A Review of Neutrosophic Sustainable Inventory Models
DOI:
https://doi.org/10.22105/kmisj.v2i3.107Keywords:
Neutrosophy, Inventory models, SustainabilityAbstract
Sustainable Inventory Management (SIM) is imperative to set a balance between economic and environmental constraints. Sustainable centric inventory model development under uncertainty fail to capture intricate demand patterns and fluctuating cost parameters. This has grounded the origin of Neutrosophic integrated inventory models based on three valued logic of truth, indeterminacy and falsity membership functions. This study reviews the state of art of Neutrosophic integrated sustainable inventory models. The existing literature is explored in the three dimensions of inventory models handling defective and imperfect items; green models with carbon emissions and sustainable costs and different modelling approaches. The advantages of blending Neutrosophic representations with sustainable inventory models are substantiated. The future directions of Neutrosophic based models are also discussed in this study.
References
Kahraman, C., Oztaysi, B., & Cevik Onar, S. (2020). Retracted: Single & interval-valued Neutrosophic AHP methods: Performance analysis of outsourcing law firms. Journal of intelligent & fuzzy systems, 38(1), 749–759. https://doi.org/10.3233/JIFS-179446
Saini, R. K., Sangal, A., & Ahirwar, A. (2022). A novel approach by using interval-valued trapezoidal Neutrosophic numbers in transportation problem. Neutrosophic sets syst, 51, 234–253. https://fs.unm.edu/nss8/index.php/111/article/view/2561
Wang, Q., Huang, Y., Kong, S., Ma, X., Liu, Y., Das, S. K., & Edalatpanah, S. A. (2021). A novel method for solving multiobjective linear programming problems with triangular Neutrosophic numbers. Journal of mathematics, 2021(1), 6631762. https://doi.org/10.1155/2021/6631762
Bhavani, G. D., Georgise, F. B., Mahapatra, G. S., & Maneckshaw, B. (2022). Neutrosophic cost pattern of inventory system with novel demand incorporating deterioration and discount on defective items using particle swarm algorithm. Computational intelligence and neuroscience, 2022(1), 7683417. https://doi.org/10.1155/2022/7683417
Martin, N., Mayan, M. K., & Smarandache, F. (2020). Neutrosophic optimization of industry 4.0 production inventory model. Neutrosophic sets and systems, 38, 470-481. https://doi.org/10.5281/zenodo.4300572
Negi, A., & Singh, O. (2025). Probabilistic inventory model for deteriorating items with uncertain demand under pentagonal fuzzy environment. Reliability: Theory & applications, 20(1(82)), 754–772. https://doi.org/10.24412/1932-2321-2025-182-754-772
Bhavani, G. D., & Mahapatra, G. S. (2023). Inventory system with generalized triangular Neutrosophic cost pattern incorporating maximum life-time-based deterioration and novel demand through PSO. Soft computing, 27(5), 2385–2402. https://doi.org/10.1007/s00500-022-07769-3
Haque, R., Rahaman, M., Alam, S., Behera, P. K., & Mondal, S. P. (2025). Generalized Neutrosophic Laplace transform and its application in an EOQ model with price and deterioration-dependent demand. Opsearch, 62(2), 550–582. https://doi.org/10.1007/s12597-024-00803-y
Chakraborty, A., Banik, B., Mondal, S. P., & Alam, S. (2020). Arithmetic and geometric operators of pentagonal Neutrosophic number and its application in mobile communication service based MCGDM problem. Neutrosophic sets and systems, 32, 61–79. https://digitalrepository.unm.edu/nss_journal/vol32/iss1/6
Mohanta, K., Jha, A. K., Dey, A., & Pal, A. (2023). An application of Neutrosophic logic on an inventory model with two-level partial trade credit policy for time-dependent perishable products: K. Mohanta et al. Soft computing, 27(8), 4795-4822. https://doi.org/10.1007/s00500-022-07619-2
