عنوان مقاله [English]
In vehicle routing problem (VRP), the objective is to find the optimum routes for a fleet of vehicles in order to serve a set of customers. These routes should have minimum costs including distance and time, and they should simultaneously satisfy some restrictions such as the maximum capacity of each vehicle, the maximum distance for each vehicle to travel, the time window to visit the specific customer, and so forth. Most enterprises own a heterogeneous fleet of vehicles or hire different types of vehicles to serve their customers. The heterogeneous fleet VRP (HFVRP) addresses the VRP with a heterogeneous fleet of vehicles which have various capacities: fixed costs and variable costs. To the best of our knowledge, all researches in this field have studied the minimization of total traveling time and traveling cost as objectives, while one of the important subjects in the real word is tardiness. In studying tardiness, we assign a due time as an upper bound; if the vehicle reaches the customer after the due time, tardiness will occur. The other important object in HFVRP is the holding cost. In order to have a balance between holding cost and traveling time, we have considered holding cost to solve the problem when a vehicle is selected. So, in this research, we will solve a bi-objective HFVRP with respect to minimizing total traveling time, tardiness, and total holding cost as an objective function. Many algorithms have developed to solve vehicle routing problems, such as genetic algorithm, ant colony optimization, and simulated annealing. For small problem with three vehicles, problem is solved through GAMS and validity of model is proved. For the large-sized problem, because of the complexity, problem is solved with Multi-Objective particle swarm optimization, and then numerical result is presented in the research. The results show that by changing the value of holding cost, the fleet and routes will be changed, and MOPSO finds good answers in short time.