Two-Warehouse Inventory Model for Non-Instantaneously Deteriorating Item Incorporating Preservation Technology, Carbon Emissions and Hybrid Payment Schemes
Abstract
This study proposes an advanced inventory model for non-instantaneously deteriorating items, integrating preservation technology, carbon emissions considerations, price-dependent demand, and a hybrid payment scheme within a two-warehouse framework. The hybrid payment method, combining partial upfront and deferred payments, enhances cash flow flexibility, which is critical for managing financial constraints in supply chain operations. The model aims to optimize inventory management by minimizing total costs while fostering environmental sustainability. Key features include investments in green technology to reduce carbon emissions and mitigate item deterioration, along with dynamic pricing strategies to respond to market demand fluctuations. Numerical analyses validate the model, revealing that preservation technology investments significantly lower total costs by extending product shelf life, while effective carbon management reduces transportation expenses. The hybrid payment scheme also proves to be a strategic tool for balancing financial obligations and operational efficiency. Sensitivity analysis conducted using MATLAB R2024a highlights the impact of changes in key parameters, such as demandelasticity, deterioration rate, and carbon tax, on the total cost. The findings provide actionable insights for managers to enhance inventory efficiency and sustainability, particularly in cost-sensitive and environmentally regulated industries.
References
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M. Pervin, “A sustainable deteriorating inventory model with backorder and controllable carbon emission by using green technology,” Environment, Development and Sustainability, pp. 1–37, 2024, doi: 10.1007/s10668-023-02984-9.
W. A. Jauhari, I. D. Wangsa, H. Hishamuddin, and N. Rizky, “A sustainable vendor-buyer inventory model with incentives, green investment, and energy usage under stochastic demand,” Cogent Business & Management, vol. 10, no. 1, 2023, doi: 10.1080/23311975.2022.2158609.
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W. A. Jauhari, I. D. Wangsa, H. Hishamuddin, and N. Rizky, “A sustainable vendor-buyer inventory model with incentives, green investment, and energy usage under stochastic demand,” Cogent Business & Management, vol. 10, no. 1, 2023, doi: 10.1080/23311975.2022.2158609.
C.K.Jaggi, S.Tiwari, andS.K.Goel, “Creditfinancingineconomicordering policies for noninstantaneous deteriorating items with price dependent demand and two storage facilities,” Annals of Operations Research, vol. 248, pp. 253–280, 2017, doi: 10.1007/s10479-016-21568.
S. Tiwari, L. E. C´ardenas-Barr´on, A. Khanna, and C. K. Jaggi, “Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment,” International Journal of Production Economics, vol. 176, pp. 154–169, 2016, doi: 10.1016/j.ijpe.2016.03.017.
A. Limi, K. Rangarajan, P. Rajadurai, A. Akilbasha, and K. Parameswari, “Three warehouse inventory model for non-instantaneous deteriorating items with quadratic demand, timevarying holding costs and backlogging over finite time horizon,” Ain Shams Engineering Journal, vol. 102826, 2024, doi: 10.1016/j.asej.2023.102826.
K. Rangarajan and K. Karthikeyan, “Two warehouse optimal inventory model for noninstantaneous deteriorating item,” International Journal of Engineering and Technology (UAE), vol. 7, no. 4.10, pp. 946–948, 2018.
R. S. Rana, D. Kumar, and K. Prasad, “Mitigating the impact of demand disruption on perishable inventory in a two-warehouse system,” Operations Management Research, vol. 17, pp. 469–504, 2024, doi: 10.1007/s12063-023-00418-4.
V.Murmu,D.Kumar,B.Sarkar,R.S.Mor,andA.K.Jha,“Sustainableinventorymanagement based on environmental policies for perishable products under first or last in and first out policy,” Journal of Industrial and Management Optimization, vol. 19, no. 7, pp. 4764–4803, 2023, doi: 10.3934/jimo.2022149.
R. S. Rana, D. Kumar, and K. Prasad, “Two warehouse dispatching policies for perishable items with freshness efforts, inflationary conditions, and partial backlogging,” Operations Management Research, vol. 15, pp. 28–45, 2022, doi: 10.1007/s12063-020-00168-7.
