IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v31y2017i7d10.1007_s11269-017-1599-4.html
   My bibliography  Save this article

Improved Dynamic Programming for Reservoir Flood Control Operation

Author

Listed:
  • Tongtiegang Zhao

    (Wuhan University
    Tsinghua University)

  • Jianshi Zhao

    (Tsinghua University)

  • Xiaohui Lei

    (Institute of Water Resources and Hydropower Research)

  • Xu Wang

    (Institute of Water Resources and Hydropower Research)

  • Bisheng Wu

    (Energy Division, Commonwealth Scientific and Industrial Research Organization)

Abstract

In flood control operation, the maximum release from a reservoir is minimized to lessen flood risks. Two properties of the minimax problem are derived by formulating the multi-period decision process as a recursive two-stage model. First, the cost-to-go function, which represents the maximum release in the remaining periods, is a non-decreasing function of the carryover storage. Second, monotonic relationships exist between the initial storage of the two-stage model and the optimal decisions of release and carryover storage. The two properties hold not only in the deterministic case with a given streamflow scenario, but also in the stochastic case with an ensemble of streamflow scenarios. The monotonic relationships are incorporated into the dynamic programming (DP) and sampling stochastic DP (SSDP). Two novel algorithms—improved DP (IDP) and improved SSDP (ISSDP)—are developed. The algorithms are applied to a case study of the Danjiangkou Reservoir in Central China. IDP and ISSDP respectively obtain the same decisions as DP and SSDP, and they are more computationally efficient. The execution times of IDP and ISSDP increase linearly with the number of storage discretizations, while those of DP and SSDP increase quadratically. With 1000 discretizations of reservoir storage, IDP and ISSDP derive optimal decisions at 0.939 and 97.453 s, respectively, whereas DP and SSDP finish at 115.931 and 6372.915 s, respectively. These results suggest that IDP and ISSDP can be useful tools for flood control operation – testing different flood scenarios and determining the optimal decisions.

Suggested Citation

  • Tongtiegang Zhao & Jianshi Zhao & Xiaohui Lei & Xu Wang & Bisheng Wu, 2017. "Improved Dynamic Programming for Reservoir Flood Control Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(7), pages 2047-2063, May.
    • Handle: RePEc:spr:waterr:v:31:y:2017:i:7:d:10.1007_s11269-017-1599-4
    DOI: 10.1007/s11269-017-1599-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11269-017-1599-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11269-017-1599-4?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. Yi-Chen E. Yang & Casey M. Brown & Winston H. Yu & Andre Savitsky, 2013. "An introduction to the IBMR, a hydro-economic model for climate change impact assessment in Pakistan's Indus River basin," Water International, Taylor & Francis Journals, vol. 38(5), pages 632-650, September.
    2. Ming Hu & Guo H. Huang & Wei Sun & Xiaowen Ding & Yongping Li & Bin Fan, 2016. "Optimization and Evaluation of Environmental Operations for Three Gorges Reservoir," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3553-3576, August.
    3. Sharon A. Johnson & Jery R. Stedinger & Christine A. Shoemaker & Ying Li & José Alberto Tejada-Guibert, 1993. "Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation," Operations Research, INFORMS, vol. 41(3), pages 484-500, June.
    4. Yongyong Zhang & Jun Xia & Tao Liang & Quanxi Shao, 2010. "Impact of Water Projects on River Flow Regimes and Water Quality in Huai River Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(5), pages 889-908, March.
    5. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    6. Pan Liu & Tri-Dung Nguyen & Ximing Cai & Xinhao Jiang, 2012. "Finding Multiple Optimal Solutions to Optimal Load Distribution Problem in Hydropower Plant," Energies, MDPI, vol. 5(5), pages 1-20, May.
    7. Hyung-Il Eum & Slobodan Simonovic, 2010. "Integrated Reservoir Management System for Adaptation to Climate Change: The Nakdong River Basin in Korea," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(13), pages 3397-3417, October.
    8. Tao Jiang & Ming Zhong & Ying-jie Cao & Long-jian Zou & Bo Lin & Ai-ping Zhu, 2016. "Simulation of Water Quality under Different Reservoir Regulation Scenarios in the Tidal River," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3593-3607, August.
    9. Bo Ming & Jian-xia Chang & Qiang Huang & Yi-min Wang & Sheng-zhi Huang, 2015. "Optimal Operation of Multi-Reservoir System Based-On Cuckoo Search Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5671-5687, December.
    10. Wang, Weiguang & Yu, Zhongbo & Zhang, Wei & Shao, Quanxi & Zhang, Yiwei & Luo, Yufeng & Jiao, Xiyun & Xu, Junzeng, 2014. "Responses of rice yield, irrigation water requirement and water use efficiency to climate change in China: Historical simulation and future projections," Agricultural Water Management, Elsevier, vol. 146(C), pages 249-261.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Deepti Rani & Sandra Mourato & Madalena Moreira, 2020. "A Generalized Dynamic Programming Modelling Approach for Integrated Reservoir Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(4), pages 1335-1351, March.
    2. Wen-jing Niu & Zhong-kai Feng & Shuai Liu & Yu-bin Chen & Yin-shan Xu & Jun Zhang, 2021. "Multiple Hydropower Reservoirs Operation by Hyperbolic Grey Wolf Optimizer Based on Elitism Selection and Adaptive Mutation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(2), pages 573-591, January.
    3. Yong-Gun Kim & Myong-Bong Jo & Pyol Kim & Song-Nam Oh & Chung-Hyok Paek & Sung-Ryol So, 2021. "Effective Optimization-Simulation Model for Flood Control of Cascade Barrage Network," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(1), pages 135-157, January.
    4. Jing Xiao & Ningpeng Dong, 2023. "Assessing the Future Water and Energy Security of a Regulated River Basin with a Coupled Land Surface and Hydrologic Model," Sustainability, MDPI, vol. 15(5), pages 1-18, February.
    5. Xinyu Wu & Shuai Yin & Chuntian Cheng & Zhiyong Chen & Huaying Su, 2023. "SSDP Model with Inflow Clustering for Hydropower System Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(3), pages 1109-1123, February.
    6. Aili Xie & Pan Liu & Shenglian Guo & Xiaoqi Zhang & Hao Jiang & Guang Yang, 2018. "Optimal Design of Seasonal Flood Limited Water Levels by Jointing Operation of the Reservoir and Floodplains," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(1), pages 179-193, January.
    7. Hai-tao Chen & Wen-chuan Wang & Kwok-wing Chau & Lei Xu & Ji He, 2021. "Flood Control Operation of Reservoir Group Using Yin-Yang Firefly Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(15), pages 5325-5345, December.
    8. Ji He & Xiaoqi Guo & Haitao Chen & Fuxin Chai & Shengming Liu & Hongping Zhang & Wenbin Zang & Songlin Wang, 2023. "Application of HSMAAOA Algorithm in Flood Control Optimal Operation of Reservoir Groups," Sustainability, MDPI, vol. 15(2), pages 1-16, January.
    9. Zhong-kai Feng & Wen-jing Niu & Zhi-qiang Jiang & Hui Qin & Zhen-guo Song, 2020. "Monthly Operation Optimization of Cascade Hydropower Reservoirs with Dynamic Programming and Latin Hypercube Sampling for Dimensionality Reduction," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(6), pages 2029-2041, April.

