Environmental degradation due to carbon emissions occurring in the production, storage and marketing of products has increased notably in recent years. To maintain a sustainable development, it is necessary to penalize commercial activities that generate high carbon emissions. This paper develops and analyzes a sustainable inventory system for a product whose demand follows a power pattern with respect to time. It is considered that the stock items have an estimated life period, after which a percentage of these items begins to deteriorate over time. The inventory system allows shortages which are fully backordered. Several sources of carbon emissions are considered in this article: transportation, stock holding and deterioration. The main objective is to determine the sustainable inventory policy that maximizes the benefit per unit of time, which is given by the difference between the income obtained from sales and the costs associated with inventory management and carbon emissions. Two scenarios are analyzed. In the first, the optimal inventory policy for a system without deterioration is derived. In the second, an algorithm to determine the optimal policy for an inventory system with non-instantaneous deterioration is proposed. Thus, our findings serve to determine the best inventory policy that helps decision-makers to obtain the lot size and the reorder point that maximize the profit per unit time under carbon emission taxes in transporting, storage and deteriorating of items. Some numerical examples are solved in order to illustrate the theoretical results previously obtained. Finally, a sensitive analysis of the optimal inventory policy with respect to some input parameters of the system is presented and interesting managerial insights from the numerical examples are proposed.
