Benders decomposition with alternative multiple cuts for a multi‐product closed‐loop supply chain network design model

Abstract

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.

Reverse Logistics: Network Design Based on Life Cycle Assessment

“…The most considered decision criterion is the total cost of the network [13][14][15][16][17], followed by the service level [18], and the generated profit [12]. In the recent literature review in [12], the only objectives considered in RL or forward/reverse chain design are: cost, profit, responsiveness (Service level), source balance, and quality.…”

“…The main decisions of the models are: location/allocation of facilities and transportation values [13][14][15][16][17][18]. Moreover, most of the works found in the literature consider the network design problem with collection, sorting, and disposal facilities owned by one company which is collecting the reverse flow and reusing it.…”

“…Most of the works found in the literature consider mainly the remanufacturing option of the disposal step [13], [14], [16][17][18] and only few consider the recycling option of the disposal step such as [15], [23]. But in our case, we are interested in recycling the reverse flow as well as remanufacturing it.…”

What you should know about location modeling

“…It is worth noting that a capacitated fixed charge location model is at the heart of one of the more effective heuristics for the vehicle routing problem (Bramel and Simchi-Levi, [5]). Finally, researchers interested in the field of reverse logistics or closed-loop supply chains are utilizing extensions of the UFLP to identify desirable sites for forward distribution centers and reverse collection, sorting, recycling and remanufacturing facilities (Easwaran and Uster, [19]; Sahyouni et al [51]; and Uster et al [63]). …”

Closed loop supply chain network design for the paper industry: A multi-objective stochastic robust approach

“…Also, one of the major challenges in the design of CLSC networks is the simultaneous study of the forward and reverse flows. Uster et al [4] emphasized that reverse flow networks, which are independent of the forward flows will create an increase in infrastructure costs and potential profit decrease related to the different recovery alternatives. Moreover, addressing uncertainty related to activities in the CLSC is another challenge.…”