capacitated multi-depot vehicle routing problem with inter-depot routes

in this paper, we study the multi-depot vehiclerouting problem with inter-depot routes, in which the vehicles can replenish atintermediate depots. vehicles leave the origin depot with load on-board andserve customers until out of load. they may visit an intermediate depot toreplenish and finally return to the origin depot, completing their route. weinitiate a mathematical mixed integer programming model for this problem. theobjective of the problem is to find routes for vehicles at a minimal cost in termsof total travel cost and replenishments cost at intermediate depots, withoutviolating the capacity constraints of the vehicles. the solution to the problemis obtained through cplex solver in commercial software gams 23.5, geneticalgorithm and tabu search algorithms. computational results indicate theeffectiveness of the proposed algorithms in terms of solution time and qualityof results.