an open routing and scheduling model with cross-docking and hard time window in supply chain

Vehicle routing problem is one of the most important issues in the industry and nowadays due to its practical applications in realworld problems, researchers are paying attention to this field of study. corporation’s willingness for satisfying customers with timely delivery of products along with reducing the warehousing and shipping costs has resulted in consideration of the routing problem in cross-dock as a new research direction for distribution supply chain networks. with regard to the enumerated matters, this paper aims to design the cross-dock and optimize the open schedule routing of vehicles simultaneously. the extended model is a mixed-integer linear programming optimization model. notably, a two-stage model with two objective functions for using in a multi-product distribution network with different carrying capacity and costs is designed. the proposed model considers the hard time window as an innovation along with the open transportation routing and considering the cost of operations within cross-docks in the objective function. the output results of the extended model show that it performs efficiently and converges to reasonable solutions very fast. noteworthy, the extended model is general and could be applied in different real-world industrial cases as a reliable decision-making tool.