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A Sustainable Deteriorating Inventory Model with Carbon Emission Reduction Policies

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  • Diptesh Kumar Roy,
  • Magfura Pervin,
  • Shashi Bajaj Mukharjee,
  • Kamal Hossain Gazi,
  • Sankar Prasad Mondal
Diptesh Kumar Roy
Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, West Bengal, India
Magfura Pervin
Department of Mathematics, Bangabasi Evening College, West Bengal, India
Shashi Bajaj Mukharjee
Faculty of Basic Science and Humanities, Dr. B C Roy Engineering College, West Bengal, India
Kamal Hossain Gazi
Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, West Bengal, India
Sankar Prasad Mondal
Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, India

Published 2026-01-25

Keywords

  • Stock and price dependent demand,
  • Permissible delay in payments; deterioration,
  • Carbon emission reduction

Copyright (c) 2026 Diptesh Kumar Roy, Magfura Pervin, Shashi Bajaj Mukharjee, Kamal Hossain Gazi, Sankar Prasad Mondal (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Roy, D. K., Pervin, M., Mukharjee, S. B., Gazi, K. H., & Mondal, S. P. (2026). A Sustainable Deteriorating Inventory Model with Carbon Emission Reduction Policies. Applied Research Advances, 2(1), 1-15. https://doi.org/10.65069/ara21202610
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Abstract

In inventory models, profit can be hugely improved by assuming demand according to the requirements of the market situation. In this study, demand is assumed to be time dependent, stock dependent or price dependent for a realistic view of market patterns. The production rate is also considered demand dependent and deterioration is taking time dependent. To address environmental concerns, carbon emissions from inventory holding and replenishment activities are integrated into the decision framework. The model is compared with and without a permissible delay in payment. Numerical examples, theorems, and graphs support the existence of the proposed model. Industrial applications and managerial insights significantly contribute to the novelty of the proposed model. Lastly, the study is concluded with future remarks. 

