A heuristic method for the inventory routing problem with time windows

This paper is to resolve the VRPTW and the inventory control decision problem simultaneously since both the vehicle routing decision with time windows and the inventory control decision affect each other and must be considered together. A mathematical model of inventory routing problem with time windows (IRPTW) is proposed. Since finding the optimal solution(s) for IRPTW is a NP-hard problem, this paper proposes a two-phase heuristic method. The first phase is to find the initial solution. The second phase is to improve the solution adopting the variable neighborhood tabu search (VNTS) selecting better neighborhood solutions, to obtain the optimal solution. Moreover, the proposed method was compared with three other heuristic methods. The experimental results indicate that the proposed method is better than the three other methods in terms of average supply chain cost (transportation cost, time window violation penalty cost and inventory cost). (C) 2011 Elsevier Ltd. All rights reserved.