Presenting a Mathematical Programming Model for Routing and Scheduling of Cross-Dock and Transportation in Green Reverse Logistics Network of COVID-19 Vaccines

Cross-docking is the practice of unloading COVID-19 vaccines from inbound delivery vehicles and loading them directly onto outbound vehicles. Cross-docking can streamline supply chains and help them move COVID-19 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 the COVID-19 vaccine to cross-dock and their freight scheduling is of great importance. Achieving the goals of green logistics to reduce fuel consumption and the emission of pollutants has been considered in this study. Accordingly, the present study developed mixed-integer linear programming (MILP) model for routing and scheduling cross-dock and transportation in the green reverse logistics network of COVID-19 vaccines. The model was multi-product (samples of COVID-19 vaccines produced by several manufacturers) and multi-level. This model focused on minimizing the logistics network costs to increase efficiency, reduce fuel consumption and pollution, maximize the consumption value of delivered COVID-19 vaccines and minimize the risk of injection complications due to COVID-19 vaccines corruption. Considering cost minimization as well as uncertainty in pharmacies demand for COVID-19 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.