Abstract:In this article, we consider a multi-product closed-loop supply chain network design problem where we locate collection centers and remanufacturing facilities while coordinating the forward and reverse flows in the network so as to minimize the processing, transportation, and fixed location costs. The problem of interest is motivated by the practice of an original equipment manufacturer in the automotive industry that provides service parts for vehicle maintenance and repair. We provide an effective problem formulation that is amenable to efficient Benders reformulation and an exact solution approach. More specifically, we develop an efficient dual solution approach to generate strong Benders cuts, and, in addition to the classical single Benders cut approach, we propose three different approaches for adding multiple Benders cuts. These cuts are obtained via dual problem disaggregation based either on the forward and reverse flows, or the products, or both. We present computational results which illustrate the superior performance of the proposed solution methodology with multiple Benders cuts in comparison to the branch-and-cut approach as well as the traditional Benders decomposition approach with a single cut. In particular, we observe that the use of multiple Benders cuts generates stronger lower bounds and promotes faster convergence to optimality. We also observe that if the model parameters are such that the different costs are not balanced, but, rather, are biased towards one of the major cost categories (processing, transportation or fixed location costs), the time required to obtain the optimal solution decreases considerably when using the proposed solution methodology as well as the branch-and-cut approach.

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W e consider a network design problem in a multiproduct closed-loop supply chain setting consisting of remanufacturing facilities and finite-capacity manufacturing, distribution, and collection facilities that serve a set of retailers. We first present a mixed-integer linear program to determine the optimal locations of the collection centers and remanufacturing facilities along with the integrated forward and reverse flows such that the total cost of facility location, processing, and transportation associated with forward and reverse flows in the network is minimized. Second, we devise two tabu search heuristics-sequential and random neighborhood search procedures-in which we effectively combine search functions using move and exchange neighborhoods to improve efficiency in exploring the solution space. We also suggest a transshipment heuristic to quickly, but effectively, estimate the objective function value (goodness) of a feasible solution in the course of a tabu search. Third, we present a Benders decomposition solution approach that incorporates the tabu search heuristics as well as Benders cuts that are strengthened to facilitate faster convergence and improved computational efficiency, especially for large-scale instances. While the solutions using tabu search heuristics make the applicability of the Benders decomposition approach possible via providing initial upper bounds and facilitating the generation of good initial Benders cuts, the lower bounds obtained by the Benders approach computationally verify the high quality of the tabu search heuristic solutions. We present computational results illustrating the efficient performance of the solution algorithms in terms of both solution quality and time, especially for larger size problems.

In this paper, we describe research to improve Frito-Lay's outbound supply chain activities by simultaneously optimizing its inventory and transportation decisions. Motivated by Frito-Lay's practice, we first develop a mixed-integer programming formulation from which we develop a large-scale, integrated multiproduct inventory lot-sizing and vehicle-routing model with explicit (1) inventory holding costs, truck loading and dispatch costs, and mileage costs; (2) production, storage, and truck capacity limitations; and (3) direct (plant-to-store) and interplant (plant-to-plant) delivery considerations. Second, we present an iterative solution approach in which we decompose the problem into inventory and routing components. The results demonstrate the impact of direct deliveries on distribution costs and show that direct deliveries and efficient inventory and routing decisions can provide significant savings opportunities over two benchmark models, one of which represents the existing Frito-Lay system. We implemented our models using an application that allows strategy evaluation, analysis of output files, and technology transfer. This application was particularly useful in evaluating potential direct-delivery locations and inventory reductions throughout the supply chain.

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