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A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities

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  • D. Haro
  • J. Paredes
  • A. Solera
  • J. Andreu

Abstract

The allocation of water resources between different users is a traditional problem in many river basins. The objective is to obtain the optimal resource distribution and the associated circulating flows through the system. Network flow programming is a common technique for solving this problem. This optimisation procedure has been used many times for developing applications for concrete water systems, as well as for developing complete decision support systems. As long as many aspects of a river basin are not purely linear, the study of non-linearities will also be of great importance in water resources systems optimisation. This paper presents a generalised model for solving the optimal allocation of water resources in schemes where the objectives are minimising the demand deficits, complying with the required flows in the river and storing water in reservoirs. Evaporation from reservoirs and returns from demands are considered, and an iterative methodology is followed to solve these two non-network constraints. The model was applied to the Duero River basin (Spain). Three different network flow algorithms (Out-of-Kilter, RELAX-IV and NETFLO) were used to solve the allocation problem. Certain convergence issues were detected during the iterative process. There is a need to relate the data from the studied systems with the convergence criterion to be able to find the convergence criterion which yields the best results possible without requiring a long calculation time. Copyright Springer Science+Business Media B.V. 2012

Suggested Citation

  • D. Haro & J. Paredes & A. Solera & J. Andreu, 2012. "A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4059-4071, November.
    • Handle: RePEc:spr:waterr:v:26:y:2012:i:14:p:4059-4071
    DOI: 10.1007/s11269-012-0129-7
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    References listed on IDEAS

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    1. Antonio Manca & Giovanni Sechi & Paola Zuddas, 2010. "Water Supply Network Optimisation Using Equal Flow Algorithms," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(13), pages 3665-3678, October.
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    3. Giovanni Sechi & Paola Zuddas, 2008. "Multiperiod Hypergraph Models for Water Systems Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(3), pages 307-320, March.
    4. 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.
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    2. Bennie Grové, 2019. "Improved Water Allocation under Limited Water Supplies Using Integrated Soil-Moisture Balance Calculations and Nonlinear Programming," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(1), pages 423-437, January.
    3. Erez Braude & Shmuel Hauser & Zilla Sinuany-Stern & Gideon Oron, 2015. "Water Allocation Between the Agricultural and the Municipal Sectors Under Scarcity: A Financial Approach Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(10), pages 3481-3501, August.
    4. Fi-John Chang & Yu-Chung Wang & Wen-Ping Tsai, 2016. "Modelling Intelligent Water Resources Allocation for Multi-users," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1395-1413, March.
    5. Fi-John Chang & Yu-Chung Wang & Wen-Ping Tsai, 2016. "Modelling Intelligent Water Resources Allocation for Multi-users," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1395-1413, March.
    6. Zhisong Chen & Huimin Wang & Xiangtong Qi, 2013. "Pricing and Water Resource Allocation Scheme for the South-to-North Water Diversion Project in China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(5), pages 1457-1472, March.
    7. Frederick Chou & Hao-Chih Lee & William Yeh, 2013. "Effectiveness and Efficiency of Scheduling Regional Water Resources Projects," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(3), pages 665-693, February.
    8. Mohammad S. Khorshidi & Mohammad Reza Nikoo & Mojtaba Sadegh & Banafsheh Nematollahi, 2019. "A Multi-Objective Risk-Based Game Theoretic Approach to Reservoir Operation Policy in Potential Future Drought Condition," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(6), pages 1999-2014, April.
    9. Ayoub Tahiri & David Ladeveze & Pascale Chiron & Bernard Archimede & Ludovic Lhuissier, 2018. "Reservoir Management Using a Network Flow Optimization Model Considering Quadratic Convex Cost Functions on Arcs," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3505-3518, August.

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