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JACIII Vol.26 No.5 pp. 684-690
doi: 10.20965/jaciii.2022.p0684
(2022)

Paper:

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Expected Value Model of an Uncertain Production Inventory Problem with Deteriorating Items

Jiayu Shen†, Yueqiang Jin, and Bing Liu

Department of Public Basic Courses, Nanjing Vocational University of Industry Technology
No.1 Yangshan North Road, Nanjing 210023, China

†Corresponding author

Received:
October 27, 2020
Accepted:
April 19, 2022
Published:
September 20, 2022
Creative Commons License
Keywords:
uncertain, production inventory, deteriorating items, optimal control, optimistic value
Abstract

In this study, we present an optimal control model for an uncertain production inventory problem with deteriorating items. The dynamics of the model includes perturbation by an uncertain canonical process. An expected value optimal control model is established based on the uncertainty theory. The aim of this study is to apply the optimal control theory to solve a production inventory problem with deteriorating items and derive an optimal inventory level and production rate that would maximize the expected revenue. The uncertainty theory is used to obtain the equation of optimality. The Hamilton–Jacobi–Bellman (HJB) principle is used to solve the equation of optimality. The results are discussed using numerical experiments for different demand functions.

Cite this article as:
J. Shen, Y. Jin, and B. Liu, “Expected Value Model of an Uncertain Production Inventory Problem with Deteriorating Items,” J. Adv. Comput. Intell. Intell. Inform., Vol.26 No.5, pp. 684-690, 2022.
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References
  1. [1] K. P. Kistner and I. Dobos, “Optimal production-inventory strategies for a reverse logistics system,” Optimization, Dynamics, and Economic Analysis, pp. 246-258, 2000.
  2. [2] E. Khmelnitsky and Y. Gerchak, “Optimal control approach to production systems with inventory-level-dependent demand,” IEEE Trans. on Automatic Control, Vol.47, No.2, pp. 289-292, 2002.
  3. [3] L. Tadj, M. Bounkhel, and Y. Benhadid, “Optimal control of a production inventory system with deteriorating items,” Int. J. of Systems Science, Vol.37, No.15, pp. 1111-1121, 2006.
  4. [4] R. Hedjar, M. Bounkhel, and L. Tadj, “Self-tuning optimal control of periodic-review production inventory systems with deteriorating items,” Advanced Modeling and Optimization, Vol.9, No.1, pp. 91-104, 2007.
  5. [5] Y. Benhadid, L. Tadj, and M. Bounkhel, “Optimal control of production inventory systems with deteriorating items and dynamic costs,” Applied Mathematics E-Notes, Vol.8, pp. 194-202, 2008.
  6. [6] A. Alshamrani and A. El-Gohary, “Optimal control of a two-item inventory system with different types of item deterioration,” Stochastics and Quality Control, Vol.26, No.2, pp. 201-213, 2011.
  7. [7] S. Li, “Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment,” Int. J. of Production Research, Vol.52, No.6, pp. 1787-1807, 2014.
  8. [8] S. Li, “Optimal control of the production-inventory system with deteriorating items and tradable emission permits,” Int. J. of Systems Science, Vol.45, No.11, pp. 2390-2401, 2014.
  9. [9] X. Pan and S. Li, “Optimal control of a stochastic production-inventory system under deteriorating items and environmental constraints,” Int. J. of Production Research, Vol.53, No.2, pp. 607-628, 2015.
  10. [10] J. N. Roul, K. Maity, S. Kar, and M. Maiti, “Multi-item reliability dependent imperfect production inventory optimal control models with dynamic demand under uncertain resource constraint,” Int. J. of Production Research, Vol.53, No.16, pp. 4993-5016, 2015.
  11. [11] K. S. Azoury and J. Miyaoka, “Optimal and simple approximate solutions to a production-inventory system with stochastic and deterministic demand,” European J. of Operational Research, Vol.286, No.1, pp. 178-189, 2020.
