A Multi-Objective EPQ Model for Deteriorating Inventory Considering Cost, Carbon Emissions, and Waste

Abstract

Modern production–inventory systems no longer operate under the single criterion of cost minimisation. Growing regulatory pressure, consumer awareness, and corporate sustainability commitments have made carbon emissions and waste generation equally important performance measures for any manufacturing firm. This article develops a multi-objective Economic Production Quantity (EPQ) model for a single deteriorating item in which the traditional cost-minimisation objective is jointly optimised with two environmental objectives: total carbon emissions arising from production, holding, and transportation activities, and the volume of physical waste generated on account of deterioration and defective output. The item is assumed to deteriorate at a constant rate once it enters inventory, and shortages are not permitted. A weighted-sum multi-objective programming approach is used to convert the three conflicting objectives into a single composite objective function, and the classical calculus-based optimisation technique is applied to derive closed-form expressions for the optimal production quantity and cycle length. A numerical example, followed by a detailed sensitivity analysis of the key parameters, is presented to illustrate the applicability of the proposed model and to generate managerial insights. The results indicate that a small increase in the unit carbon-emission cost produces a disproportionately larger reduction in the optimal lot size, which in turn lowers total waste but raises the effective holding-and-shortage related cost. The model offers production managers a practical decision-support tool for balancing economic and environmental performance in deteriorating-item inventory systems.