    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. King, Robert P. & Lohano, Heman D., 2006. "Accuracy of Numerical Solution to Dynamic Programming Models," Staff Papers 14230, University of Minnesota, Department of Applied Economics.
    2. Ming, Bo & Liu, Pan & Guo, Shenglian & Cheng, Lei & Zhou, Yanlai & Gao, Shida & Li, He, 2018. "Robust hydroelectric unit commitment considering integration of large-scale photovoltaic power: A case study in China," Applied Energy, Elsevier, vol. 228(C), pages 1341-1352.
    3. Cervellera, Cristiano & Chen, Victoria C.P. & Wen, Aihong, 2006. "Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1139-1151, June.
    4. Saiyan Liu & Yangyang Xie & Hongyuan Fang & Qiang Huang & Shengzhi Huang & Jingcai Wang & Zhen Li, 2020. "Impacts of Inflow Variations on the Long Term Operation of a Multi-Hydropower-Reservoir System and a Strategy for Determining the Adaptable Operation Rule," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(5), pages 1649-1671, March.
    5. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    6. Cervellera, Cristiano, 2023. "Optimized ensemble value function approximation for dynamic programming," European Journal of Operational Research, Elsevier, vol. 309(2), pages 719-730.
    7. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    8. Ding, Yimin & Wang, Weiguang & Song, Ruiming & Shao, Quanxi & Jiao, Xiyun & Xing, Wanqiu, 2017. "Modeling spatial and temporal variability of the impact of climate change on rice irrigation water requirements in the middle and lower reaches of the Yangtze River, China," Agricultural Water Management, Elsevier, vol. 193(C), pages 89-101.
    9. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    10. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    11. Chuanxiong Kang & Cheng Chen & Jinwen Wang, 2018. "An Efficient Linearization Method for Long-Term Operation of Cascaded Hydropower Reservoirs," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3391-3404, August.
    12. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    13. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    14. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    15. Changming Ji & Chuangang Li & Boquan Wang & Minghao Liu & Liping Wang, 2017. "Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4571-4586, November.
    16. Ghassan, Hassan B. & Al-Jefri, Essam H., 2015. "الحساب الجاري في المدى البعيد عبر نموذج داخلي الزمن [The Current Account in the Long Run through the Intertemporal Model]," MPRA Paper 66527, University Library of Munich, Germany.
    17. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    18. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.
    19. Syed Asif Ali Naqvi & Abdul Majeed Nadeem & Muhammad Amjed Iqbal & Sadia Ali & Asia Naseem, 2019. "Assessing the Vulnerabilities of Current and Future Production Systems in Punjab, Pakistan," Sustainability, MDPI, vol. 11(19), pages 1-13, September.
    20. Ohno, Katsuhisa & Boh, Toshitaka & Nakade, Koichi & Tamura, Takayoshi, 2016. "New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system," European Journal of Operational Research, Elsevier, vol. 249(1), pages 22-31.

    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:spr:waterr:v:31:y:2017:i:7:d:10.1007_s11269-017-1599-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.