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Facility Location Modeling and Inventory Management with Multisourcing

Department of Decision Sciences, College of Business, San Francisco State University, San Francisco, California 94132
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
School of Mathematics and Computer Science, Lake Superior State University, Sault Ste. Marie, Michigan 49783
lozsen{at}sfsu.edu
m-daskin{at}northwestern.edu
ccoullard{at}lssu.edu

In this paper we consider a centralized logistics system in which a single company owns the production facility and the set of retailers and establishes warehouses that will replenish the retailers' inventories. We analyze the potential savings that the company will achieve by allowing its retailers to be sourced by more than one warehouse probabilistically, through the use of information technology. We facilitate the discussion on the impact of multisourcing by introducing a capacitated location-inventory model that minimizes the sum of the fixed warehouse location costs, the transportation costs, and the inventory costs. The model is formulated as a nonlinear integer-programming problem that has a cost term that is neither concave nor convex. We propose a Lagrangian relaxation solution algorithm to solve the model and successfully test the algorithm on problems with 88 and 150 retailers. Based on the model properties and the sensitivity analysis results, we conclude that multisourcing becomes a more valuable option as transportation costs increase, i.e., constitute a larger portion of the total logistics cost. In addition, we show that in practice only a small portion of the retailers need to be multisourced to achieve significant cost savings.

Key Words: supply chain network design; nonlinear transportation problem; Lagrangian relaxation
History: Received: April 2006; revised: December 2008; accepted: December 2008.