Article2012

A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

Alper Atamtürk · Gemma Berenguer · Zuo‐Jun Max Shen

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Facility Location and Emergency Management Supply Chain and Inventory Management Optimization and Mathematical Programming

Abstract

We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases with uncapacitated facilities, capacitated facilities, correlated retailer demand, stochastic lead times, and multicommodities. We show how to formulate these problems as conic quadratic mixed-integer problems. Valid inequalities, including extended polymatroid and extended cover cuts, are added to strengthen the formulations and improve the computational results. Compared to the existing modeling and solution methods, the new conic integer programming approach not only provides a more general modeling framework but also leads to fast solution times in general.

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References

1997Network and Discrete Location: Models, Algorithms and Applications.1992Production and Operations Analysis 2010Multicommodity Distribution System Design by Benders Decomposition * † ‡1995Network and Discrete Location 1974Multicommodity Distribution System Design by Benders Decomposition 2003A Joint Location-Inventory Model 2002An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results 1990Optimal Investment in Product-Flexible Manufacturing Capacity

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