IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v23y2009i5p1001-1023.html
   My bibliography  Save this article

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

Author

Listed:
  • P. Guo
  • G. Huang
  • L. He
  • H. Zhu

Abstract

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria. Copyright Springer Science+Business Media B.V. 2009

Suggested Citation

  • P. Guo & G. Huang & L. He & H. Zhu, 2009. "Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(5), pages 1001-1023, March.
    • Handle: RePEc:spr:waterr:v:23:y:2009:i:5:p:1001-1023
    DOI: 10.1007/s11269-008-9311-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11269-008-9311-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11269-008-9311-3?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. Vaz, A. Ismael F. & Fernandes, Edite M. G. P. & Gomes, M. Paula S. F., 2004. "Robot trajectory planning with semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 153(3), pages 607-617, March.
    2. H. Lu & G. Huang & G. Zeng & I. Maqsood & L. He, 2008. "An Inexact Two-stage Fuzzy-stochastic Programming Model for Water Resources Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(8), pages 991-1016, August.
    3. Maqsood, Imran & Huang, Guo H. & Scott Yeomans, Julian, 2005. "An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 208-225, November.
    4. Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    5. B. Luo & I. Maqsood & G. Huang, 2007. "Planning water resources systems with interval stochastic dynamic programming," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(6), pages 997-1014, June.
    6. L. Dai & C. H. Chen & J. R. Birge, 2000. "Convergence Properties of Two-Stage Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 489-509, September.
    7. Yong Li & Guo Huang, 2008. "Interval-parameter Two-stage Stochastic Nonlinear Programming for Water Resources Management under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(6), pages 681-698, June.
    8. Simon Wu & Jonathan Li & G. Huang, 2008. "Characterization and Evaluation of Elevation Data Uncertainty in Water Resources Modeling with GIS," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(8), pages 959-972, August.
    9. Goberna, M. A. & Lopez, M. A., 2002. "Linear semi-infinite programming theory: An updated survey," European Journal of Operational Research, Elsevier, vol. 143(2), pages 390-405, December.
    10. Huang, G. H., 1998. "A hybrid inexact-stochastic water management model," European Journal of Operational Research, Elsevier, vol. 107(1), pages 137-158, May.
    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. Qiang Fu & Ke Zhao & Dong Liu & Qiuxiang Jiang & Tianxiao Li & Changhong Zhu, 2016. "Two-Stage Interval-Parameter Stochastic Programming Model Based on Adaptive Water Resource Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(6), pages 2097-2109, April.
    2. Pradeep Dogra & V. Sharda & P. Ojasvi & Shiv Prasher & R. Patel, 2014. "Compromise Programming Based Model for Augmenting Food Production with Minimum Water Allocation in a Watershed: a Case Study in the Indian Himalayas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(15), pages 5247-5265, December.
    3. L. Zhang & C. Li, 2014. "An Inexact Two-Stage Water Resources Allocation Model for Sustainable Development and Management Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 3161-3178, August.
    4. Ruihuan Li & Ping Guo & Jianbing Li, 2018. "Regional Water Use Structure Optimization Under Multiple Uncertainties Based on Water Resources Vulnerability Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(5), pages 1827-1847, March.
    5. M. Li & P. Guo & G. Yang & S. Fang, 2014. "IB-ICCMSP: An Integrated Irrigation Water Optimal Allocation and Planning Model Based on Inventory Theory under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 241-260, January.
    6. H. Lu & G. Huang & L. He, 2012. "Simulation-Based Inexact Rough-Interval Programming for Agricultural Irrigation Management: A Case Study in the Yongxin County, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4163-4182, November.
    7. Zhang, Fan & Guo, Ping & Engel, Bernard A. & Guo, Shanshan & Zhang, Chenglong & Tang, Yikuan, 2019. "Planning seasonal irrigation water allocation based on an interval multiobjective multi-stage stochastic programming approach," Agricultural Water Management, Elsevier, vol. 223(C), pages 1-1.
    8. Zhang, Fan & Zhang, Chenglong & Yan, Zehao & Guo, Shanshan & Wang, Youzhi & Guo, Ping, 2018. "An interval nonlinear multiobjective programming model with fuzzy-interval credibility constraint for crop monthly water allocation," Agricultural Water Management, Elsevier, vol. 209(C), pages 123-133.
    9. C. Li & L. Zhang, 2015. "An Inexact Two-Stage Allocation Model for Water Resources Management Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(6), pages 1823-1841, April.
    10. Gaiqiang Yang & Ping Guo & Mo Li & Shiqi Fang & Liudong Zhang, 2016. "An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 701-729, January.
    11. Li, Mo & Guo, Ping & Singh, Vijay P. & Yang, Gaiqiang, 2016. "An uncertainty-based framework for agricultural water-land resources allocation and risk evaluation," Agricultural Water Management, Elsevier, vol. 177(C), pages 10-23.
    12. Gaiqiang Yang & Ping Guo & Mo Li & Shiqi Fang & Liudong Zhang, 2016. "An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 701-729, January.
    13. A. Ganji & M. Shekarriz fard, 2010. "A Modified Constrained State Formulation of Stochastic Soil Moisture for Crop Water Allocation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(3), pages 547-561, February.