  12. [12] M. A. Halim, A. Paul, M. Mahmoud, B. Alshahrani, A. Y. M. Alazzawi, and G. M. Ismail, “An overtime production inventory model for deteriorating items with nonlinear price and stock dependent demand,” Alexandria Engineering J., Vol.60, No.3, pp. 2779-2786, 2021.
  13. [13] C. Lu, M. Gu, T. Lee, and C. Yang, “Impact of carbon emission policy combinations on the optimal production-inventory decisions for deteriorating items,” Expert Systems with Applications, Vol.201, Article No.117234, 2022.
  14. [14] B. Liu, “Uncertainty Theory (2nd Edition),” Springer-Verlag Berlin Heidelberg, 2007.
  15. [15] B. Liu, “Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty,” Springer-Verlag Berlin Heidelberg, 2010.
  16. [16] R. Gao, “Stability in mean for uncertain differential equation with jumps,” Applied Mathematics and Computation, Vol.346, pp. 15-22, 2019.
  17. [17] R. Gao, N. Ma, and G. Sun, “Stability of solution for uncertain wave equation,” Applied Mathematics and Computation, Vol.356, pp. 469-478, 2019.
  18. [18] L. Jia, W. Lio, and X. Yang, “Numerical method for solving uncertain spring vibration equation,” Applied Mathematics and Computation, Vol.337, pp. 428-441, 2018.
  19. [19] L. Jia and Y. Sheng, “Stability in distribution for uncertain delay differential equation,” Applied Mathematics and Computation, Vol.343, pp. 49-56, 2019.
  20. [20] Y. Sheng and G. Shi, “Stability in mean of multi-dimensional uncertain differential equation,” Applied Mathematics and Computation, Vol.353, pp. 178-188, 2019.
  21. [21] X. Wang, Y. Ning, and Z. Peng, “Some results about uncertain differential equations with time-dependent delay,” Applied Mathematics and Computation, Vol.366, Article No.124747, 2020.
  22. [22] K. Yao, H. Ke, and Y. Sheng, “Stability in mean for uncertain differential equation,” Fuzzy Optimization and Decision Making, Vol.14, pp. 365-379, 2015.
  23. [23] K. Yao, “Uncertain differential equation with jumps,” Soft Computing, Vol.19, pp. 2063-2069, 2015.
  24. [24] L. Chen, J. Peng, B. Zhang, and I. Rosyida, “Diversified models for portfolio selection based on uncertain semivariance,” Int. J. of Systems Science, Vol.48, No.3, pp. 637-648, 2017.
  25. [25] Y. Gao, M. Wen, and S. Ding, “(s,S) policy for uncertain single period inventory problem,” Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.21, No.6, pp. 945-953, 2013.
  26. [26] H. Ke, H. Liu, and G. Tian, “An uncertain random programming model for project scheduling problem,” Int. J. of Intelligent Systems, Vol.30, No.1, pp. 66-79, 2015.
  27. [27] Z. Qin and S. Kar, “Single-period inventory problem under uncertain environment,” Applied Mathematics and Computation, Vol.219, No.18, pp. 9630-9638, 2013.
  28. [28] K. Wang and Q. Yang, “Hierarchical facility location for the reverse logistics network design under uncertainty,” J. of Uncertain Systems, Vol.8, No.4, pp. 255-270, 2014.
  29. [29] M. Wen, Z. Qin, and R. Kang, “The α-cost minimization model for capacitated facility location-allocation problem with uncertain demands,” Fuzzy Optimization and Decision Making, Vol.13, pp. 345-356, 2014.
  30. [30] B. Zhang, H. Li, S. Li, and J. Peng, “Sustainable multi-depot emergency facilities location-routing problem with uncertain information,” Applied Mathematics and Computation, Vol.333, pp. 506-520, 2018.
  31. [31] L. Chen, J. Peng, Z. Liu, and R. Zhao, “Pricing and effort decisions for a supply chain with uncertain information,” Int. J. of Production Research, Vol.55, No.1, pp. 264-284, 2017.
  32. [32] H. Ke and J. Liu, “Dual-channel supply chain competition with channel preference and sales effort under uncertain environment,” J. of Ambient Intelligence and Humanized Computing, Vol.8, pp. 781-795, 2017.
