Sustainability is essential for growing environmental concern especially those related to carbon emissions by the supply chain, and production. In today’s era, mitigating carbon emissions, and waste has become a major concern for a manufacturing firm or industry. Different tax policies are employed for high-emission industrial, and commercial activities. This study proposes a sustainable inventory system for decaying products that are socially, economically, and environmentally savvy. It is assumed that the demand is advertisement, price, and time-sensitive. The price and advertisement of a product attract the customers to buy more or less. Most of the products have a fixed life span or expiration date for maintaining their quality in original properties. Therefore, the customers prefer the products of maximum life span. This model is designed with a sustainable goal that the incurred total cost is minimized over a planning horizon, together with the determination of optimal price, time period of positive inventory, and the cycle length. The practical utility, and a better understanding of this model are shown with the help of a numerical example. A sensitivity analysis of some crucial parameters is conducted, and it is based on their variations.
References
[1]
Panda, S., Saha, S. and Basu, M. (2008) An EOQ Model for Perishable Products with Discounted Selling-Price, and Stock-Dependent Demand. Central European Journal of Operations Research, 17, 31-53. https://doi.org/10.1007/s10100-008-0073-z
[2]
Sarkar, B. and Sarkar, S. (2013) An Improved Inventory Model for Deteriorating Items with Stock-Dependent Demand, Time-Varying Deterioration, and Partial-Backlogging. Economic Modeling Journal, 30, 924-932. https://doi.org/10.1016/j.econmod.2012.09.049
[3]
Shah, N.H., Soni, H.N. and Patel, K.A. (2013) Optimizing Inventory and Marketing Policy for Non-Instantaneous Deteriorating Items with Generalized Type Deterioration Rate, and Holding Cost. Omega, 41, 421-430. https://doi.org/10.1016/j.omega.2012.03.002
[4]
Chen, X., Benjaafar, S. and Elomri, A. (2013) The Carbon-Constrained EOQ Model for Deteriorating Items. Operations Research Letters, 41, 172-179. https://doi.org/10.1016/j.orl.2012.12.003
[5]
Choudhury, K.D., Karmakar, B., Das, M. and Dutta, T.K. (2015) An Inventory Model for Deteriorating Items with Stock-Dependent Demand, Time-Varying Holding Cost, and Shortages. Opsearch, 52, 55-74. https://doi.org/10.1007/s12597-013-0166-x
[6]
Hovelaque, V. and Bironneau, L. (2015) The Carbon-Constrained EOQ Model with Carbon Emission Dependent Demand. International Journal of Production Economics, 164, 285-291. https://doi.org/10.1016/j.ijpe.2014.11.022
[7]
Shaikh, A.A. (2017) An Inventory Model for Deteriorating Items with Frequency of Advertisement, and Selling Price Dependent Demand Under Mixed Type of Trade-Credit Policy. International Journal of Logistics System and Management, 28, 375-395. https://doi.org/10.1504/IJLSM.2017.086949
[8]
Mishra, U., Cardenas-Barron, L.E., Tiwari, S., Shaikh, A.A. and Trevino-Garza, G. (2017) An Inventory Model with Price and Stock-Dependent Demand for Controllable Deterioration Rate, Shortages Under Preservation Technology Investment. Annals of Operations Research, 254, 165-190. https://doi.org/10.1007/s10479-017-2419-1
[9]
Mishra, U. (2018) Optimizing A Three-Rates-of-Production Inventory Model for Deteriorating Items Under Market Selling-Price and Advertisement Cost. International Journal of Management Science, and Engineering Management, 13, 295-305. https://doi.org/10.1080/17509653.2018.1445046
[10]
Kazemi, N., Abdul-Rashid, S.H., Ghazilla, R.A.R., Shekarian, E. and Zanoni, S. (2018) EOQ Models for Deteriorating Items with Imperfect Quality and Carbon Emission. International Journal of Systems Science Operations & Logistics, 5, 99-115. https://doi.org/10.1080/23302674.2016.1240254
[11]
Shaikh, A.A., Khan, A.A., Panda, G.C. and Konstantaras, I. (2019) An EOQ Model for Decaying Items with Price-Discounted Facility and Stock-Varying Demand and Partial Backlogging. International Transactions in Operations Research, 26, 1365-1395. https://doi.org/10.1111/itor.12632
[12]
Tiwari, S., Ahmed, W. and Sarkar, B. (2019) Sustainable Ordering Policies for Non-Instantaneous Deteriorating Items Under Carbon Emission and Multi Trade-Credit Policies. Journal of Cleaner Production, 240, Article 118183. https://doi.org/10.1016/j.jclepro.2019.118183
[13]
Taleizadeh, A.A., Hazarkhani, B. and Moon, I. (2020) Joint Pricing and Inventory Decisions with Carbon Emission Considerations, Partial Backlogging, and Planned Discount. Annals of Operations Research, 290, 95-113. https://doi.org/10.1007/s10479-018-2968-y