Miriam, M. R., Martin, N., Aleeswari, A., & Broumi, S. (2023). Rework warehouse inventory model for product distribution with quality conservation in Neutrosophic environment. International journal of Neutrosophic science (IJNS), 21(2), 150–160. https://doi.org/10.54216/IJNS.210215
WashimaKhatun, M., Pal, S., Chakraborty, A., & Shaw, A. K. (2024). A novel technique to detect an optimal two layer supply chain model for imperfect items under various Neutrosophic environment. International journal of applied and computational mathematics, 10(3), 121. https://doi.org/10.1007/s40819-024-01748-y
supakar, P., Kumar, N., Mahato, S. K., & Pal, P. (2024). Neutrosophic trade-credit EOQ model for deteriorating items considering expiration date of the items using different variants of particle swarm optimizations. International journal of system assurance engineering and management, 15(3), 1147–1171. https://doi.org/10.1007/s13198-023-02197-4
Rahaman, M., Haque, R., Salahshour, S., Alam, S., & Prasad, M. S. (2025). Analysis of a demand-driven production inventory model in a trapezoidal Neutrosophic number-ruled decision environment. Yugoslav journal of operations research, 35(4), 797-836. https://doi.org/10.2298/YJOR240515052R
Priskilla, B., Baranidharan, B., & Mahapatra, G. S. (2025). Optimizing defective product distribution for sustainability and profitability in manufacturing model under Neutrosophic environment. Neutrosophic sets and systems, 86(1), 28. https://digitalrepository.unm.edu/nss_journal/vol86/iss1/28
Surya, R., Mullai, M., & Vetrivel, G. (2024). Neutrosophic inventory system for decaying items with price dependent demand. Neutrosophic sets and systems, 66(1), 4. https://digitalrepository.unm.edu/nss_journal/vol66/iss1/4
Gudeta, G. A., Thillaigovindan, N., & Wole, G. A. (2025). Inventory control of single perishable item in Neutrosophic environment: With stock-based demand, preservation technology, shortage and two-stage price discount for imperfect items. Neutrosophic sets and systems, 77(1), 11. https://doi.org/10.5281/zenodo.14120586
Rahaman, M., Haque, R., Salahshour, S., Sobczak, A., Azizzadeh, F., Alam, S., & Mondal, S. P. (2025). Solution of an uncertain EPQ model using the Neutrosophic differential equation approach. Operations research and decisions, 35(2), 55–92. http://dx.doi.org/10.37190/ord250203
Kausar, N., Broumi, S., & Cagin, T. (2025). The analysis of pentagonal fuzzy numbers in a Neutrosophic fuzzy inventory management modelling with minimal insufficient supply required and fuzzy consumption. International journal of Neutrosophic science (IJNS), 25(4), 472-483. https://doi.org/10.54216/IJNS.250440
Alioğulları, E., Türkan, Y. S., Çakmak, E., & Tirkolaee, E. B. (2024). Evaluation of risk strategies for supply chain sustainability with interval-valued Neutrosophic fuzzy EDAS. Heliyon, 10(19), 1-22. https://doi.org/10.1016/j.heliyon.2024.e38607
Dubey, A., & Kumar, R. (2024). Neutrosophic inventory management: A cost-effective approach. Economics, 18(1), 1-15. https://doi.org/10.1515/econ-2022-0101
Arshi, M., Hadi-Vencheh, A., Aazami, A., & Jamshidi, A. (2024). A nonlinear model to solve multiple attribute decision-making problems with interval-valued Neutrosophic numbers. International journal of industrial engineering, 35(4), 1-15. (In Persian). https://doi.org/10.23055/ijietap.2023.30.3.8023
Dubey, A., Dey, A., Broumi, S., & Kumar, R. (2024). A survey on Neutrosophic principles for inventory management problem. Neutrosophic sets and systems, 68(1), 19. https://digitalrepository.unm.edu/nss_journal/vol68/iss1/19.