  33. [33] H. Ke, H. Huang, and X. Gao, “Pricing decision problem in dual-channel supply chain based on experts’ belief degrees,” Soft Computing, Vol.22, pp. 5683-5698, 2018.
  34. [34] H. Ke, Y. Wu, and H. Huang, “Competitive pricing and remanufacturing problem in an uncertain closed-loop supply chain with risk-sensitive retailers,” Asia-Pacific J. of Operational Research, Vol.35, No.1, Article No.1850003, 2018.
  35. [35] J. Shen and Y. Zhu, “Chance-constrained model for uncertain job shop scheduling problem,” Soft Computing, Vol.20, pp. 2383-2391, 2016.
  36. [36] J. Shen and Y. Zhu, “Uncertain flexible flow shop scheduling problem subject to breakdowns,” J. of Intelligent and Fuzzy Systems, Vol.32, pp. 207-214, 2017.
  37. [37] J. Shen and K. Zhu, “An uncertain single machine scheduling problem with periodic maintenance,” Knowledge-Based Systems, Vol.144, pp. 32-41, 2018.
  38. [38] J. Shen and Y. Zhu, “An uncertain programming model for single machine scheduling problem with batch delivery,” J. of Industrial and Management Optimization, Vol.15, No.2, pp. 577-593, 2019.
  39. [39] J. Shen and Y. Zhu, “A parallel-machine scheduling problem with periodic maintenance under uncertainty,” J. of Ambient Intelligence and Humanized Computing, Vol.10, pp. 3171-3179, 2019.
  40. [40] J. Shen, “An uncertain parallel machine problem with deterioration and learning effect,” Computational and Applied Mathematics, Vol.38, Article No.3, 2019.
  41. [41] Y. Chen and Y. Zhu, “Optimistic value model of indefinite LQ optimal control for discrete-time uncertain systems,” Asian J. of Control, Vol.20, No.1, pp. 495-510, 2018.
  42. [42] Y. Chen and Y. Zhu, “Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems,” J. of Industrial and Management Optimization, Vol.14, No.3, pp. 913-930, 2018.
  43. [43] L. Deng and Y. Chen, “Optimal control of uncertain systems with jump under optimistic value criterion,” European J. of Control, Vol.38, pp. 7-15, 2017.
  44. [44] B. Li, Y. Sun, G. Aw, and K. Teo, “Uncertain portfolio optimization problem under a minimax risk measure,” Applied Mathematical Modelling, Vol.76, pp. 274-281, 2019.
  45. [45] B. Li and Y. Zhu, “The piecewise parametric optimal control of uncertain linear quadratic models,” Int. J. of Systems Science, Vol.50, No.5, pp. 961-969, 2019.
  46. [46] B. Li, Y. Zhu, Y. Sun, G. Aw, and K. Teo, “Deterministic conversion of uncertain manpower planning optimization problem,” IEEE Trans. on Fuzzy Systems, Vol.26, No.5, pp. 2748-2757, 2018.
  47. [47] B. Li, Y. Zhu, Y. Sun, G. Aw, and K. Teo, “Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint,” Applied Mathematical Modelling, Vol.56, pp. 539-550, 2018.
  48. [48] B. Li and Y. Zhu, “Parametric optimal control of uncertain systems under an optimistic value criterion,” Engineering Optimization, Vol.50, No.1, pp. 55-69, 2018.
  49. [49] Y. Zhu, “Uncertain optimal control with application to a portfolio selection model,” Cybernetics and Systems: An Int. J., Vol.41, No.7, pp. 535-547, 2010.
  50. [50] K. Yao and J. Zhou, “Uncertain random renewal reward process with application to block replacement policy,” IEEE Trans. on Fuzzy Systems, Vol.24, No.6, pp. 1637-1647, 2016.
  51. [51] K. Yao and J. Zhou, “Ruin time of uncertain insurance risk process,” IEEE Trans. on Fuzzy Systems, Vol.26, No.1, pp. 19-28, 2018.
  52. [52] K. Yao and J. Zhou, “Renewal reward process with uncertain interarrival times and random rewards,” IEEE Trans. on Fuzzy Systems, Vol.26, No.3, pp. 1757-1762, 2018.
  53. [53] B. Liu, “Some research problems in uncertainty theory,” J. of Uncertain Systems, Vol.3, No.1, pp. 3-10, 2009.
  54. [54] B. Liu, “Fuzzy process, hybrid process and uncertain process,” J. of Uncertain Systems, Vol.2, No.1, pp. 3-16, 2008.

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Last updated on Apr. 18, 2024