The Fuzzy Multi-Depot Vehicle Routing P roblem with Simul aneous Pick up and Deliv ery: ormulation and A Heuri stic Algorithm

In this paper, the fuzzy multi-dep ot vehicle routing problem with simultaneo us pickup and delivery (FMDVRP-SPD) is investigated. In FMDVRP-SPD, a set of cust omers with simultane ous pickup and delivery demands should be supplied by a fleet of ve hicles that start and e nd their to rs at the same depot. In the problem, both pickup and delivery demands of c ustomers ar e fuzzy variables. The objective of FMDVR P-SPD is to minimiz the total cost of a distribution system, in cluding vehicle traveling cost and vehicle fixed cost. To model the probl em, a fuzzy chance-constrained programming model s propose based on the fuzzy credibility theory. A heuristic algorithm combining K-means clustering algorithm a nd ant colo ny optimiz ation is developed for solving the problem. T o achieve an appropri te threshold value of parameters of the mo el, named vehicle indexes , and to an alyze their influences o n the final solution, n umerical experiments are carried out. More over, the efficiency of the he uristic al orithm is demonstrated by using a standard benchmar k set of test problems.

کلیدواژه ها:

Vehicle routing problem ، Simultaneo us pickupend delivery ، Fuzzy demand ، clustering K-means algorithm.