J. A. Buzacott, “Economic order quantities with inflation,” Operations Research Quarterly, vol. 26, pp. 553–558, 1975.
P. Meena, S. Meena, A. K. Sharma, P. T. Singh, and G. Kumar, “Managing inventory of nonimmediately degrading items with partial backlog and discounting cash flow under inflation,” Materials Today: Proceedings, vol. 50, pp. 155–162, 2022, doi: 10.1016/j.matpr.2021.11.348.
T. K. Datta, “Effect of green technology investment on a production-inventory system with carbon tax,” Advances in Operations Research, Article ID 4834839, 2017, doi: 10.1155/2017/4834839.
A.Limi,K.Rangarajan, C.Jana, E.Ghith, T.Lamoudan, G.-W.Weber, andA.A.Abdelhamid, “Analyzing how inflation affects non-instantly decaying goods with demand linked to ads and selling price in a dual-warehouse setup,” Alexandria Engineering Journal, vol. 106, pp. 517–529, 2024, doi: 10.1016/j.aej.2024.08.014.
D. Pal, A. K. Manna, I. Ali, P. Roy, and A. A. Shaikh, “A two-warehouse inventory model with credit policy and inflation effect,” Decision Analytics Journal, vol. 10, no. 100406, 2024, doi: 10.1016/j.dajour.2022.100406.
M. Choudhury and G. C. Mahata, “Non-instantaneous deteriorating items inventory models with fixed lifetime products under hybrid partial prepayment and trade credit in supply chain,” Journal of Industrial and Management Optimization, vol. 20, no. 1, pp. 221–259, 2024.
G. Li, X. He, J. Zhou, and H. Wu, “Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items,” Omega, vol. 84, pp. 114–126, 2018, doi: 10.1016/j.omega.2018.04.010.
R. S. Rana, D. Kumar, and K. Prasad, “Sustainable production-inventory system for perishables under dynamic fuel pricing and preservation technology investment,” Environmental Science and Pollution Research, vol. 30, pp. 90121–90147, 2023, doi: 10.1007/s11356-02328252-y.
W. A. Jauhari, I. Pujawan, and M. Suef, “Sustainable inventory management with hybrid production system and investment to reduce defects,” Annals of Operations Research, vol. 324, pp. 543–572, 2023, doi: 10.1007/s10479-022-04666-8.
A. H. M. Mashud, M. Pervin, U. Mishra, Y. Daryanto, M.-L. Tseng, and M. K. Lim, “A sustainable inventory model with controllable carbon emissions in green-warehouse farms,” Journal of Cleaner Production, vol. 298, no. 126777, 2021, doi: 10.1016/j.jclepro.2021.126777.
D. Chakraborty, D. K. Jana, and T. K. Roy, “Multi-warehouse partial backlogging inventory system with inflation for non-instantaneous deteriorating multi-item under imprecise environment,” Soft Computing, vol. 24, no. 19, pp. 14471–14490, 2020, doi: 10.1007/s00500-02004920-6.
Y. He and H. Huang, “Optimizing inventory and pricing policy for seasonal deteriorating products with preservation technology investment,” Journal of Industrial Engineering, Article ID 793568, 2013.
A. Limi, K. Rangarajan, and P. Rajadurai, “Recent review on non-instantaneous deteriorating items in inventory models (2006–2022),” International Journal of Services and Operations Management, vol. 1, no. 1, 2023 (in press), doi: 10.1504/IJSOM.2023.10061336.
T. P. Dye and C. Y. Dye, “A production inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time,” Journal of Computational and Applied Mathematics, vol. 239, pp. 25–36, 2013, doi: 10.1016/j.cam.2012.09.020.
Y. W. Lok, S. S. Supadi, and K. B. Wong, “Optimal investment in preservation technology for non-instantaneous deteriorating items under carbon emissions consideration,” Computers & Industrial Engineering, vol. 183, no. 109446, 2023, doi: 10.1016/j.cie.2023.109446.
A. H. M. Mashud, H.-M. Wee, and C.-V. Huang, “Preservation technology investment, trade credit, and partial backordering model for a non-instantaneous deteriorating inventory,” RAIRO-Operations Research, vol. 55, no. S51, pp. S51–S77, 2021, doi: 10.1051/ro/2021017.
