Cross-docking is the practice of unloading Coronavirus vaccines from inbound delivery vehicles and loading them directly onto outbound vehicles. Cross-docking can streamline supply chains and help them move Coronavirus vaccines to pharmacies faster and more efficiently by eliminating or minimizing warehouse storage costs, space requirements, and inventory handling. Regarding their short shelf-life, the movement of Coronavirus vaccine to cross-dock and their freight scheduling is of great importance. Achieving the goals of green logistics in order to reduce fuel consumption and emission of pollutants has been considered in this study. Accordingly, the present study developed a mixed-integer linear programming (MILP) model for routing and scheduling of cross-dock and transportation in green reverse logistics network of Coronavirus vaccines. The model was multi-product and multi-level and focused on minimizing the logistics network costs to increase efficiency, reduce fuel consumption and pollution, maximizing the consumption value of delivered Coronavirus vaccines and minimizing risk of injection complication due to Coronavirus vaccines corruption. Considering cost minimization (i.e., earliness and tardiness penalty costs of pharmacies order delivery, cost of fuel consumption and environmental pollution caused by outbound vehicles crossover, the inventory holding costs at the temporary storage area of the cross-dock and costs of crossover and use of outbound vehicles) as well as uncertainty in pharmacies demand for Coronavirus vaccines, the model was an NP-hard problem. In this model, the problem-solving time increased exponentially according to the problem dimensions; hence, this study proposed an efficient method using the NSGA II algorithm.
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