Variable neighborhood search for the bi-objective post-sales network design problem: A fitness landscape analysis approach

• In this study, designing a post-sales network operated by a 3PL company is investigated.
• A bi-objective MILP model is proposed to minimize total costs and tardiness.
• An effective novel VNS with three new encoding–decoding mechanisms is proposed.
• A landscape analysis approach is used to find a competing neighborhood order.
• Computational experiments demonstrate robustness of the proposed method.

Post-sales services are important markets in electronics industry due to their impact on marginal profit, market share, and their ability to retain customers. In this study, designing a multi-product four-layer post-sales reverse logistics network operated by a 3PL is investigated. A bi-objective MILP model is proposed to minimize network design costs as well as total weighted tardiness of returning products to customers. To solve the proposed model, a novel multi-start variable neighborhood search is suggested that incorporates nine neighborhood structures and three new encoding–decoding mechanisms. In particular, a fitness landscape measure is employed to select an effective neighborhood order for the proposed VNS. Extensive computational experiments show the effectiveness of the proposed heuristic and the three encoding–decoding mechanisms. The proposed method finds significantly better Pareto optimal sets in comparison with the original Priority method based on the number and the quality of obtained Pareto optimal solutions. In addition, it shows high efficiency by finding near-optimal solutions for the single objective versions of the problem.