U. Mishra, J. T. Aguilera, S. Tiwari, and L. E. C´ ardenas-Barr´ on, “Retailer’s joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments,” Mathematical Problems in Engineering, vol. 2018, pp. 1–14, 2018, doi: 10.1155/2018/6962417.
S. P. Chiu, J. J. Liao, S. L. Kang, H. M. Srivastava, and S. D. Lin, “Sustainable inventory managements for non-instantaneous deteriorating items: Preservation technology and green technology approaches with advanced purchase discounts and joint emission regulations,” Sustainability, vol. 16, no. 6805, 2024.
S. V. S. Padiyar, V. C. Kuraie, D. Makholia, S. R. Singh, V. Singh, and N. Joshi, “An imperfect production inventory model for instantaneous deteriorating items with preservation investment under inflation on time value of money,” Contemporary Mathematics, pp. 1422–1446, 2024.
U. Mishra, J. Z. Wu, Y. C. Tsao, and M. L. Tseng, “Sustainable inventory system with controllable non-instantaneous deterioration and environmental emission rates,” Journal of Cleaner Production, vol. 244, no. 118807, 2020, doi: 10.1016/j.jclepro.2019.118807.
A. A. Taleizadeh, B. Hazarkhani, and I. Moon, “Joint pricing and inventory decisions with carbon emission considerations, partial backordering and planned discounts,” Annals of Operations Research, vol. 290, pp. 95–113, 2020, doi: 10.1007/s10479-017-2536-6.
H. M. Wee and Y. Daryanto, “Imperfect quality item inventory models considering carbon emissions,” in Optimization and Inventory Management, N. H. Shah and M. Mittal, Eds. Singapore: Springer Nature, 2020, pp. 137–159.
M. Pervin, “A sustainable deteriorating inventory model with backorder and controllable carbon emission by using green technology,” Environment, Development and Sustainability, pp. 1–37, 2024, doi: 10.1007/s10668-023-02984-9.
W. A. Jauhari, I. D. Wangsa, H. Hishamuddin, and N. Rizky, “A sustainable vendor-buyer inventory model with incentives, green investment, and energy usage under stochastic demand,” Cogent Business & Management, vol. 10, no. 1, 2023, doi: 10.1080/23311975.2022.2158609.
M. Suef, W. A. Jauhari, I. Pujawan, et al., “Investigating carbon emissions in a singlemanufacturer multi-retailer system with stochastic demand and hybrid production facilities,” Process Integration and Optimization for Sustainability, vol. 7, pp. 743–764, 2023, doi: 10.1007/s41660-023-00320-3.
W. A. Jauhari, D. N. Affifah, P. W. Laksono, and D. M. Utama, “A closed-loop supply chain inventory model with stochastic demand, exchange rate, green investment, and carbon tax,” Cleaner Logistics and Supply Chain, vol. 13, no. 100168, 2024, doi: 10.1016/j.clscn.2024.100168.
W. A. Jauhari, I. D. Wangsa, H. Hishamuddin, and N. Rizky, “A sustainable vendor-buyer inventory model with incentives, green investment, and energy usage under stochastic demand,” Cogent Business & Management, vol. 10, no. 1, 2023, doi: 10.1080/23311975.2022.2158609.
C.K.Jaggi, S.Tiwari, andS.K.Goel, “Creditfinancingineconomicordering policies for noninstantaneous deteriorating items with price dependent demand and two storage facilities,” Annals of Operations Research, vol. 248, pp. 253–280, 2017, doi: 10.1007/s10479-016-21568.
S. Tiwari, L. E. C´ardenas-Barr´on, A. Khanna, and C. K. Jaggi, “Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment,” International Journal of Production Economics, vol. 176, pp. 154–169, 2016, doi: 10.1016/j.ijpe.2016.03.017.
A. Limi, K. Rangarajan, P. Rajadurai, A. Akilbasha, and K. Parameswari, “Three warehouse inventory model for non-instantaneous deteriorating items with quadratic demand, timevarying holding costs and backlogging over finite time horizon,” Ain Shams Engineering Journal, vol. 102826, 2024, doi: 10.1016/j.asej.2023.102826.
