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A Branch and Bound based solution method for solving Vehicle Routing Problem with Fuzzy Stochastic Demands
  • Vishnu Pratap Singh,
  • Kirti Sharma,
  • Debjani Chakraborty
Vishnu Pratap Singh
Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur
Author Profile
Kirti Sharma
Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur
Debjani Chakraborty
Department of Mathematics, Indian Institute of Technology Kharagpur

Abstract

In this paper, Capacitated vehicle routing problem(CVRP) with fuzzy stochastic demands have been presented. Discrete fuzzy random variables have been used to represent the demands of the customers. The objective of CVRP with fuzzy stochastic demands is to obtain a set of routes which originates as well as terminates at the source node and while traversing the route, the demands of all the customers present in the network are satisfied. The task here is to carry out all these operations with minimum cost. CVRP in imprecise and random environment has been considered here, and an a priori route construction technique has been adopted for which branch and bound algorithm has been used. The recourse policy used in this work is reactive, i.e. recourse to depot is only done only upon the occurrence of the failure. The delivery policy considered here is full delivery. Demands of the customers are the only source of impreciseness and randomness in the problem under construction. Parametric Graded Mean Integration Representation(PGMIR) method has been used for the comparison purposes, whenever required. A numerical example with 4 customers have been solved to present the proposed methodology.