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

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.

Evaluation of freight forwarder risk to transportation market entry

“…In paper [4] authors 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. They propose a model that determines plant and distribution centers locations, shipment levels from plants to the distribution centers, safety-stock levels at distribution centers, and the assignment of retailers to distribution centers by minimizing the sum of fixed facility location costs, transportation costs, and safety-stock costs.…”

Development of a model for international cargo delivery process

“…The majority of existing methods and models for rationalization of the delivery schemes [2][3][4] do not consider the probabilistic characteristics of transport process parameters, and that reduces the efficiency of managerial and organizational decisions. As the most advanced models, which consider stochastic nature of transportation process, should be noted the multi-agent approach to delivery problem with uncertain demand information [5] and the real-time model of control of freight forwarder transportation networks [6].…”

A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements

“…Joint location-inventory models have gained increased attention recently (see [22,23,24,26,30,31,32,37]). The problem analyzed by Shen et al [32] is closely related to our work.…”