Integrated inventory routing problem with quality time windows and loading cost for deteriorating items under discrete time

We investigate an integrated inventory routing problem (IRP) in which one supplier with limited production capacity distributes a single item to a set of retailers using homogeneous vehicles. In the objective function we consider a loading cost which is often neglected in previous research. Considering the deterioration in the products, we set a soft time window during the transportation stage and a hard time window during the sales stage, and to prevent jams and waiting cost, the time interval of two successive vehicles returning to the supplier's facilities is required not to be overly short. Combining all of these factors, a two-echelon supply chain mixed integer programming model under discrete time is proposed, and a two-phase algorithm is developed. The first phase uses tabu search to obtain the retailers' ordering matrix. The second phase is to generate production scheduling and distribution routing, adopting a saving algorithm and a neighbourhood search, respectively. Computational experiments are conducted to illustrate the effectiveness of the proposed model and algorithm.