Dynamic stochastic-fuzzy optimization for inventory decision systems under mixeduncertainty

Authors

https://doi.org/10.48313/uda.v3i1.97

Abstract

This paper formulates a dynamic programming model of an inventory system in a mixed uncertainty environment where stochasticity and non-stationarity are present in a structurally different manner. The aleatory uncertainty due to demand and supply variation is modeled by stochastic processes, while the epistemic uncertainties on the cost parameters, on the service level goals, and on the managerial risk perception are represented by fuzzy sets. The proposed model integrates these two forms of uncertainty within a unified multistage decision framework and formulates a cost minimization problem that evolves through state-dependent inventory dynamics. Rigorous theoretical development is presented to establish the well-posedness of the optimization problem and to characterize fundamental properties of the optimal policy under hybrid uncertainty. A numerical example using real inventory data, along with a graphical analysis and a detailed sensitivity analysis, illustrates the applicability of the proposed model. The insights show the impact of mixed uncertainty considerations on optimal replenishment policy and also provide practical guidance to decision makers in complex and information-imperfect supply chain scenarios.

Keywords:

Mixed uncertainty modeling, Fuzzy set theory, Hybrid uncertainty modeling, Multistage decision framework, Supply chain optimization

References

  1. [1] Huber, J., Müller, S., Fleischmann, M., & Stuckenschmidt, H. (2019). A data-driven newsvendor problem: From data to decision. European journal of operational research, 278(3), 904-915. https://doi.org/10.1016/j.ejor.2019.04.043
  2. [2] Ben Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust optimization. Princeton university press. https://doi.org/10.1515/9781400831050
  3. [3] Bertsekas, D. (2012). Dynamic programming and optimal control: Volume I (Vol. 4). Athena scientific. https://web.mit.edu/dimitrib/www/DP1_Short_View.pdf
  4. [4] Bertsimas, D., Brown, D. B., & Caramanis, C. (2011). Theory and applications of robust optimization. SIAM review, 53(3), 464-501. https://doi.org/10.1137/080734510
  5. [5] Bijvank, M., & Vis, I. F. (2011). Lost-sales inventory theory: A review. European journal of operational research, 215(1), 1-13. https://doi.org/10.1016/j.ejor.2011.02.004
  6. [6] Bertsimas, D., & Thiele, A. (2006). A robust optimization approach to inventory theory. Operations research, 54(1), 150-168. https://doi.org/10.1287/opre.1050.0238
  7. [7] Choi, T. M. (2021). Risk analysis in logistics systems: A research agenda during and after the COVID-19 pandemic. Transportation research part E: Logistics and transportation review, 145, 102190. https://doi.org/10.1016/j.tre.2020.102190
  8. [8] de Kok, T. (2018). Inventory management: Modeling real-life supply chains and empirical validity. Foundations and trends® in technology, information and operations management, 11(4), 343-437. https://doi.org/10.1561/0200000057
  9. [9] Sarkar, B., & Mahapatra, A. S. (2017). Periodic review fuzzy inventory model with variable lead time and fuzzy demand. International transactions in operational research, 24(5), 1197-1227. https://doi.org/10.1111/itor.12177
  10. [10] Dolgui, A., Ivanov, D., & Sokolov, B. (2018). Ripple effect in the supply chain: An analysis and recent literature. International journal of production research, 56(1-2), 414-430. https://doi.org/10.1080/00207543.2017.1387680
  11. [11] Dubois, D., & Prade, H. (2003, May). Possibility theory and its applications: a retrospective and prospective view. In the 12th IEEE international conference on fuzzy systems, 2003. FUZZ'03. (Vol. 1, pp. 5-11). IEEE. https://doi.org/10.1109/FUZZ.2003.1209314
  12. [12] Fildes, R., Ma, S., & Kolassa, S. (2022). Retail forecasting: Research and practice. International Journal of Forecasting, 38(4), 1283-1318. https://doi.org/10.1016/j.ijforecast.2019.06.004
  13. [13] Fransoo, J. C., & Lee, C. Y. (2013). The critical role of ocean container transport in global supply chain performance. Production and operations management, 22(2), 253-268. https://doi.org/10.1111/j.1937-5956.2011.01310.x
  14. [14] Gallego, G., & Van Ryzin, G. (1994). Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management science, 40(8), 999-1020. https://doi.org/10.1287/mnsc.40.8.999
  15. [15] Huh, W. T., & Janakiraman, G. (2010). On the optimal policy structure in serial inventory systems with lost sales. Operations research, 58(2), 486-491. https://doi.org/10.1287/opre.1090.0716
