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Multireservoir System Optimization using Fuzzy Mathematical Programming

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  • P. Jairaj
  • S. Vedula

Abstract

For a multireservoir system, where the number of reservoirs islarge, the conventional modelling by classical stochastic dynamicprogramming (SDP) presents difficulty, due to the curse ofdimensionality inherent in the model solution. It takes a longtime to obtain a steady state policy and also it requires largeamount of computer storage space, which form drawbacks inapplication. An attempt is made to explore the concept of fuzzysets to provide a viable alternative in this context. Theapplication of fuzzy set theory to water resources systems isillustrated through the formulation of a fuzzy mathematicalprogramming model to a multireservoir system with a number ofupstream parallel reservoirs, and one downstream reservoir. Thestudy is aimed to minimize the sum of deviations of the irrigationwithdrawals from their target demands, on a monthly basis, over ayear. Uncertainty in reservoir inflows is considered by treatingthem as fuzzy sets. The model considers deterministic irrigationdemands. The model is applied to a three reservoir system in theUpper Cauvery River basin, South India. The model clearlydemonstrates that, use of fuzzy linear programming inmultireservoir system optimization presents a potentialalternative to get the steady state solution with a lot lesseffort than classical stochastic dynamic programming. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • P. Jairaj & S. Vedula, 2000. "Multireservoir System Optimization using Fuzzy Mathematical Programming," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 14(6), pages 457-472, December.
    • Handle: RePEc:spr:waterr:v:14:y:2000:i:6:p:457-472
    DOI: 10.1023/A:1011117918943
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
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    1. 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.
    2. Mike Spiliotis & Dionissis Latinopoulos & Lampros Vasiliades & Kyriakos Rafailidis & Eleni Koutsokera & Ifigenia Kagalou, 2022. "Flexible Goal Programming for Supporting Lake Karla’s (Greece) Sustainable Operation," Sustainability, MDPI, vol. 14(7), pages 1-19, April.
    3. Abdüsselam Altunkaynak & Mehmet Özger & Mehmet Çakmakci, 2005. "Water Consumption Prediction of Istanbul City by Using Fuzzy Logic Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 19(5), pages 641-654, October.
    4. Fuxing Wang & Oliver Saavedra Valeriano & Xinguo Sun, 2013. "Near Real-Time Optimization of Multi-Reservoir during Flood Season in the Fengman Basin of China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(12), pages 4315-4335, September.
    5. 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.
    6. Deepti Rani & Maria Moreira, 2010. "Simulation–Optimization Modeling: A Survey and Potential Application in Reservoir Systems Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(6), pages 1107-1138, April.
    7. Zeng, Xieting & Kang, Shaozhong & Li, Fusheng & Zhang, Lu & Guo, Ping, 2010. "Fuzzy multi-objective linear programming applying to crop area planning," Agricultural Water Management, Elsevier, vol. 98(1), pages 134-142, December.
    8. Zeng, X.T. & Huang, G.H. & Chen, H.L. & Li, Y.P. & Kong, X.M. & Fan, Y.R., 2016. "A simulation-based water-environment management model for regional sustainability in compound wetland ecosystem under multiple uncertainties," Ecological Modelling, Elsevier, vol. 334(C), pages 60-77.
    9. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    10. Sumant Choudhari & P. Anand Raj, 2010. "Multiobjective Multireservoir Operation in Fuzzy Environment," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2057-2073, August.
    11. S. Wang & G. Huang, 2012. "Identifying Optimal Water Resources Allocation Strategies through an Interactive Multi-Stage Stochastic Fuzzy Programming Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(7), pages 2015-2038, May.
    12. Q. Tan & G. Huang & Y. Cai, 2013. "Multi-Source Multi-Sector Sustainable Water Supply Under Multiple Uncertainties: An Inexact Fuzzy-Stochastic Quadratic Programming Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(2), pages 451-473, January.
    13. 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.
    14. Yan Han & Yue-Fei Huang & Guang-Qian Wang & Imran Maqsood, 2011. "A Multi-objective Linear Programming Model with Interval Parameters for Water Resources Allocation in Dalian City," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(2), pages 449-463, January.
    15. Li, Y.P. & Huang, G.H. & Nie, S.L., 2009. "A robust interval-based minimax-regret analysis approach for the identification of optimal water-resources-allocation strategies under uncertainty," Resources, Conservation & Recycling, Elsevier, vol. 54(2), pages 86-96.
    16. Rama Mehta & Sharad Jain, 2009. "Optimal Operation of a Multi-Purpose Reservoir Using Neuro-Fuzzy Technique," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(3), pages 509-529, February.
    17. D. Morankar & K. Srinivasa Raju & D. Nagesh Kumar, 2013. "Integrated Sustainable Irrigation Planning with Multiobjective Fuzzy Optimization Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(11), pages 3981-4004, September.
    18. Hamid Safavi & Iman Chakraei & Abdolreza Kabiri-Samani & Mohammad Golmohammadi, 2013. "Optimal Reservoir Operation Based on Conjunctive Use of Surface Water and Groundwater Using Neuro-Fuzzy Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(12), pages 4259-4275, September.

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