock policy; probability; regenerative processes: Harris recurrent inventory processes (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:42:y:1994:i:5:p:913-925

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