Sindhuja, N., Kumari, M. S., Kalaiarasi, K., GJ, M., & HY, S. (2024). Energizing inventory management to optimize energy consumption of handling shortages by Neutrosophic fuzzy trapezoidal number. International journal of Neutrosophic science (IJNS), 24(1), 219-236. https://doi.org/10.54216/IJNS.240120
Das, K., & Islam, S. (2024). A deterministic multi-item inventory model with quadratic demand under Neutrosophic and pythagorean hesitant fuzzy programming approach. Results in control and optimization, 14, 100367. https://doi.org/10.1016/j.rico.2023.100367
Pattnaik, S., Nayak, M. M., & Kumar, P. (2023). An inventory control model in the framework of COVID-19 disruptions considering overage items with Neutrosophic fuzzy uncertainty. Neutrosophic sets and systems, 56(1), 9. https://digitalrepository.unm.edu/nss_journal/vol56/iss1/9
Deb, S. C., & Islam, S. (2023). Application of Neutrosophic interval valued goal programming to a supply chain inventory model for deteriorating items with time dependent demand. Neutrosophic sets and systems, 53(1), 35. https://digitalrepository.unm.edu/nss_journal/vol53/iss1/35
Mohanta, K., Sarkar, S., Dey, A., De, D., & Pal, A. (2023). Cost optimization of an inventory control problem in Neutrosophic environment for smart manufacturing. https://doi.org/10.21203/rs.3.rs-2590887/v1
Rajeswari, S., Sugapriya, C., Pillai, N. D., Broumi, S., & Smarandache, F. (2022). Application of triangular fuzzy Neutrosophic number to an effective economic order quantity model. In Handbook of research on advances and applications of fuzzy sets and logic (pp. 639-665). IGI Global Scientific Publishing. https://doi.org/10.4018/978-1-7998-7979-4.ch029
Surya, R., & Mullai, M. (2022). Neutrosophic multi-item inventory control models with constraints. Journal of intelligent & fuzzy systems, 43(6), 8127–8136. https://doi.org/10.3233/JIFS-221143
Rajeswari, S., Sugapriya, C., Nagarajan, D., Broumi, S., & Smarandache, F. (2021). Octagonal fuzzy Neutrosophic number and its application to reusable container inventory model with container shrinkage. Computational and applied mathematics, 40(8), 308. https://doi.org/10.1007/s40314-021-01600-9
Islam, S., & Das, K. (2021). Multi-objective inventory model with deterioration under space constraint: Neutrosophic hesitant fuzzy programming approach. Neutrosophic sets and systems, 47(1), 10. https://digitalrepository.unm.edu/nss_journal/vol47/iss1/10
Pal, S., & Chakraborty, A. (2020). Triangular Neutrosophic based production reliability model of deteriorating item with ramp type demand under shortages and time discounting. Neutrosophic sets and systems, 35(1), 20. https://digitalrepository.unm.edu/nss_journal/vol35/iss1/20
Das, S. K., & Islam, S. (2019). Fuzzy multi item inventory model with deterioration and demand dependent production cost under space constraint: Neutrosophic hesitant fuzzy programming approach. Infinite Study. https://doi.org/10.5281/zenodo.3382560
Dubey, A., & Kumar, R. (2024). Enhancing inventory models using fuzzy extended principles for optimization. Journal of fuzzy extension and applications, 5(4), 622–633. https://doi.org/10.22105/jfea.2024.449723.1425
Barman, H., Roy, S. K., Sakalauskas, L., & Weber, G. W. (2023). Inventory model involving reworking of faulty products with three carbon policies under Neutrosophic environment. Advanced engineering informatics, 57, 102081. https://doi.org/10.1016/j.aei.2023.102081
