Vehicle routing scheduling problem with cross docking and split deliveries

•We model a vehicle routing scheduling problem with cross docking.•The deliveries to customers can be split.•A simulated annealing algorithm is proposed.•A hybrid algorithm including ant system and simulated annealing is provided.•Results prove the superior performance of the hybrid algorithm.

One of the most important issues in managing a supply chain which makes the materials flow more efficiently from suppliers to customers is cross docking. In this paper a vehicle routing and scheduling problem in a network consisting of suppliers, customers and a cross dock is considered. A set of homogenous vehicles transfer products from suppliers to customers through a cross dock. Each vehicle has a limited capacity and both suppliers and customers must be visited within their time windows, also a customer can be visited more than once by different vehicles. A mixed integer non linear mathematical formulation of this problem is provided. A simulated annealing and a hybrid metaheuristic algorithm combining ant colony system and simulated annealing are proposed. These two proposed metaheuristics are implemented on different data sets. The experimental results show the superior performance of the hybrid algorithm compared with the proposed simulated annealing algorithm.