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In this study, a sustainable inventory model is devised to obtain the retailer’s optimal pricing and replenishment policies for degrading items having a certain lifetime incorporating partial back order as a shortage and dynamic demand under two different scenarios (a) carbon cap and trade policy (b) carbon tax policy. The primary objective of this study is to maximize the retailer’s annual total profit. The retailer’s profit function has been optimized with the help of convexity/concavity criteria employing classical optimization techniques. Based on a real case study, two different numerical examples and corresponding optimal solutions have been shown for both models with the help of Lingo 17 software. Moreover, the impact of the major inventory parameters and prominent managerial insights are presented for the robustness of the proposed model that can cooperate with industrial managers/decision-makers for the overall improvement of his/her industry to take effective and qualitative decisions.

Inventory models for deteriorating items with fixed lifetime, partial backordering and carbon emissions policies