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

Paul Glasserman · SRIDHAR R. TAYUR

111 citations0/0 files storedOperations Research

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Supply Chain and Inventory Management Management and Optimization Techniques Advanced Queuing Theory Analysis

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.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 111 citations exist upstream.

References

1987Applied Probability and Queues 2004Optimal Policies for a Multi-Echelon Inventory Problem 1962The stability of a queue with non-independent inter-arrival and service times 1993Inventory Control in a Fluctuating Demand Environment 1985Queues and Point Processes.1986An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion 1984Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model 1989Optimal Inventory Policies for Assembly Systems Under Random Demands

Cited by

2004Optimal Policies for a Capacitated Two-Echelon Inventory System 2008Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity 1997Bounds and Asymptotics for Planning Critical Safety Stocks 2004Managing Inventory and Supply Performance in Assembly Systems with Random Supply Capacity and Demand 2005Comparative analysis on value of information sharing in supply chains 2005

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.