A bi-objective model for pickup and delivery pollution-routing problem with integration and consolidation shipments in cross-docking system

Cross-docking is one of the effective strategies in logistic systems that lead to the reduction of inventory costs and timely delivery of cargos. Overall, activities related to cross-docks include three general classes of loading, sorting, and unloading of cargo. By sorting, it means integration and consolidation. However, most research works merely take loading and unloading related consideration into account. Observing the considerations associated with integration and consolidation processes in cross-docking can demonstrate the effectiveness of this strategy among other logistical systems alone. Increasing social awareness on sustainable development has also led to the emergence of concepts related to green and sustainable supply chain management. Thus, current research provides an integrated model for coordination between decisions related to pickup the cargo from the suppliers, vehicle routing from suppliers to the cross-dock, allocation of inbound vehicles to cross-dock, integration, and consolidation of cargo in cross-dock, allocation of sorted cargo to outbound vehicle, and vehicle routing from cross-dock to customers. The mathematical programming model provided in this research has two purposes. Firstly, it seeks for minimizing total system cost, and secondly, it aims at minimizing total fuel consumption by vehicles, which leads to the reduction of greenhouse gases. Additionally, in order to solve the proposed model, three multi-objective meta-heuristic algorithms, non-dominated ranking genetic algorithm (NRGA), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective particle swarm optimization (MOPSO) are developed. The results show that taking into account the processes of integration and consolidation in the cross-docking, processes of collecting products from suppliers and delivering them to customers makes it possible to obtain the more accurate estimates of the final date of delivering the products to the customers. Furthermore, the above considerations reduce the system costs and, as a result, make economic savings. Therefore, it is reasonable to justify the use of cross-docking. As a result, a sustainable and integrated structure is achieved in cross-docking planning.