Cross dock scheduling with fixed outbound trucks departure times under substitution condition

•A multi-period multi-commodity cross dock scheduling model is proposed.•The delayed loads are stored to send at the next periods.•The problem is modeled in a mixed integer linear mathematical model.•A heuristic algorithm is proposed to solve the model.•Product substitution is considered in a cross dock system.

Nowadays, cross docking is used as a concept to improve the response time and it reduces the inventory holding cost significantly. In some operational cases, inbound trucks leave the cross dock outbound doors in predefined departure times. In this paper, we propose an inbound truck scheduling model based on fixed outbound trucks’ departure times. Indeed, it is assumed that delayed loads are stored in temporary storage until the next outbound trucks’ departure time with the same destination. Furthermore, according to the post-distribution concept, it is assumed the other destination loads can be replaced with the delayed loads. This paper finds the best sequence of inbound trucks based on the loads substitution concept. To solve the model, a heuristic algorithm is developed and numerical tests are given to compare the results with the optimal solution. The results show using loads substitution concept will reduce cross dock holding costs until 27%.