Capacitated Multi-depot Vehicle Routing Problem with Inter-depot Routes

In this paper، we study the multi-depot vehicle routing problem with inter-depot routes، in which the vehicles can replenish at intermediate depots. Vehicles leave the origin depot with load on-board and serve customers until out of load. They may visit an intermediate depot to replenish and finally return to the origin depot، completing their route. We initiate a mathematical mixed integer programming model for this problem. The objective of the problem is to find routes for vehicles at a minimal cost in terms of total travel cost and replenishments cost at intermediate depots، without violating the capacity constraints of the vehicles. The solution to the problem is obtained through CPLEX solver in commercial software GAMS 23. 5، Genetic Algorithm and Tabu Search algorithms. Computational results indicate the effectiveness of the proposed algorithms in terms of solution time and quality of results.