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References

  1. Kaushik, J. (2025). An inventory model for deteriorating items with block chain process: how will it transform inventory management system. Cogent Business & Management, 12(1), 2442547. https://doi.org/10.1080/23311975.2024.2442547
  2. Kumar, N., Dahiya, S., & Kumar, S. (2022). Two warehouse inventory model for deteriorating items with fixed shelf-life stock-dependent demand and partial backlogging. Journal of Mathematics and Computer Science, 12(85). https://doi.org/10.28919/jmcs/7142
  3. Agi, M. A. N., & Soni, H. N. (2019). Joint pricing and inventory decisions for perishable products with age-, stock, and price-dependent demand rate. Journal of the Operational Research Society, 71(1), 85-99. https://doi.org/10.1080/01605682.2018.1525473
  4. Shah, N. H., & Naik, M. K. (2018). Inventory policies for price-sensitive stock-dependent demand and quantity discounts. International Journal of Mathematical, Engineering and Management Sciences, 3(3), 245–257. https://dx.doi.org/10.33889/IJMEMS.2018.3.3-017
  5. Dey, B. K., Sarkar, B., Sarkar, M., & Pareek, S. (2019). An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment. RAIRO Operations Research, 53(1), 39-57. https://doi.org/10.1051/ro/2018009
  6. Pervin, M., Roy, S. K., & Weber, G. W. (2019). Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: a trade-credit policy. Journal of Industrial and Management Optimization, 15(3), 1345-1373. https://doi.org/10.3934/jimo.2018098
  7. Mishra, U. (2017). An inventory model for Weibull deterioration with stock and price dependent demand. International Journal of Applied and Computational Mathematics, 3, 1951–1967. https://doi.org/10.1007/s40819-016-0217-0
  8. Pervin, M., Roy, S. K., & Weber, G. W. (2020). Deteriorating inventory with preservation technology under price-and stock-sensitive demand. Journal of Industrial and Management Optimization, 16(4). https://doi.org/10.3934/jimo.2019019
  9. Uthayakumar, R., & Karuppasamy, S. K. (2017). A pharmaceutical inventory model for variable demand and variable holding cost with partially backlogged under permissible delay in payments in healthcare industries. International Journal of Applied and Computational Mathematics, 3(1), 327–341. https://doi.org/10.1007/s40819-017-0358-9
  10. Gupta, M., Tiwari, S., & Jaggi, C. K. (2020). Retailer’s ordering policies for time-varying deteriorating items with partial backlogging and permissible delay in payments in a two-warehouse environment. Annals of Operations Research, 295, 139–161. https://doi.org/10.1007/s10479-020-03673-x
  11. Pervin, M., Roy, S. K., & Weber, G. W. (2017). A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items. Numerical Algebra, Control and Optimization, 7(1), 21-50. https://doi.org/10.3934/naco.2017002
  12. Shaikh, A. A., Bhunia, A. K., Cárdenas-Barrón, L. E., Sahoo, L., & Tiwari, S. (2018). A fuzzy inventory model for a deteriorating item with variable demand, permissible delay in payments and partial backlogging with shortage follows inventory (SFI) policy. International Journal of Fuzzy Systems, 20, 1606–1623. https://doi.org/10.1007/s40815-018-0466-7
  13. Tiwari, S., Daryanto, Y., & Wee, H. M. (2018). Sustainable inventory management with deteriorating and imperfect quality items considering carbon emission. Journal of Cleaner Production, 192, 281-292. https://doi.org/10.1016/j.jclepro.2018.04.261
  14. Rahman, M. S., Duary, A., & Khan, M. A. A. (2022). Interval valued demand related inventory model under all units’ discount facility and deterioration via parametric approach. Artificial Intelligence Review, 55, 2455–2494. https://doi.org/10.1007/s10462-021-10069-1
  15. Das, S. C., Manna, A. K., & Rahman, M. S. (2021). An inventory model for non-instantaneous deteriorating items with preservation technology and multiple credit periods-based trade credit financing via particle swarm optimization. Soft Computing, 25, 5365–5384. https://doi.org/10.1007/s00500-020-05535-x
  16. Barman, A., Das, R., & De, P. K. (2022). An analysis of optimal pricing strategy and inventory scheduling policy for a non-instantaneous deteriorating item in a two-layer supply chain. Applied Intelligence, 52, 4626–4650. https://doi.org/10.1007/s10489-021-02646-2
  17. Paul, A., Pervin, M., Roy, S. K., Weber, G. W., & Mirzazadeh, A. (2021). Effect of price-sensitive demand and default risk on optimal credit period and cycle time for a deteriorating inventory model. RAIRO Operations Research, 55, S2575-S2592. https://doi.org/10.1051/ro/2020108
  18. Das, S. K., Pervin, M., & Roy, S. K. (2023). Multi-objective solid transportation-location problem with variable carbon emission in inventory management: a hybrid approach. Annals of Operations Research, 324, 283–309. https://doi.org/10.1007/s10479-020-03809-z
  19. Yadav, A. S., Kumar, A., & Yadav, K. K. (2025). Optimization of an inventory model for deteriorating items with both selling price and time-sensitive demand and carbon emission under green technology investment. International Journal on Interactive Design and Manufacturing, 19, 1297–1313. https://doi.org/10.1007/s12008-023-01689-8
  20. Mashud, A. H. M., Roy, D., & Chakrabortty, R. K. (2022). An optimum balance among the reduction in ordering cost, product deterioration and carbon emissions: a sustainable green warehouse. Environmental Science and Pollution Research, 29, 78029–78051. https://doi.org/10.1007/s11356-022-21008-0
  21. Barman, H., Pervin, M., & Roy, S. K. (2022). Impacts of green and preservation technology investments on a sustainable EPQ model during COVID-19 pandemic. RAIRO Operations Research, 56, 2245–2275. https://doi.org/10.1051/ro/2022102
  22. Kuo, T. C., Tseng, M. L., & Chen, H. M. (2018). Design and analysis of supply chain networks with low carbon emissions. Computational Economics, 52, 1353–1374. https://doi.org/10.1007/s10614-017-9675-7
  23. Haque, R., Pervin, M., & Mondal, S. P. (2024). A sustainable manufacturing–remanufacturing inventory model with price and green sensitive demand for defective and usable items. RAIRO Operations Research, 58(4), 3439–3467. https://doi.org/10.1051/ro/2024067
  24. Jiang, Y., Li, B., & Qu, X. (2016). A green vendor-managed inventory analysis in supply chains under carbon emissions trading mechanism. Clean Technologies and Environmental Policy, 18, 1369–1380. https://doi.org/10.1007/s10098-015-1048-0