The Fuzzy Multi-Depot Vehicle Routing Problem with Simultaneous Pickup and Delivery: Formulation and A Heuristic Algorithm

In this paper, the fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery (fmdvrp-spd) is investigated. in fmdvrp-spd, a set of customers with simultaneous pickupand delivery demands should be supplied by a fleet of vehicles that start and end their tours at the same depot. in the problem, both pickup and delivery demands of customers are fuzzy variables. theobjective of fmdvrp-spd is to minimize the total cost of adistribution system, including vehicle traveling cost and vehicle fixed cost. to model the problem, a fuzzy chance-constrained programming model is proposed based on the fuzzy credibility theory. a heuristic algorithm combining k-means clustering algorithm and ant colony optimization is developed for solving the problem. to achieve an appropriate threshold value of parameters of the model, named vehicle indexes, and to analyze their influences on the final solution, numerical experiments are carried out. moreover, the efficiency of the heuristic algorithm is demonstrated by using a standard benchmark set of test problems.