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.

Historically, both the theory and practice of supply chain management have placed an emphasis on manufacturing and distribution operations, i.e., the forward channel, which consists of suppliers, manufacturers, distributors, retailers, and customers. Recently, increased attention to product recovery practices has extended the scope of traditional supply chain management by drawing attention to collection, demanufacturing, and remanufacturing operations, i.e., the reverse channel, which consists of final-users, collectors, demanufacturers, and remanufacturers. To optimize the performance of the extended supply chain, there is a need to establish an effective and efficient infrastructure via optimal network design. As a result, network design for product recovery has attracted the attention of a growing number of researchers in the past decade. In an attempt to draw more academic attention to this area, this annotated bibliography provides a detailed account of the published literature. The article is organized into two main sections that focus on (i) reverse supply chain network design, which is concerned with establishing an infrastructure to manage the reverse channel only and (ii) closed-loop supply chain network design, which is concerned with establishing an infrastructure to manage both forward and reverse channels in a coordinated manner. Specifically, we describe the operational characteristics of the underlying supply chain system considered in each paper, highlight the features of the network design model proposed therein, and discuss the proposed solution approach along with a brief description of significant computational work, if available. In conclusion, a critical review of the published literature is given and potential areas for future research are identified.

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We study an emergency response network design problem that integrates relief (supply) and evacuation (demand) sides under disaster location and intensity uncertainties which, in turn, dictate uncertainty in terms of the location and amount of demand. Representing these uncertainties by discrete scenarios, we present a stochastic programming framework in which two second stage objectives, the average and worst case costs, are combined. In our model, we minimize, over all of the scenarios, the fixed costs of opening supply centers and shelters, and the weighted sum of average and worst case flow costs. Thus, the model gives the decision maker the flexibility to put relative emphasis on the worst case and average flow cost minimization and explore outcomes in terms of total costs and network configurations. To solve large scale instances with varying relative weights, we devise alternative Benders Decomposition approaches. We implement these by using an advanced callback feature of the solver while simultaneously incorporating several performance-enhancing steps that help to improve runtimes significantly. We conduct a detailed computational study to highlight the efficiency of our proposed solution methodology. Furthermore, we apply our approach in a realistic case study based on Geographical Information Systems data on coastal Texas and present interesting insights about the problem and the resulting network structures for varying weights assigned to objectives.

This study considers an integrated closed-loop supply chain (CLSC) network design problem under uncertainty with regard to product demand and return quantities. To incorporate uncertainty in decision making, we formulate a two-stage stochastic mixed integer linear programming model to determine the optimal locations of (re)manufacturing and processing facilities along with their capacity levels and forward and reverse product flows in the CLSC network to minimize total design and expected operation costs. For the solution of the model and its analysis, we develop a Benders Decomposition approach enhanced for computational efficiency using induced constraints, strengthened Benders cuts, and multiple Benders cuts as well as mean-value scenario based lower-bounding inequalities obtained by dual subproblem disaggregation. Computational results illustrate that the enhancements provide substantial improvements in terms of solution times and quality. Using our model and the solution approach in a sample average approximation framework, we provide further analysis of network designs based on inspection location and recovery rates. Although product inspection at retailer or collection center locations generally reduce costs by avoiding unnecessary use of resources, our analysis also indicates that parameters such as product type and reason-for-return, expected recovery rates, inspection costs, and transportation costs can be instrumental in deciding where the return product inspection should take place and, in turn, dictating the overall cost as well as the structure of the CLSC network.