This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Vidyarthi, N. Articles by Jewkes, E. Search for Related Content

Integrated Production-Inventory-Distribution System Design with Risk Pooling: Model Formulation and Heuristic Solution

Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
nkvidyar{at}uwaterloo.ca
ecelebi{at}uwaterloo.ca
elhedhli{at}uwaterloo.ca
emjewkes{at}uwaterloo.ca

In this paper, we consider a multiproduct two-echelon production-inventory-distribution system design model that captures risk-pooling effects by consolidating the safety-stock inventory of the retailers at distribution centers (DCs). We propose a model that determines plant and DC locations, shipment levels from plants to the DCs, safety-stock levels at DCs, and the assignment of retailers to DCs by minimizing the sum of fixed facility location costs, transportation costs, and safety-stock costs. The model is formulated as a nonlinear mixed-integer programming problem and linearized using piecewise-linear functions. The formulation is strengthened using redundant constraints. Lagrangean relaxation is applied to decompose the problem by echelon. A lower bound is provided by the Lagrangean relaxation, while a heuristic is proposed that uses the solution of the subproblems to construct an overall feasible solution. Computational results reveal that the Lagrangean relaxation provides a sharp lower bound and a heuristic solution that is within 5% of the optimal solution.

Key Words: production-inventory-distribution system design; risk pooling; piecewise linearization; Lagrangean relaxation
History: Received: October 2004; revised: March 2006; accepted: July 2006.