A Vehicle Routing Problem with Inventory in a Hybrid Uncertain Environment

Manufacturers, who re-supply a large number of customers, continually struggle with the question of how to formulate a replenishment strategy. The purpose of this paper is to determine the optimal 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 the inventory control decision problem simultaneously since the regular VRP does not. Both the vehicle routing decision for delivery and the inventory control decision affect each other and must be considered together. Hence, a mathematical model of vehicle routing problem with inventory is proposed whose demands are assumed to be hybrid variables (HVRPI) in which fuzziness and randomness are considered together. Then, the problem is transformed into its equivalent deterministic form and presented as a multi-objective mixed integer nonlinear programming. Since finding the optimal solution(s) for HVRPI is a NP-hard, a solution algorithm is presented composed of the constrained Nelder–Mead method and a Tabu search algorithm for the vehicle routing to solve the complex problem. The usefulness of the model is validated by experimental results. The findings indicate that the proposed model can provide a practical tool to significantly reduce the logistic cost.