A Fuzzy Approach for Vehicle Routing Problem with Simultaneous Pickup and Delivery and Time Windows using Improved PSO (Case Study)

Most studies on decision making issue have supposed the problem in deterministic environment, and because uncertainty makes the decisions taken suboptimal, so in this paper we propose a credibility based fuzzy model for the Vehicle Routing Problem with Simultaneous Delivery and Pickup and Time Windows (VRPSDPTW). The dispatching cost of vehicles and customers’ time windows are supposed to be trapezoidal fuzzy numbers. We also proposed a hybrid meta-heuristic algorithm called Improved Particle Swarm Optimization (IPSO) for solving the problem. The proposed algorithm is the combination of Particle Swarm Optimization (PSO) and some removal and insertion techniques which helps to improve the searching ability and maintain diversity of solutions. Finally, to demonstrate the applicability of the proposed model in the real world we studied the distribution of dairy products among customers by a distribution company in Fars province. The computational results show that distributors can use this method to reduce operating costs of the company.