A novel mathematical modeling approach for integrating a periodic vehicle routing problem and cross-docking system

Abstract

To remain competitive in a globalized market, manufacturers must effectively respond to customer demands in various situations. In parallel, logistics companies have adopted cross-docking systems as a key component of lean supply chain management to handle high transportation volumes. By integrating this pivotal component in the supply chain, goods are efficiently distributed to retailers via cross-dock facilities. This article introduces, for the first time, an integrated framework for the periodic vehicle routing problem with cross-docking (PVRPCD) system between supplier and retailer locations. The goal is to optimize three key decisions: 1. Vehicle scheduling and routing for each period, 2. The loading and unloading quantities of goods at the cross-dock, and 3. The selection of a daily combination from periodic retailer demands to minimize the costs incurred by transportation and cross-docking operations. To formulate the PVRPCD, a novel mixed-integer linear programming (MILP) model is designed. Given the computational complexity of large-scale instances, a heuristic algorithm is designed to produce near-optimal initial solutions, which are then embedded into two metaheuristic algorithms: variable neighborhood search (VNS) and population-based variable neighborhood search (PBVNS). These algorithms incorporate four shaking and four local search operators to enhance solution quality and scalability. To validate the effectiveness of the metaheuristic algorithms, computational experiments are conducted using benchmark instances. The optimal solutions obtained via the CPLEX solver for small-scale instances serve as a baseline for comparison. The computational results illustrate that both algorithms effectively solve small-scale problems. Nevertheless, PBVNS consistently outperforms VNS in terms of solution quality, though it requires more computation time. Despite the increased solution time, the improvement in solution quality justifies the additional computational effort. Finally, sensitivity analyses on key PVRPCD parameters provide managerial insights for decision-makers, offering a profound understanding into the influence of model parameters on solution performance.