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The multiple trip vehicle routing problem with backhauls in random fuzzy environment: using (α,β)-cost minimization model under the Hurwicz criterion

ABSTRACT In the literature on VRP issues, many works have been studied in deterministic environments. Such proposed models cannot show the appropriate demands of different customers in the real world. One of the most important VRP problems that are widely applicable in real life is nondeterministic multiple trip vehicle routing problem with backhauls (MT-VRPB). In this paper, we focus on MT-VRPB in the random fuzzy environment using cost minimization model under the Hurwicz criterion. This model can deal with various MT-VRPB in random, fuzzy and random fuzzy environments. Regarding to the structure of the proposed model and in order to solve it, a hybrid intelligent algorithm based on the integration of the simplex algorithm, fuzzy simulations, and a firefly algorithm is proposed. The effectiveness and sensitive analysis of the proposed algorithm is demonstrated by solving some numerical examples.