Replenishment policy in a logistics system with environmental considerations

One of the most applicable models in inventory and production planning is the economic lot sizing model, which recently extended by environmental considerations and the sustainability concept. The theoretical sustainable lot sizing model is only a basic model that ignores many real-world conditions in the modern cloud manufacturing environments, for example, the possibility of shortage and stockout in the inventory system. In this work, we have presented new sustainable lot-sizing models in which different shortage conditions are considered. We developed a basic model for the time that shortage in not allowed, and full lost sale, full backordering and partial backordering models when shortages are allowed. We proposed an integrated procedure for determining the optimal values of the variables of the proposed models. The models and proposed procedure application are illustrated with numerical examples based on an Iranian petrochemical company's data. Finally, applying sensitivity analysis, the model's results have been analysed and discussed. These results show that the partial backordering case is a general and more realistic model which can be used in many real cases.