  16. [16] Ivanov, D. (2020). Predicting the impacts of epidemic outbreaks on global supply chains: A simulation-based analysis on the coronavirus outbreak (COVID-19/SARS-CoV-2) case. Transportation research part E: Logistics and transportation review, 136, 101922. https://doi.org/10.1016/j.tre.2020.101922
  17. [17] Klibi, W., & Martel, A. (2013). The design of robust value-creating supply chain networks. OR spectrum, 35(4), 867-903. https://doi.org/10.1007/s00291-013-0327-6
  18. [18] Kourentzes, N., & Fildes, R. (2023). The dynamics of judgemental adjustments in demand planning. Available at SSRN 4534744. https://dx.doi.org/10.2139/ssrn.4534744
  19. [19] Tang, S. Y., & Kouvelis, P. (2011). Supplier diversification strategies in the presence of yield uncertainty and buyer competition. Manufacturing & service operations management, 13(4), 439-451. https://doi.org/10.1287/msom.1110.0337
  20. [20] Shekarian, E., Kazemi, N., Abdul Rashid, S. H., & Olugu, E. U. (2017). Fuzzy inventory models: A comprehensive review. Applied soft computing, 55, 588-621. https://doi.org/10.1016/j.asoc.2017.01.013
  21. [21] Mahata, G. C., & Goswami, A. (2009). An EOQ model with fuzzy lead time, fuzzy demand and fuzzy cost coefficients. International journal of engineering and applied sciences, 5(5), 295-302. https://www.researchgate.net/profile/Gour-Mahata/publication/277716527
  22. [22] Levi, R., Roundy, R. O., & Shmoys, D. B. (2007). Provably near-optimal sampling-based policies for stochastic inventory control models. Mathematics of operations research, 32(4), 821-839. https://doi.org/10.1287/moor.1070.0272
  23. [23] Mula, J., Poler, R., & Garcia Sabater, J. P. (2007). Material requirement planning with fuzzy constraints and fuzzy coefficients. Fuzzy sets and systems, 158(7), 783-793. https://doi.org/10.1016/j.fss.2006.11.003
  24. [24] Pishvaee, M. S., & Razmi, J. (2012). Environmental supply chain network design using multi-objective fuzzy mathematical programming. Applied mathematical modelling, 36(8), 3433-3446. https://doi.org/10.1016/j.apm.2011.10.007
  25. [25] Powell, W. B. (2016). A unified framework for optimization under uncertainty. In optimization challenges in complex, networked and risky systems (pp. 45-83). Informs. https://doi.org/10.1287/educ.2016.0149
  26. [26] Puterman, M. L. (2014). Markov decision processes: discrete stochastic dynamic programming. John wiley & sons. http://dx.doi.org/10.1002/9780470316887
  27. [27] Mišić, V. V., & Perakis, G. (2020). Data analytics in operations management: A review. Manufacturing & service operations management, 22(1), 158-169. https://doi.org/10.1287/msom.2019.0805
  28. [28] Shapiro, A., Dentcheva, D., & Ruszczynski, A. (2021). Lectures on stochastic programming: Modeling and theory. Society for industrial and applied mathematics. https://epubs.siam.org/doi/pdf/10.1137/1.9781611976595.bm
  29. [29] Zhang, Y., Shen, Z. J. M., & Song, S. (2016). Distributionally robust optimization of two‐stage lot‐sizing problems. Production and operations management, 25(12), 2116-2131. https://doi.org/10.1111/poms.12602
  30. [30] Silver, E. A., Pyke, D. F., & Thomas, D. J. (2016). Inventory and production management in supply chains. CRC press. https://books.google.nl/books?id=uY2ODwAAQBAJ&redir_esc=y
  31. [31] Simchi Levi, D., Kaminsky, P., & Simchi Levi, E. (1999). Designing and managing the supply chain: Concepts, strategies, and cases. New York: McGraw-hill. https://d1wqtxts1xzle7.cloudfront.net/31133595/FAI-09__PROC_5850__Brannon__R-libre.pdf?1392197854
  32. [32] Mahapatra, G. S., Adak, S., & Kaladhar, K. (2019). A fuzzy inventory model with three parameter Weibull deterioration with reliant holding cost and demand incorporating reliability. Journal of intelligent & fuzzy systems, 36(6), 5731-5744. https://doi.org/10.3233/JIFS-181595
  33. [33] Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy sets and systems, 159(2), 193-214. https://doi.org/10.1016/j.fss.2007.08.010
  34. [34] Zipkin, P. (2008). On the structure of lost-sales inventory models. Operations research, 56(4), 937-944. https://doi.org/10.1287/opre.1070.0482

Downloads

Published

2026-03-16

Issue

Vol. 3 No. 1 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Behera, J. (2026). Dynamic stochastic-fuzzy optimization for inventory decision systems under mixeduncertainty. Uncertainty Discourse and Applications, 3(1), 54-71. https://doi.org/10.48313/uda.v3i1.97

Similar Articles

21-30 of 57

You may also start an advanced similarity search for this article.