Integrating Vehicle Scheduling and Open Routing Decisions in a Cross-Docking Center with Multiple Docks

ABSTRACT

Society is facing a series of challenges, as the growth in urban population, the expansion of e-commerce, the pandemic moment (COVID-19), and many others leading to changes in companies’ supply chain, like reducing product delivery time and attention to consumer welfare, the environmental impact, to mention a few. The efficient management of logistic solutions such as cross-docking can contribute to improving the supply chain performance. Here we focus on the integration of scheduling of trucks and routing decisions;the integration of these strategies can significantly reduce costs and help organize the distribution centers and the customers’ services. This article analyzes the integrated problem in which trucks’ scheduling in a cross-docking center with multiple docks is combined with the associated open vehicle routing problem, called Open Vehicle Routing Problem With Cross-Docking (OVRPCD). This approach aims to minimize penalties caused by delays in servicing customers. First, a mixed-integer linear programming model is proposed to solve small instances optimally. Next, two heuristics are proposed to contribute to the solution of the two problems in an integrated way. These heuristics are the Vehicle Routing Cross-Docking Heuristic (VRCDH) and the Cross-Docking Vehicle Routing Heuristic (CDVRH), each focusing on one of the problems. We also propose a Prioritization Lagrangian Heuristic (PLH) based on a model decomposition to improve the solutions found. These three heuristics are compared, considering two search approaches (i) a constructive version (HC) using the swap heuristic;and (ii) a version using the Variable Neighborhood Search (VNS) metaheuristic framework. The VNS-enhanced versions of the heuristics outperform the previous ones. Still, the same relation holds regarding the three heuristics, i.e. the PLH heuristic outperforms the VRCDH one, while the latter outperforms the CDVRH one. Finally, we propose a polynomial-time framework, called Robust Dynamic Prioritization Lagrangian Heuristic (RDPLH), which extends PLH, considering trucks’ release dates and travel times uncertainties, approximating our problem to a real cross-docking center. The framework’s simplicity and the quality of the results allow us to assert that this approach can be used in real cross-docking centers (CDCs).