[14]
Mishra, U., Wu, J.Z. and Sarkar, B. (2021) Optimum Sustainable Inventory Management with Back Order, and Deterioration Under Controllable Carbon Emission. Journal of Cleaner Production, 279, 1-18. https://doi.org/10.1016/j.jclepro.2020.123699
[15]
Daryanto, Y., Wee, H.M. and Wu, K.H. (2021) Revising Sustainable EOQ Model for Decaying Products Under Carbon Emission. International Journal of Manufacturing Technology and Management, 35, 1-11. https://doi.org/10.1504/IJMTM.2021.114697
[16]
San-Jose, L.A., Sicilia, J. and Abdul-Jalbar, B. (2021) Optimal Policy for an Inventory System with Price, Time and Frequency of Advertisement-Dependent Demand. Computers and Operations Research, 128, 1-13. https://doi.org/10.1016/j.cor.2020.105169
[17]
Sarkar, B., Sarkar, M., Ganguly, B. and Cardenas-Barron, L.E. (2021) Combined Effect of Carbon Emission and Production Quantity Improvement for Fixed Lifetime Production in A Supply Chain Management. International Journal of Production Economics, 231, 1-14. https://doi.org/10.1016/j.ijpe.2020.107867
[18]
Mishra, U., Mashud, A.H.M., Tseng, M.L. and Wu, J.Z. (2021) Optimizing a Sustainable Supply Chain Inventory Model for Controllable Deterioration, and Carbon Emission Rates in a Greenhouse Farm. Mathematics, 9, Article 495. https://doi.org/10.3390/math9050495
[19]
Das, S.K., Pervin, M., Roy, S.K. and Weber, G.W. (2021) A Hybrid Approach for a Multi-Objective Solid Transportation Location Problem with Variable Carbon Emission in Inventory Management. Annals of Operations Research, 1, Article 27.
[20]
Taleizadeh, A.A., Aliabadi, L. and Thaichon, P. (2022) A Sustainable Inventory System with Price-Sensitive Demand, Carbon Emissions, Partial Trade-Credit Policy, and Partial Backordering. Operations Research, 22, 4471-4516. https://doi.org/10.1007/s12351-021-00683-w
[21]
Mishra, R.K. and Mishra, V.K. (2022) An Optimum Sustainable Inventory Model for Non-Instantaneous Deterioration and Quality Assessment Under Carbon Emissions and Complete Back Ordering Shortage. Arab Journal for Science, and Engineering, 47, 3929-3944. https://doi.org/10.1007/s13369-021-06402-z
[22]
Kumar, S., Sigroha, M., Kumar, K. and Sarkar, B. (2022) Manufacturing Re-Manufacturing Based Supply Chain Management Under Advertisement and Carbon Emission Process. Rairo Operations Research, 56, 831-851. https://doi.org/10.1051/ro/2021189
[23]
Kugele, A.S.H., Ahmad, W. and Sarkar, B. (2022) Geometric Programming Solution of Second Degree Difficulty for Carbon Emission Controlled Reliable Smart Production System. Rairo Operations Research, 56, 1013-1029. https://doi.org/10.1051/ro/2022028
[24]
Sankari, J., Mohan, C. and Ramasamy, U. (2023) A Sustainable Inventory Model for Growing Items Considering Carbon Emissions Product Expiry and Profit Sharing Policy. Journal of Future Sustainability, 3, 201-222. https://doi.org/10.5267/j.jfs.2023.2.002
[25]
Pervin, M. and Weber, G.W. (2023) Sustainable Inventory Model with Environmental Impact for Non-Instantaneous Deteriorating Items with Composite Demand. Rairo Operations Research, 57, 237-261. https://doi.org/10.1051/ro/2023005
[26]
Sobia, S., Pardeepa, M. and Valliathal, M. (2024) A Deterministic Inventory Model for Constant Deteriorating Items with A Generalized Exponential Diminishing Demand, and Stable Holding Cost. The International Journal of Interdisciplinary Organizational Studies, 19, 2286-2294.
[27]
Kumar, S., Kumar, M., Singh, S. and Jaiswal, D. (2024) Sustainable Inventory System for Decaying Products with Expiration Date, Carbon Emission, and Price-Sensitive Exponentially Decreasing Demand. Tuijin Jishu/Journal of Propulsion Technology, 45, 330-343.
[28]
Guo, Z. and Zhang, Y. (2025) Solving the Optimal Order Quantity with Unknown Parameters for Products with Stock-Dependent Demand and Variable Holding Cost Rate. Journal of Combinatorial Optimization, 49, 1-22. https://doi.org/10.1007/s10878-025-01260-z
[29]
Rangarajan, R.S.K., Dey, B.K., Alrasheedi, A.F., Ivkovic, N. and Jana, C. (2025) A Sustainable Production Inventory Model for Power-Pattern Demand with Carbon Emissions and Self Life Considerations. International Journal of Computational Intelligence Systems, 18, 1-32. https://doi.org/10.1007/s44196-025-00861-0
[30]
Alharbi, M. (2025) Investigating a Sustainable Inventory System with Controlled Non-Instantaneous Deterioration for Green Products via the Dragonfly Algorithm. Sustainability, 17, Article 1156. https://doi.org/10.3390/su17031156
