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

Authors:
Navneet Vidyarthi;Emre Çelebi;Samir Elhedhli;Elizabeth Jewkes
Affiliations:
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
Venue:
Transportation Science
Year:
2007

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Abstract

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.