IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v178y2024ics0960077923011608.html
   My bibliography  Save this article

Stochastic optimal control and piecewise parameterization and optimization method for inventory control system improvement

Author

Listed:
  • Li, Bo
  • Huang, Tian

Abstract

In recent decades, stochastic control systems have been widely used in industrial production, biomedicine, aerospace, military strategy and so on. In this paper, an approximate optimal strategy derived from a stochastic linear quadratic (SLQ) optimal control problem is considered, and a piecewise parameterization and optimization (PPAO) method is proposed. Firstly, using the principle of dynamic programming, the control form of SLQ optimal control problem is relevant to a Riccati differential equation. It is well known that the Riccati differential equation is difficult to be solved analytically. Thus, we present a PPAO method for finding an approximate optimal strategy for stochastic control problems. Here, a piecewise parameter control can be obtained by solving first-order differential equations rather than Riccati differential equations. Finally, the inventory control problems with different dimensions are used to justify the feasibility of PPAO method, and the results compared with the original optimal control are given. The results show that parametric control greatly simplifies the control form, and a small model error is ensured.

Suggested Citation

  • Li, Bo & Huang, Tian, 2024. "Stochastic optimal control and piecewise parameterization and optimization method for inventory control system improvement," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923011608
    DOI: 10.1016/j.chaos.2023.114258
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923011608
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114258?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wu, Zhen & Zhuang, Yi, 2018. "Linear-quadratic partially observed forward–backward stochastic differential games and its application in finance," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 577-592.
    2. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    3. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    4. Viswanathan, S. & Piplani, Rajesh, 2001. "Coordinating supply chain inventories through common replenishment epochs," European Journal of Operational Research, Elsevier, vol. 129(2), pages 277-286, March.
    5. Fleischmann, Moritz & Kuik, Roelof, 2003. "On optimal inventory control with independent stochastic item returns," European Journal of Operational Research, Elsevier, vol. 151(1), pages 25-37, November.
    6. Li, Bo & Huang, Tian, 2022. "Control variable parameterization and optimization method for stochastic linear quadratic models," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    8. Pan Mu & Lei Wang & Chongyang Liu, 2020. "A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 234-247, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kaijie Zhu & Ulrich W. Thonemann, 2009. "Coordination of pricing and inventory control across products," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 175-190, March.
    2. Nan Yang & Renyu Zhang, 2022. "Dynamic pricing and inventory management in the presence of online reviews," Production and Operations Management, Production and Operations Management Society, vol. 31(8), pages 3180-3197, August.
    3. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    4. Yu, Yimin & Shou, Biying & Ni, Yaodong & Chen, Li, 2017. "Optimal production, pricing, and substitution policies in continuous review production-inventory systems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 631-649.
    5. Oben Ceryan & Ozge Sahin & Izak Duenyas, 2013. "Dynamic Pricing of Substitutable Products in the Presence of Capacity Flexibility," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 86-101, April.
    6. Boxiao Chen & Xiuli Chao & Cong Shi, 2021. "Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 726-756, May.
    7. Li‐Ming Chen & Amar Sapra, 2013. "Joint inventory and pricing decisions for perishable products with two‐period lifetime," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(5), pages 343-366, August.
    8. Qing Li & Xiaoli Wu & Ki Ling Cheung, 2009. "Optimal Policies for Inventory Systems with Separate Delivery-Request and Order-Quantity Decisions," Operations Research, INFORMS, vol. 57(3), pages 626-636, June.
    9. Reza Maihami & Behrooz Karimi & Seyyed Mohammad Taghi Fatemi Ghomi, 2017. "Effect of two-echelon trade credit on pricing-inventory policy of non-instantaneous deteriorating products with probabilistic demand and deterioration functions," Annals of Operations Research, Springer, vol. 257(1), pages 237-273, October.
    10. Peng Hu & Stephen Shum & Man Yu, 2016. "Joint Inventory and Markdown Management for Perishable Goods with Strategic Consumer Behavior," Operations Research, INFORMS, vol. 64(1), pages 118-134, February.
    11. Awi Federgruen & Zhe Liu & Lijian Lu, 2022. "Dual sourcing: Creating and utilizing flexible capacities with a second supply source," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2789-2805, July.
    12. Xiuyan Ma, 2019. "Pricing to the Scenario: Price-Setting Newsvendor Models for Innovative Products," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    13. Liu, An & Wang, Xinyu & Tang, Jiafu, 2024. "Optimizing multi-channel procurement planning under disruption risks," International Journal of Production Economics, Elsevier, vol. 275(C).
    14. Peng Hu & Ye Lu & Miao Song, 2019. "Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 847-877, April.
    15. Li, Yang & Liu, Feng, 2021. "Joint inventory and pricing control with lagged price responses," International Journal of Production Economics, Elsevier, vol. 241(C).
    16. Eugene A. Feinberg & Yan Liang, 2022. "On the optimality equation for average cost Markov decision processes and its validity for inventory control," Annals of Operations Research, Springer, vol. 317(2), pages 569-586, October.
    17. Wei, Ying & Chen, Youhua (Frank), 2011. "Joint determination of inventory replenishment and sales effort with uncertain market responses," International Journal of Production Economics, Elsevier, vol. 134(2), pages 368-374, December.
    18. Alireza Kabirian, 2012. "The economic production and pricing model with lot-size-dependent production cost," Journal of Global Optimization, Springer, vol. 54(1), pages 1-15, September.
    19. Li, Mengmeng & Mizuno, Shinji, 2022. "Dynamic pricing and inventory management of a dual-channel supply chain under different power structures," European Journal of Operational Research, Elsevier, vol. 303(1), pages 273-285.
    20. Jadidi, Omid & Taghipour, Sharareh & Zolfaghari, Saeed, 2016. "A two-price policy for a newsvendor product supply chain with time and price sensitive demand," European Journal of Operational Research, Elsevier, vol. 253(1), pages 132-143.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923011608. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.