    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. C. Li & L. Zhang, 2015. "An Inexact Two-Stage Allocation Model for Water Resources Management Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(6), pages 1823-1841, April.
    2. L. Zhang & C. Li, 2014. "An Inexact Two-Stage Water Resources Allocation Model for Sustainable Development and Management Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 3161-3178, August.
    3. Chen, Shu & Shao, Dongguo & Tan, Xuezhi & Gu, Wenquan & Lei, Caixiu, 2017. "An interval multistage classified model for regional inter- and intra-seasonal water management under uncertain and nonstationary condition," Agricultural Water Management, Elsevier, vol. 191(C), pages 98-112.
    4. Y. Li & G. Huang & S. Nie, 2009. "Water Resources Management and Planning under Uncertainty: an Inexact Multistage Joint-Probabilistic Programming Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(12), pages 2515-2538, September.
    5. Zhenfang Liu & Yang Zhou & Gordon Huang & Bin Luo, 2019. "Risk Aversion Based Inexact Stochastic Dynamic Programming Approach for Water Resources Management Planning under Uncertainty," Sustainability, MDPI, vol. 11(24), pages 1-22, December.
    6. Zhu, Y. & Huang, G.H. & Li, Y.P. & He, L. & Zhang, X.X., 2011. "An interval full-infinite mixed-integer programming method for planning municipal energy systems - A case study of Beijing," Applied Energy, Elsevier, vol. 88(8), pages 2846-2862, August.
    7. Wang, S. & Huang, G.H., 2014. "An integrated approach for water resources decision making under interactive and compound uncertainties," Omega, Elsevier, vol. 44(C), pages 32-40.
    8. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    9. Wang, S. & Huang, G.H., 2015. "A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management," European Journal of Operational Research, Elsevier, vol. 240(2), pages 572-581.
    10. Gaivoronski, Alexei & Sechi, Giovanni M. & Zuddas, Paola, 2012. "Cost/risk balanced management of scarce resources using stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 214-224.
    11. He, Li & Huang, Guo H. & Lu, Hongwei, 2011. "Bivariate interval semi-infinite programming with an application to environmental decision-making analysis," European Journal of Operational Research, Elsevier, vol. 211(3), pages 452-465, June.
    12. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    13. Li, G.C. & Huang, G.H. & Lin, Q.G. & Zhang, X.D. & Tan, Q. & Chen, Y.M., 2011. "Development of a GHG-mitigation oriented inexact dynamic model for regional energy system management," Energy, Elsevier, vol. 36(5), pages 3388-3398.
    14. H. Lu & G. Huang & G. Zeng & I. Maqsood & L. He, 2008. "An Inexact Two-stage Fuzzy-stochastic Programming Model for Water Resources Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(8), pages 991-1016, August.
    15. Chenglong Zhang & Qiong Yue & Ping Guo, 2019. "A Nonlinear Inexact Two-Stage Management Model for Agricultural Water Allocation under Uncertainty Based on the Heihe River Water Diversion Plan," IJERPH, MDPI, vol. 16(11), pages 1-18, May.
    16. Li, Y.P. & Huang, G.H. & Wang, G.Q. & Huang, Y.F., 2009. "FSWM: A hybrid fuzzy-stochastic water-management model for agricultural sustainability under uncertainty," Agricultural Water Management, Elsevier, vol. 96(12), pages 1807-1818, December.
    17. Liu, Y. & Huang, G.H. & Cai, Y.P. & Cheng, G.H. & Niu, Y.T. & An, K., 2009. "Development of an inexact optimization model for coupled coal and power management in North China," Energy Policy, Elsevier, vol. 37(11), pages 4345-4363, November.
    18. Li, W. & Li, Y.P. & Li, C.H. & Huang, G.H., 2010. "An inexact two-stage water management model for planning agricultural irrigation under uncertainty," Agricultural Water Management, Elsevier, vol. 97(11), pages 1905-1914, November.
    19. Zhang, Xiaodong & Huang, Guo H. & Nie, Xianghui, 2009. "Optimal decision schemes for agricultural water quality management planning with imprecise objective," Agricultural Water Management, Elsevier, vol. 96(12), pages 1723-1731, December.
    20. Li, Y.P. & Huang, G.H. & Yang, Z.F. & Nie, S.L., 2008. "IFMP: Interval-fuzzy multistage programming for water resources management under uncertainty," Resources, Conservation & Recycling, Elsevier, vol. 52(5), pages 800-812.

    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:23:y:2009:i:5:p:1001-1023. 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.