Sarkar, D., & Srivastava, P. K. (2022). A dynamic optimization approach for multi-item multi-objective fixed-place Neutrosophic fuzzy inventory and green management system. Mathematics in engineering, science & aerospace (MESA), 13(2). https://logon.ebsco.zone/api/dispatcher/oauth/authorize?client_id=awgycIx57MrwnDQ5h4Ue6
Kar, C., Roy, T. K., & Maiti, M. (2022). EOQ model with price, marketing, service and green dependent Neutrosophic demand under uncertain resource constraint: A geometric programming approach. Neutrosophic sets and systems, 51(1), 49. https://digitalrepository.unm.edu/nss_journal/vol51/iss1/49
Garg, H., Rajeswari, S., Sugapriya, C., & Nagarajan, D. (2022). A model for container inventory with a trapezoidal bipolar Neutrosophic number. Arabian journal for science and engineering, 47(11), 15027–15047. https://doi.org/10.1007/s13369-022-06788-4
Sugapriya, C., Rajeswari, S., Nagarajan, D., Zararsız, Z., & Mahad Al Amri, Z. S. (2022). An effective container inventory model under bipolar Neutrosophic environment. Neutrosophic sets and systems, 50(1), 19. https://digitalrepository.unm.edu/nss_journal/vol50/iss1/19
Mohanta, K., Sarkar, S., Dey, A., De, D., & Pal, A. (2023). Coptimization of an inventory control problem in Neutrosophic environment for smart manufacturing. https://doi.org/10.21203/rs.3.rs-2590887/v1
Kar, C., De, M., Maiti, M., & Das, P. (2024). Multi-objective perishable multi-item green inventory models with uncertain finite time horizons and constraints by Neutrosophic optimisation approach. International journal of mathematics in operational research, 27(2), 167–198. https://doi.org/10.1504/IJMOR.2024.137053
Supakar, P., Manna, A. K., Mahato, S. K., & Bhunia, A. K. (2024). Application of artificial bee colony algorithm on a green production inventory problem with preservation for deteriorating items in Neutrosophic fuzzy environment. International journal of system assurance engineering and management, 15(2), 672–686. https://doi.org/10.1007/s13198-022-01692-4
Loganayaki, S., Rajeswari, N., Kirupa, K., & Broumi, S. (2024). Optimization of triangular Neutrosophic based economic order quantity model under preservation technology and power demand. Neutrosophic sets and systems, 65(1), 11. https://books.google.nl/books?id=nHI_EQAAQBAJ&printsec=frontcover#v=onepage&q&f=false
Saeed, A., Jian, M., Imran, M., Freen, G., & ur Rehman Majid, A. (2024). Green-resilient model for smartphone closed-loop supply chain network design: A novel four-valued refined Neutrosophic optimization. Computers & industrial engineering, 190, 110087.https://doi.org/10.1016/j.cie.2024.110087
Pal, S., Chakraborty, A., & Mahapatra, G. S. (2025). A case study of the impact of carbon emissions and inflation on nonlinear dense Neutrosophic fuzzy inventory system of varying demand with delayed deterioration. RAIRO-operations research, 59(1), 193-218. https://doi.org/10.1051/ro/2024078
Mukherjee, A. K., Maity, G., Jablonsky, J., Roy, S. K., & Weber, G. W. (2025). Multi-objective sustainable inventory model with shortages and radio frequency identification under uncertain environment. International journal of systems science: Operations & logistics, 12(1), 2470917. https://doi.org/10.1080/23302674.2025.2470917
Nafei, A., Huang, C. Y., Chen, S. C., Huo, K. Z., Lin, Y. C., & Nasseri, H. (2023). Neutrosophic autocratic multi-attribute decision-making strategies for building material supplier selection. Buildings, 13(6), 1373. https://doi.org/10.3390/buildings13061373.
