An EPQ Model for Deteriorating Inventory under Carbon Emission Regulations and Sustainable Production
DOI:
https://doi.org/10.31305/rrijm2026.v06.n01.013Keywords:
Economic Production Quantity (EPQ), Deteriorating Inventory, Carbon Emission, Carbon Tax, Sustainable Production, Green Supply Chain, Inventory OptimisationAbstract
Growing environmental concern and the tightening of statutory carbon-emission regulations have compelled manufacturing firms to look beyond the traditional cost-minimisation objective of inventory management and to internalise the environmental cost of their production activity. This paper develops an Economic Production Quantity (EPQ) model for a single deteriorating item manufactured at a finite production rate under a carbon-tax regulatory regime. Inventory is assumed to deteriorate at a constant rate once produced, and the total relevant cost per unit time is constructed by combining the classical set-up, production, holding and deterioration costs with an explicit carbon-emission cost arising from production, storage and disposal of deteriorated units. Closed-form expressions for the optimal cycle length, production quantity and minimum total cost are derived using a first-order perturbation approximation that is valid for small deterioration rates, and the convexity of the cost function is established analytically. A numerical example illustrates the working of the model, and a detailed sensitivity analysis is carried out with respect to the deterioration rate, the carbon-tax rate, the demand rate and the holding-cost parameter. The results show that while the total cost is highly sensitive to the demand rate and moderately sensitive to the holding-cost parameter, it is only mildly affected by the carbon-tax rate, implying that a firm can absorb reasonable carbon-tax escalation without materially altering its production-lot-sizing policy. The study offers managerial insights for production planners operating under emission-trading or carbon-tax regulations and provides a foundation for extending sustainable production–inventory research to more general deterioration and demand structures.
References
Bazan, E., Jaber, M. Y., & Zanoni, S. (2015). Supply chain models with greenhouse gas emissions, energy usage and different coordination decisions. Applied Mathematical Modelling, 39(17), 5131–5151. DOI: https://doi.org/10.1016/j.apm.2015.03.044
Bonney, M., & Jaber, M. Y. (2011). Environmentally responsible inventory models: Non-classical models for a non-classical era. International Journal of Production Economics, 133(1), 43–53. DOI: https://doi.org/10.1016/j.ijpe.2009.10.033
Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5(4), 323–326. DOI: https://doi.org/10.1080/05695557308974918
Daryanto, Y., & Wee, H. M. (2019). Low carbon economic production quantity model for imperfect quality deteriorating items. International Journal of Industrial Engineering and Engineering Management, 1(1), 1–8. DOI: https://doi.org/10.24002/ijieem.v1i1.2291
Ghare, P. M., & Schrader, G. F. (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238–243.
Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management.
Hua, G., Cheng, T. C. E., & Wang, S. (2011). Managing carbon footprints in inventory management. International Journal of Production Economics, 132(2), 178–185. DOI: https://doi.org/10.1016/j.ijpe.2011.03.024
Keswani, M., Dwivedi, V., & Khedlekar, U. K. (2025). Analyzing the impact of sustainability on EPQ model: Investigating price and sustainability level dependent demand using center-radius optimisation techniques with metaheuristic algorithms in interval-valued environment. Department of Mathematics & Statistics, Dr. Harisingh Gour Vishwavidyalaya. DOI: https://doi.org/10.3934/jimo.2025001
Moon, I., Yun, W. Y., & Sarkar, B. (2022). Effects of variable setup cost, reliability, and production costs under controlled carbon emissions in a reliable production system. DOI: https://doi.org/10.1504/EJIE.2022.123748
Sarkar, B. (2012). An EOQ model with delay in payments and time-varying deterioration rate. Mathematical and Computer Modelling, 55(3–4), 367–377. DOI: https://doi.org/10.1016/j.mcm.2011.08.009
Taleizadeh, A. A., Soleymanfar, V. R., & Govindan, K. (2018). Sustainable economic production quantity models for inventory systems with shortage. DOI: https://doi.org/10.1016/j.jclepro.2017.10.222
