A Mathematical Model for Scheduling of Transportation, Routing, and Cross-Docking in the Reverse Logistics Network of the Green Supply Chain

Document Type : Research Paper


1 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

2 Department of Industrial Management, Semnan University, Semnan, Iran

3 Faculty of Economics, Management and Administrative Science, Semnan University, Semnan, Iran



Cross-docking refers to the practice 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 multiproduct, multi-stage, and non-deterministic polynomial-time that is an NP-hard problem. We use the non-ominated sorting genetic algorithm II (NSGA-II) to solve the model. A numerical example has been solved to illustrate the efficiency of the method.


Articles in Press, Accepted Manuscript
Available Online from 08 September 2023
  • Receive Date: 29 August 2020
  • Revise Date: 26 December 2020
  • Accept Date: 08 January 2021