K. Rangarajan and K. Karthikeyan, “Two warehouse optimal inventory model for noninstantaneous deteriorating item,” International Journal of Engineering and Technology (UAE), vol. 7, no. 4.10, pp. 946–948, 2018.
R. S. Rana, D. Kumar, and K. Prasad, “Mitigating the impact of demand disruption on perishable inventory in a two-warehouse system,” Operations Management Research, vol. 17, pp. 469–504, 2024, doi: 10.1007/s12063-023-00418-4.
V.Murmu,D.Kumar,B.Sarkar,R.S.Mor,andA.K.Jha,“Sustainableinventorymanagement based on environmental policies for perishable products under first or last in and first out policy,” Journal of Industrial and Management Optimization, vol. 19, no. 7, pp. 4764–4803, 2023, doi: 10.3934/jimo.2022149.
R. S. Rana, D. Kumar, and K. Prasad, “Two warehouse dispatching policies for perishable items with freshness efforts, inflationary conditions, and partial backlogging,” Operations Management Research, vol. 15, pp. 28–45, 2022, doi: 10.1007/s12063-020-00168-7.
J. A. Buzacott, “Economic order quantities with inflation,” Operations Research Quarterly, vol. 26, pp. 553–558, 1975.
P. Meena, S. Meena, A. K. Sharma, P. T. Singh, and G. Kumar, “Managing inventory of nonimmediately degrading items with partial backlog and discounting cash flow under inflation,” Materials Today: Proceedings, vol. 50, pp. 155–162, 2022, doi: 10.1016/j.matpr.2021.11.348.
T. K. Datta, “Effect of green technology investment on a production-inventory system with carbon tax,” Advances in Operations Research, Article ID 4834839, 2017, doi: 10.1155/2017/4834839.
A.Limi,K.Rangarajan, C.Jana, E.Ghith, T.Lamoudan, G.-W.Weber, andA.A.Abdelhamid, “Analyzing how inflation affects non-instantly decaying goods with demand linked to ads and selling price in a dual-warehouse setup,” Alexandria Engineering Journal, vol. 106, pp. 517–529, 2024, doi: 10.1016/j.aej.2024.08.014.
D. Pal, A. K. Manna, I. Ali, P. Roy, and A. A. Shaikh, “A two-warehouse inventory model with credit policy and inflation effect,” Decision Analytics Journal, vol. 10, no. 100406, 2024, doi: 10.1016/j.dajour.2022.100406.
M. Choudhury and G. C. Mahata, “Non-instantaneous deteriorating items inventory models with fixed lifetime products under hybrid partial prepayment and trade credit in supply chain,” Journal of Industrial and Management Optimization, vol. 20, no. 1, pp. 221–259, 2024.
G. Li, X. He, J. Zhou, and H. Wu, “Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items,” Omega, vol. 84, pp. 114–126, 2018, doi: 10.1016/j.omega.2018.04.010.
R. S. Rana, D. Kumar, and K. Prasad, “Sustainable production-inventory system for perishables under dynamic fuel pricing and preservation technology investment,” Environmental Science and Pollution Research, vol. 30, pp. 90121–90147, 2023, doi: 10.1007/s11356-02328252-y.
W. A. Jauhari, I. Pujawan, and M. Suef, “Sustainable inventory management with hybrid production system and investment to reduce defects,” Annals of Operations Research, vol. 324, pp. 543–572, 2023, doi: 10.1007/s10479-022-04666-8.
A. H. M. Mashud, M. Pervin, U. Mishra, Y. Daryanto, M.-L. Tseng, and M. K. Lim, “A sustainable inventory model with controllable carbon emissions in green-warehouse farms,” Journal of Cleaner Production, vol. 298, no. 126777, 2021, doi: 10.1016/j.jclepro.2021.126777.
Published
2025-07-31
How to Cite
LIMI, Anthony; RANGARAJAN, Kumar.
Two-Warehouse Inventory Model for Non-Instantaneously Deteriorating Item Incorporating Preservation Technology, Carbon Emissions and Hybrid Payment Schemes.
Yugoslav Journal of Operations Research, [S.l.], july 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1362>. Date accessed: 31 aug. 2025.
doi: https://doi.org/10.2298/YJOR240715029L.
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Section
Research Articles
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