A fuzzy correlation based heuristic for Dual-mode integrated Location routing problem

This paper focuses on a variant location routing problem (LRP) named Dual-mode integrated Location Routing Problem (DMI-LRP) in modern supply logistics system. The warehouses in DMI-LRP supply the demands of retailers and online-shopping customers simultaneously and the retailers and customers follow two different order cycles. The problem is presented in a two-echelon structure where products are transported from the plant to the distribution centers (DCs) in the first echelon, and from the DCs to retailers and customers in the second echelon. The mathematical formulation is given together with some valid inequalities to strengthen the model for exact method. We propose the fuzzy correlation (FC) based location for DCs and allocation for retailers and customers in LRP. Also, a fuzzy correlation arc based adaptive neighborhood search (FCA-AVNS) algorithm is designed for path planning. The proposed method is tested on three adapted benchmark instances and the results are compared with exact method and another three heuristics. The numerical experiments demonstrate the feasibility and efficiency of the proposed method especially in solving large-scale problems.