Optimizing the Service Card in Multi-Depot, Multi-Product and Multi-Level Vehicle Routing Problems with the Aim of Minimizing the Total Distribution Costs

Optimizing the service card in multi-depot, multi-product and multi-level vehicle routing problem is one of the most important and at the same time, the most complex problems in the transportation problems contexts. Numerous exact heuristic and meta-heuristic algorithms have been developed for different vehicle routing problems. In this paper, a binary linear programming (BLP) based model for optimizing the service card in multi-depot, multi-product and multi-level vehicle routing problems with the aim of minimizing the total distribution costs has been proposed. In other words, the purpose of this paper is to determine the optimum transportation for each product in vehicle routing problems for every route, grape and level with minimum distribution costs. Then, an effective algorithm has been developed to solve the problem. The proposed algorithm using the limited resource leveling based on the Lagrange coefficients; transform the multiproduct problem into multiple single-product problems. When each mathematical model for single product vehicle routing problems is solved, the assigned capacity and the required capacity values for each product are compared and then the available and total capacity is calculated. Finally, resource leveling and service card optimization processes are applied to all single-product problems. Therefore, after several steps if no considerable improvement is observed in the solution, then the optimal solution is achieved for the original problem. Design of experiments and validation tests used in the paper indicate the optimal utilization of the limited resources and a considerable reduction in the total distribution costs. Validity of the proposed algorithm against the binary linear programming model has been verified at 95% and computational time has been reduced by 5 times.