An optimization model for routing—location of vehicles with time windows and cross-docking structures in a sustainable supply chain of perishable foods

The effective distribution of perishable food items is a critical aspect of managing the food industry's supply chain, given their physical–chemical, biological characteristics and composition, which make them highly susceptible to rapid deterioration. This research presents a transport model incorporating a cross-dock system to efficiently deliver goods from production plants to markets. The model incorporates a vehicle routing model that considers time windows for pick-ups and deliveries, optimal cross-dock center locations, a heterogeneous vehicle fleet of limited capacity, and scheduling product collections, arrivals, and departures. The model is a mixed-integer non-linear optimization model that effectively minimizes logistics costs and environmental impacts by considering various parameters such as speed, waiting times, loading and unloading times, and costs associated with the entire operation. The findings demonstrate that the cross-dock structure is highly conducive to distributing perishable goods, achieved by minimizing collection and distribution operations, adhering to designated time windows, and efficiently allocating resources. The GAMS 23.6.5 software is used to program the model, employing various solution strategies, including experimental tests with scenarios, as well as the "posterior," "Pareto optimization," and "weighted sum" methods. The case study in Sincelejo (Sucre, Colombia) reported the best solution, representing 60% of logistics and 40% of environmental costs. The results show complete compliance with routes, no inventory generation, and the necessity of two inbounds and two outbound vehicles for collection from suppliers and delivery to retailers. This study presents an efficient model for managing the transportation of perishable goods, contributing to sustainable distribution activities, and environmental conservation in the food industry's supply chain.