A Vehicle Routing Problem with Inventory in a Hybrid Uncertain Environment

Manufacturers, who re-supply a large number of customers, continually struggle with thequestion of how to formulate a replenishment strategy. the purpose of this paper is to determine theoptimal set of routes for a group of vehicles in the transportation network under defined constraints –which is known as the vehicle routing problem (vrp) – delivering new items, and resolving theinventory control decision problem simultaneously since the regular vrp does not. both the vehiclerouting decision for delivery and the inventory control decision affect each other and must beconsidered together. hence, a mathematical model of vehicle routing problem with inventory isproposed whose demands are assumed to be hybrid variables (hvrpi) in which fuzziness andrandomness are considered together. then, the problem is transformed into its equivalent deterministicform and presented as a multi-objective mixed integer nonlinear programming. since finding theoptimal solution(s) for hvrpi is a np-hard, a solution algorithm is presented composed of theconstrained nelder–mead method and a tabu search algorithm for the vehicle routing to solve thecomplex problem. the usefulness of the model is validated by experimental results. the findingsindicate that the proposed model can provide a practical tool to significantly reduce the logistic cost.