Pythagorean Fuzzy EOQ Model With Stock- and Hybrid Price-Dependent Demand Under Preservation Technology and Advance Payment
Abstract
This research implements the impact of an advance payment policy on inventory management while incorporating preservation technology to mitigate product deterioration. In a real scenario, the sum of the membership and non-membership degrees of uncertain parameters is greater than one. Hence, the primary objective is to optimize cycle time, selling price and maximum profit by utilizing an advanced payment policy, hybrid price-dependent demand rate under interval-valued Pythagorean fuzzy numbers to handle imprecise parameters. Two inventory models are developed: one incorporating preservation technology and another without it. Then, the corresponding fuzzy models are obtained under interval-valued Pythagorean fuzzy environment. A novel ranking method is employed to defuzzify the models and then the defuzzified models are solved by using analytic solution method of maximization problem. The models are validated through numerical examples by assuming hypothetical data, and the results are compared across crisp, Pythagorean fuzzy, and intuitionistic fuzzy frameworks. Key findings indicate that adopting preservation technology significantly improves profitability and reduces deterioration losses. Moreover, the Pythagorean fuzzy approach proves to be more effective in capturing uncertainty compared to intuitionistic fuzzy sets. These findings suggest that businesses can enhance inventory decision-making by leveraging advanced fuzzy techniques to optimize financial and operational outcomes.
References
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A. Paul, M. Pervin, S. K. Roy, G. W. Weber, and A. Mirzazadeh, “Effect of pricesensitive demand and default risk on optimal credit period and cycle time for a deteriorating inventory model,” RAIRO-Operations Research, vol. 55, pp. S2575–S2592, 2021. doi: 10.1051/ro/2020108
A. H. M. Mashud, D. Roy, Y. Daryanto, and M. H. Ali, “A sustainable inventory model with imperfect products, deterioration, and controllable emissions,” Mathematics, vol. 8, no. 11, p. 2049, 2020. doi: 10.3390/math8112049
N. Shah, U. Chaudhari, and M. Y. Jani, “Optimal control analysis for service, inventory and preservation technology investment,” International Journal of Systems Science: Operations &Logistics, vol. 6, no. 2, pp. 130–142, 2019. doi: 10.1080/23302674.2018.1447167
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M. A. A. Khan, A. A. Shaikh, G. C. Panda, and I. Konstantaras, “Two-warehouse inventory modelfor deteriorating items with partial backlogging and advance payment scheme,” RAIROOperations Research, vol. 53, no. 5, pp. 1691–1708, 2019. doi: 10.1051/ro/2018093
A. A. Shaikh, S. C. Das, A. K. Bhunia, G. C. Panda, and M. A. A. Khan, “A two-warehouse eoq model with interval-valued inventory cost and advance payment for deteriorating item under particle swarm optimization,” Soft Computing, vol. 23, no. 24, pp. 13531–13546, 2019. doi: 10.1007/s00500-019-03890-y
A. H. M. Mashud, H. M. Wee, B. Sarkar, and Y. H. C. Li, “A sustainable inventory system with the advanced payment policy and trade-credit strategy for a two-warehouse inventory system,” Kybernetes, vol. 50, no. 5, pp. 1321–1348, 2020. doi: 10.1108/K-01-2020-0052
A.H.M.Mashud,M.R.Hasan,Y.Daryanto, andH.M.Wee,“Aresilienthybridpaymentsupply chain inventory model for post covid-19 recovery,” Computers & Industrial Engineering, vol. 157, p. 107249, 2021. doi: 10.1016/j.cie.2021.107249
R. Mondal, S. Das, S. C. Das, A. A. Sheikh, and A. K. Bhunia, “Pricing strategies and advance payment-based inventory model with partially backlogged shortages under interval uncertainty,” International Journal of Systems Science: Operations & Logistics, vol. 10, no. 1, p. 2070296, 2023. doi: 10.1080/23302674.2022.2070296
E. Shekarian, E. U. Olugu, S. H. Abdul-Rashid, and N. Kazemi, “An economic order quantity model considering different holding costs for imperfect quality items subject to fuzziness and learning,” Journal of Intelligent & Fuzzy Systems, vol. 30, no. 5, pp. 2985–2997, 2019. doi: 10.3233/IFS-1519
H. Barman, M. Pervin, S. K. Roy, and G. W. Weber, “Back-ordered inventory model with inf lation in a cloudy-fuzzy environment,” Journal of Industrial and Management Optimization, vol. 17, no. 4, pp. 1913–1941, 2021. doi: 10.3934/jimo.2020052
P. Poswal, A. Chauhan, Y. K. Rajoria, R. Boadh, and A. Goel, “Fuzzy optimization model of two parameter weibull deteriorating rate with quadratic demand and variable holding cost under allowable shortages,” Yugoslav Journal of Operations Research, vol. 32, no. 4, pp. 453470, 2022. doi: 10.2298/YJOR220115021P
P. Kaur and A. Priya, “Selection of inventory policy under pythogrean fuzzy environment,” Science & Technology Asia, vol. 25, no. 1, pp. 62–71, 2020. doi: https://ph02.tcithaijo.org/index.php/SciTechAsia/article/view/240319
S. K. DeandG.C.Mahata, “Solution of an imperfect quality eoq model with backorder under fuzzy lock leadership game approach,” International Journal of Intelligent Systems, vol. 36, no. 1, pp. 421–446, 2021. doi: 10.1002/int.22305
M. M. Nayak, S. Patnaik, and M. Acharya, “An eoq model for defective items under pythagorean fuzzy environment,” Journal of Optimization in Industrial Engineering, vol. 15, no. 1, pp. 47–55, 2022. doi: 10.22094/JOIE.2021.1885939.1708
M. Rahaman, S. P. Mondal, S. Alam, and S. K. De, “A study of a lock fuzzy epq model with deterioration and stock and unit selling price-dependent demand using preservation technology,” Soft Computing, vol. 26, pp. 2721–2740, 2022. doi: 10.1007/s00500-021-06598-0
A.K.Mukherjee, G.Maity, J.Jablonsky, S. K. Roy, andG.W.Weber, “Asustainableinventory optimisation considering imperfect production under uncertain environment,” International Journal of Systems Science: Operations & Logistics, vol. 11, no. 1, p. 2379540, 2024. doi: 10.1080/23302674.2024.2379540
E. Alio˘ gulları, Y. S. T¨ urkan, E. C¸akmak, and E. B. Tirkolaee, “Evaluation of risk strategies for supply chain sustainability with interval-valued neutrosophic fuzzy edas,” Heliyon, vol. 10, no. 19, 2024. doi: 10.1016/j.heliyon.2024.e38607
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Published
2025-08-27
How to Cite
BARMAN, Haripriya et al.
Pythagorean Fuzzy EOQ Model With Stock- and Hybrid Price-Dependent Demand Under Preservation Technology and Advance Payment.
Yugoslav Journal of Operations Research, [S.l.], aug. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1365>. Date accessed: 26 sep. 2025.
doi: https://doi.org/10.2298/YJOR241115025B.
Issue
Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
