A new bi-objective vehicle routing-scheduling problem with cross-docking: Mathematical model and algorithms

Abstract This paper addresses a vehicle routing problem with cross-docking (VRPCD) that considers truck scheduling, splitting pickup and delivery orders with time-windows at supplier and retailer locations, while optimizing two conflicting objectives (i.e., cost efficiency and responsiveness). The objectives are to minimize the total operational cost and the sum of the maximum earliness and tardiness. A new bi-objective mixed-integer linear programming model is presented and a multi-objective meta-heuristic evolutionary algorithm is proposed for solving the problem. Numerical results indicate the effectiveness of our proposed algorithm comparing with two multi-objective meta-heuristic algorithms (i.e., non-dominated sorting genetic algorithm (NSGA-II) and Pareto archived evolution strategy (PAES)). Also, we report findings from a hypothetical case study in a retail chain in Houston, Texas.