Palanivel, M., & Venkadesh, M. (2025). Integrated strategies for sustainable production inventory model with carbon emission reduction with green technology. Operations research forum, 6(2), 51. https://doi.org/10.1007/s43069-025-00445-w
Momena, A. F., Haque, R., Rahaman, M., Salahshour, S., & Mondal, S. P. (2024). The existence and uniqueness conditions for solving Neutrosophic differential equations and its consequence on optimal order quantity strategy. Logistics, 8(1), 18. https://doi.org/10.3390/logistics8010018
Haque, R., Rahaman, M., Alrasheedi, A. F., Chalishajar, D., & Mondal, S. P. (2025). Fractional calculus for Neutrosophic-valued functions and its application in an inventory lot-sizing problem. Fractal and fractional, 9(7), 433. https://doi.org/10.3390/fractalfract9070433
Kumar, S., & Singh, S. (2025). Optimization of inventory management for deteriorating items with quality-dependent demand under Neutrosophic environments and payment delay policies. International journal of scientific research in science, engineering and technology, 12, 1395–1408. https://doi.org/10.32628/IJSRSET2512185
Kalaiarasi, K., Anitha, N., Swathi, S., & Ranjitha, B. (2024). Optimization of Neutrosophic vendor-buyer economic order quantity model using particle swarm optimization. International journal of Neutrosophic science (IJNS), 23(4), 181-193. https://doi.org/10.54216/IJNS.230414
GJ, M., Anitha, N., Pushpalatha, A. P., Laxmi, K. V., Premalatha, M., & Selvaraj, M. (2024). Optimization of Neutrosophic EOQ model for effective demand management in uncertain environment using genetic optimization. International journal of Neutrosophic science (IJNS), 24(3), 1-12. https://doi.org/10.54216/IJNS.240305
Boloș, M. I., Sabău-Popa, C. D., & Rus, L. (2023). Optimal management of production stocks with the Neutrosophic fuzzy numbers. Economic computation & economic cybernetics studies & research, 57(2), 21-40. https://doi.org/10.24818/18423264/57.2.23.02
Kalaiarasi, K., & Swathi, S. (2023). Neutrosophic inventory model with quick return for damaged materials and python-analysis. In 2023 Neutrosophic superhyperalgebra and new types of topologies (PP. 219-258). Infinite Study. https://philpapers.org/archive/SMANSA-2.pdf
Mullai, M., & Surya, R. (2020). Neutrosophic inventory backorder problem using triangular Neutrosophic numbers. Neutrosophic sets and systems, 31(1), 11. https://fs.unm.edu/nss8/index.php/111/article/view/438
Das, K., & Islam, S. (2022). A multi-objective shortage follow inventory (SFI) model involving ramp-type demand, time varying holding cost and a marketing cost under Neutrosophic programming approach. Neutrosophic sets and systems, 49, 48-69. https://doi.org/10.5281/zenodo.6426371
Jayanthi, K. (2022). A fuzzy differential approach to an overage management with customer acquisition inventory problem via Neutrosophic fuzzy geometric programming technique. Journal of algebraic statistics, 13(3). https://logon.ebsco.zone/api/dispatcher/oauth/authorize?client_id=awgycix57mrwndq5h4ue6ycvep0r5mt9&grant
Miriam, M. R., Martin, N., Rezaei, A., & Edalatpanah, S. A. (2025). Neutrosophic inventory model with coordinated rework stations and distribution centers with ant colony optimization. In Neutrosophic and plithogenic inventory models for applied mathematics (pp. 247-286). IGI Global Scientific Publishing. https://doi.org/10.4018/979-8-3693-3204-7.ch011
Grützner, L., Voss, D., & Breitner, M. H. (2025). Mature inventory management for supply chain automation: An interlinked process-reference model. Electronic markets, 35(1), 34. https://doi.org/10.1007/s12525-025-00783-x
Dwivedi, V., Keswani, M., Khedlekar, U. K., & Kumar, L. (2025). Optimizing pharmaceutical inventory and investment strategies during pandemics: A dynamic approach integrating environmental emission rates and advanced optimization algorithms. Operations research and decisions, 3(2), 23-35. http://dx.doi.org/10.37190/ord250202
