A robust approach to multiple vehicle location-routing problems with time windows for optimization of cross-docking under uncertainty

The concern about significant changes in the logistics environment, such as the diversification of demands and supply quantities in pickup and delivery processes, has spurred an interest in designing scalable and robust cross-docking planning. In this study, a robust optimization model is introduced to deal with the inherent uncertainty of input data in the location and vehicle routing scheduling problems in cross-docking distribution networks. For this purpose, a new two-phase deterministic mixed-integer linear programming (MILP) model is proposed for locating cross-docks and scheduling vehicle routing with multiple cross-docks. Then, the robust counterpart of the proposed two-phase MILP model is proposed by employing the recent developments in robust optimization theory. Finally, to evaluate the robustness of obtained solutions by the new robust optimization model, a comparison is made with the obtained solutions by the deterministic MILP model in a number of realizations based on different test problems. Moreover, a meta-heuristic algorithm, namely self-adaptive imperialist competitive algorithm (SAICA), is presented for the multiple vehicle location-routing problems. Finally, this study provides various computational test problems to demonstrate the applicability and capability of the proposed robust two-phase MILP model and meta-heuristic solution approach.