a multi-objective optimization model for split pollution routing problem with controlled indoor activities in cross docking under uncertainty

Cross docking is a logistics strategy that strives to reduce inventory holding costs, shipping costs, and delays in delivering the products. in this research, an optimization model is presented for split loading and unloading products by suppliers and customers, vehicle routing with fuzzy possibilistic time window constraints among them, assignment of vehicles to cross dock, consolidation and integration of products in cross dock, and allocation of sorted products to outbound vehicles. the mathematical model provided in this study has three objective functions. the first and second objectives minimize total cost and fuel consumption, and the third one maximizes satisfaction degrees of suppliers and customers. with the intention of solving the model, two multi-objective meta-heuristic algorithms, namely multi-objective grey wolf optimizer (mogwo) and multi-objective imperialist competitive algorithm (moica) were utilized. with the intention of illustrating the accuracy of the suggested model and solution approaches, a broad range of numerical instances were considered and the results were investigated.