Although many researchers have studied the VRP problems in a deterministic environment, their proposed models cannot satisfactorily accommodate various customer demands in an appropriate time in the real world. Thus, this paper focuses on the Multiple Trip Vehicle Routing Problem with Backhauls (MT-VRPB)in random fuzzy environment using cost minimization model under the Hurwicz criterion. This as one of the most important problems in VRP problems widely used in real life. Furthermore, it is proved that this model can deal with various MT-VRPB in random, fuzzy and random fuzzy environments. In order to solve this model, the simplex algorithm, fuzzy simulations and a firefly algorithm are integrated to produce a hybrid intelligent algorithm.
