Modeling and solving Multi-objective Vehicle Routing Problem of Distribution Companies with Fuzzy and Stochastic Constraints (Case Study)

Vehicle routing problem is one of the most important problems in transportation programming. Vehicle routing problem plays an important role in distribution companies because the much of the system costs are related to it. In this paper, a mix integer nonlinear programming model is presented considering the existing demand in distribution companies and real world's restrictions, including Stochastic service time, fuzzy demand and time window limitation. Then, the nonlinear model is equated with the linear model using analytical techniques, for its validity evaluation, GAMS software was utilized. Also, With respect to the fact that this problem is NP-Hard, non-dominated sorting genetic algorithm and multi-objective ant colony optimization algorithm are designed. To demonstrate the efficiency of designed algorithms, evaluation indicators of multi-objective meta-heuristic algorithm's efficiency are utilized. The results indicates that the non-dominated sorting genetic algorithm is more efficient. The issue of the company in questioned via the proposed algorithm. And according to company's management need, practical approach are presented.