A Mathematical Model for the Vehicles Routing Problem with Multiple Depots, Considering the Possibility of Return Using the Tabu Search Algorithm

The current study examines an essential type of vehicle routing problem (VRP). This type is one where customers are served by limited-capacity vehicles from multiple depots and is known as Multi-Depot Capacitated Vehicle Routing Problem (MDCVRP). The novelty of this study is that in the present case, cars, after Leaving the Depot, can go back to any other depot. Those issues seem to occur in most real-world issues where information, messages, or news are sent electronically from somewhere. The purpose of the problem is to minimize the costs associated with routing. Regarding the literature on such issues, it has been proven in previous studies and research that these problems are among the hard-NP problems, and to solve them using the metaheuristic method, the exact methods justify it. After changing the basic model, this study developed a Tabu Search (TS) algorithm. The study results demonstrate that if the equipment can return to any depot, the cost is significantly reduced in contrast to the case where equipment is forced to return to their depot.