Anand, M. C. J., Anjana, V. A., Ashwini, R., Varsha, P., Savanur, V. V., & Devana, P. S. (2024). Optimizing electricity distribution through Neutrosophic transportation problem using contingency technique. 2024 IEEE third international conference on power electronics, intelligent control and energy systems (ICPEICES) (pp. 376-381). IEEE. https://doi.org/10.1109/ICPEICES62430.2024.10719090
Kousar, S., Sangi, M. N., Kausar, N., Pamučar, D., Ozbilge, E., & Cagin, T. (2023). Multi-objective optimization model for uncertain crop production under Neutrosophic fuzzy environment: A case study. AIMS mathematics, 8(3), 7584–7605. https://www.aimspress.com/article/doi/10.3934/math.2023380
Cakmak, E., & Guney, E. (2023). Spare parts inventory classification using Neutrosophic fuzzy EDAS method in the aviation industry. Expert systems with applications, 224, 120008. https://doi.org/10.1016/j.eswa.2023.120008
Adhami, A. Y., Melethil, A., & Ahmad, F. (2023). Neutrosophic programming approach to multilevel decision-making model for supplier selection problem in a fuzzy situation. RAIRO-operations research, 57(3), 1307-1328. https://doi.org/10.1051/ro/2023064
Badhotiya, G. K., Soni, G., Nepal, B., & Mittal, M. L. (2022). Integrated production-distribution planning optimization using Neutrosophic programming. International journal of industrial engineering, 29(2). https://doi.org/10.23055/ijietap.2022.29.2.7497
Daham, H. A. (2022). Neutrosophic discrete facility location problems. International journal of neutrosophic science (IJNS), 19(1), 30-46. https://doi.org/10.54216/IJNS.xxxxxx
Jdid, M., Alhabib, R., Khalid, H. E., & Salama, A. A. (2022). The Neutrosophic treatment of the static model for the inventory management with safety reserve. International journal of Neutrosophic science (IJNS), 18(2), 262-271. https://doi.org/10.54216/IJNS.180209
Mondal, B., Garai, A., Mukhopadhyay, A., & Majumder, S. K. (2021). Inventory policies for seasonal items with logistic-growth demand rate under fully permissible delay in payment: A Neutrosophic optimization approach. Soft computing, 25(5), 3725–3750. https://doi.org/10.1007/s00500-020-05402-9
Haq, A., Gupta, S., & Ahmed, A. (2021). A multi-criteria fuzzy Neutrosophic decision-making model for solving the supply chain network problem. Neutrosophic sets and systems, 46, 50-66. https://fs.unm.edu/NSS/MulticriteriaFuzzyNeutrosophic5.pdf
Piper, R. G. (1982). Fish hatchery management. US department of the interior, fish and wildlife service. https://dn790002.ca.archive.org/0/items/fishhatcherymana00pipe/fishhatcherymana00pipe.pdf
Kar, C., Mondal, B., & Roy, T. K. (2018). An inventory model under space constraint in Neutrosophic environment: A Neutrosophic geometric programming approach. Neutrosophic sets and systems, 2, 93 – 109. https://doi.org/10.5281/zenodo.1408663
Islam, S. (2021). Fuzzy multi-objective inventory model for deteriorating items, with shortages under space constraint: Neutrosophic hesitant fuzzy programming approach. In Neutrosophic operational research: Methods and applications (pp. 197-219). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-57197-9_11
Ahmad, F., Adhami, A. Y., & Smarandache, F. (2019). Neutrosophic optimization model and computational algorithm for optimal shale gas water management under uncertainty. Symmetry, 11(4), 544. https://doi.org/10.3390/sym11040544
Islam, S., & Kundu, T. (2018). Application of Neutrosophic optimization technique on multi-objective reliability optimization model. Neutrosophic sets and systems, 2, 13-27. https://www.researchgate.net/publication/325106961
Moorthy, C. B., Rajani, D., Pushpalatha, A. P., Ramya, S., Selvaraj, A., & Tiwari, M. (2024). Enhancing inventory management through advanced technologies and mathematical methods: Utilizing Neutrosophic fuzzy logic. International journal of Neutrosophic science (IJNS), 24(4). https://www.researchgate.net/profile/Mohit-Tiwari-6/publication/381095530_
Jdid, M., Alhabib, R., & Salama, A. A. (2023). The static model of inventory management without a deficit with Neutrosophic logic. Research on the topics of Neutrosophic operations research, 16(1), 24-48. https://doi.org/10.54216/IJNS.160104