A Benders decomposition-based approach for logistics service network design

Abstract

Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service provider seeks to cost-effectively source and fulfill customer demands of products within a multi-echelon distribution network. However, many industrial settings yield instances of the LSNDP that are too large to be solved in reasonable run-times by off-the-shelf optimization solvers. We introduce an exact Benders decomposition algorithm based on partial decompositions that strengthen the master problem with information derived from aggregating subproblem data. More specifically, the proposed Meta Partial Benders Decomposition intelligently switches from one master problem to another by changing both the amount of subproblem information to include in the master as well as how it is aggregated. Through an extensive computational study, we show that the approach outperforms existing benchmark methods and we demonstrate the benefits of dynamically refining the master problem in the course of a partial Benders decomposition-based scheme.

A time-expanded network reduction matheuristic for the logistics service network design problem

“…The model is solved with a generic commercial solver and the results highlight the potential to significantly improve logistics costs by integrating the regional distribution center into the humanitarian supply chain. Belieres et al [4] described the problem studied in this article. The problem is solved through a decomposition algorithm based on a partial Benders decomposition [10].…”

“…Constraints (3) enforce the fulfillment of all customer demands. Constraints (4) ensure that a sufficient number of vehicles are allocated on each transportation arc. Constraints (5) ensure that warehouse storage capacities are never exceeded.…”

“…Then, the efficiency of the heuristic is evaluated in 5.2. In 5.3, we introduce a solution algorithm that combines TENMR with the Meta Partial Benders Decomposition solution method proposed by Belieres et al [5]. Finally, we perform a qualitative analysis of the solutions produced by this approach and we discuss the impact of the new distribution strategies in 5.4.…”

“…To improve the convergence speed of the Benders algorithm, Meta-PBD intelligently switches from one master problem to another by changing both the number of super-products to include in the master as well as how these super-products are built. We refer the interested reader to [5] for more details on Meta-PBD.…”

Multi-period green reverse logistics network design: An improved Benders-decomposition-based heuristic approach

“…Randazzo, Luna and Mahey (2001) found an initial solution using the shortest path algorithm, and Easwaran and Üster (2009) , and Jiang, Tang and Xue (2009) used a Tabu search to yield an initial feasible solution. Correspondingly, Belieres, Hewitt, Jozefowiez, Semet and Van Woensel (2020) proposed a new primal heuristic to enhance the Benders decomposition method along with valid inequalities and a strengthened master problem for large-sized industrial problems. Lai, Sohn, Tseng and Chiang (2010) and Poojari and Beasley (2009) used a genetic algorithm to obtain a (sub-optimal) solution for the master problem in the BD approach.…”