A mathematical model for scheduling of transportation, routing, and cross-docking in the reverse logistics network of the green supply chain

Cross-docking refers to the practices of unloading materials from inbound vehicles and then loading them directly into outbound ones. Removing or minimizing warehousing costs, space requirements, as well as inventory utilization, cross-docking simplifies supply chains and makes them deliver goods to markets in a faster and more efficient manner. Accordingly, a mixed-integer linear programming ($MILP $) model is developed in the present study to schedule transportation routing and cross-docking in a reverse logistics network ($RLN$). Furthermore, different traffic modes are also considered to reduce fuel consumption, which reduces emissions and pollution. The proposed model is a multi-product, multi-stage, and non-deterministic polynomial-time that is an NP-hard problem. We use the non-dominated sorting genetic algorithm II ($NSGA-II$) to solve the model. A numerical example has been solved to illustrate the efficiency of the method.