Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2013), Article ID 105391, 11 pages.

Monthly Optimal Reservoirs Operation for Multicrop Deficit Irrigation under Fuzzy Stochastic Uncertainties

Liudong Zhang, Ping Guo, Shiqi Fang, and Mo Li

Full-text: Open access


An uncertain monthly reservoirs operation and multicrop deficit irrigation model was proposed under conjunctive use of underground and surface water for water resources optimization management. The objective is to maximize the total crop yield of the entire irrigation districts. Meanwhile, ecological water remained for the downstream demand. Because of the shortage of water resources, the monthly crop water production function was adopted for multiperiod deficit irrigation management. The model reflects the characteristics of water resources repetitive transformation in typical inland rivers irrigation system. The model was used as an example for water resources optimization management in Shiyang River Basin, China. Uncertainties in reservoir management shown as fuzzy probability were treated through chance-constraint parameter for decision makers. Necessity of dominance (ND) was used to analyse the advantages of the method. The optimization results including reservoirs real-time operation policy, deficit irrigation management, and the available water resource allocation could be used to provide decision support for local irrigation management. Besides, the strategies obtained could help with the risk analysis of reservoirs operation stochastically.

Article information

J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 105391, 11 pages.

First available in Project Euclid: 1 October 2014

Permanent link to this document

Digital Object Identifier


Zhang, Liudong; Guo, Ping; Fang, Shiqi; Li, Mo. Monthly Optimal Reservoirs Operation for Multicrop Deficit Irrigation under Fuzzy Stochastic Uncertainties. J. Appl. Math. 2014, Special Issue (2013), Article ID 105391, 11 pages. doi:10.1155/2014/105391.

Export citation


  • P. S. Ashofteh, O. B. Haddad, and M. A. Mariño, “Climate change impact on reservoir performance indexes in agricultural water supply,” Journal of Irrigation and Drainage Engineering, vol. 139, no. 2, pp. 85–97, 2012.
  • M. Moradi-Jalal, O. Bozorg Haddad, B. W. Karney, and M. A. Mariño, “Reservoir operation in assigning optimal multi-crop irrigation areas,” Agricultural Water Management, vol. 90, no. 1-2, pp. 149–159, 2007.
  • W. S. Butcher, “Stochastic dynamic programming for optimum reservoir operation1,” Water Resources Bulletin, vol. 7, no. 1, pp. 115–123, 1971.
  • J. R. Stedinger, B. F. Sule, and D. P. Loucks, “Stochastic dynamic programming models for reservoir operation optimization,” Water Resources Research, vol. 20, no. 11, pp. 1499–1505, 1984.
  • A. Dos Santos Teixeira and M. A. Mariño, “Coupled reservoir operation-irrigation scheduling by dynamic programming,” Journal of Irrigation and Drainage Engineering, vol. 128, no. 2, pp. 63–73, 2002.
  • S. Vedula and P. P. Mujumdar, “Optimal reservoir operation for irrigation of multiple crops,” Water Resources Research, vol. 28, no. 1, pp. 1–9, 1992.
  • S. Vedula and D. N. Kumar, “An integrated model for optimal reservoir operation for irrigation of multiple crops,” Water Resources Research, vol. 32, no. 4, pp. 1101–1108, 1996.
  • P. P. Mujumdar and T. S. V. Ramesh, “Real-time reservoir operation for irrigation,” Water Resources Research, vol. 33, no. 5, pp. 1157–1164, 1997.
  • A. Evers, R. Elliott, and E. Stevens, “Integrated decision making for reservoir, irrigation, and crop management,” Agricultural Systems, vol. 58, no. 4, pp. 529–554, 1998.
  • P. E. Georgiou and D. M. Papamichail, “Optimization model of an irrigation reservoir for water allocation and crop planning under various weather conditions,” Irrigation Science, vol. 26, no. 6, pp. 487–504, 2008.
  • A. S. Prasad, N. Umamahesh, and G. Viswanath, “Short-term real-time reservoir operation for irrigation,” Journal of Water Resources Planning and Management, vol. 139, no. 2, pp. 149–158, 2012.
  • A. Afshar, M. A. Marino, and A. Abrishamchi, “Reservoir planning for irrigation district,” Journal of Water Resources Planning and Management, vol. 117, no. 1, pp. 74–85, 1991.
  • S. Vedula, P. P. Mujumdar, and G. Chandra Sekhar, “Conjunctive use modeling for multicrop irrigation,” Agricultural Water Management, vol. 73, no. 3, pp. 193–221, 2005.
  • E. G. Reichard, “Groundwater-surface water management with stochastic surface water supplies: a simulation optimization approach,” Water Resources Research, vol. 31, no. 11, pp. 2845–2865, 1995.
  • M. Karamouz and H. V. Vasiliadis, “Bayesian stochastic optimization of reservoir operation using uncertain forecasts,” Water Resources Research, vol. 28, no. 5, pp. 1221–1232, 1992.
  • R. S. V. Teegavarapu and S. P. Simonovic, “Modeling uncertainty in reservoir loss functions using fuzzy sets,” Water Resources Research, vol. 35, no. 9, pp. 2815–2823, 1999.
  • X. Li, S. Guo, P. Liu, and G. Chen, “Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty,” Journal of Hydrology, vol. 391, no. 1-2, pp. 124–132, 2010.
  • F.-J. Chang, S.-C. Hui, and Y.-C. Chen, “Reservoir operation using grey fuzzy stochastic dynamic programming,” Hydrological Processes, vol. 16, no. 12, pp. 2395–2408, 2002.
  • A. Seifi and K. W. Hipel, “Interior-point method for reservoir operation with stochastic inflows,” Journal of Water Resources Planning and Management, vol. 127, no. 1, pp. 48–57, 2001.
  • M. N. Azaiez, M. Hariga, and I. Al-Harkan, “A chance-constrained multi-period model for a special multi-reservoir system,” Computers and Operations Research, vol. 32, no. 5, pp. 1337–1351, 2005.
  • P. Guo and G. H. Huang, “Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties,” Stochastic Environmental Research and Risk Assessment, vol. 23, no. 3, pp. 349–359, 2009.
  • A. J. Askew, “Chance–-constrained dynamic programing and the optimization of water resource systems,” Water Resources Research, vol. 10, no. 6, pp. 1099–1106, 1974.
  • D. Z. Fu, Y. P. Li, and G. H. Huang, “A factorial-based dynamic analysis method for reservoir operation under fuzzy-stochastic uncertainties,” Water Resources Management, vol. 27, no. 13, pp. 4591–4610, 2013.
  • M. E. Jensen, “Water consumption by agricultural plants,” Water Deficits and Plant Growth, vol. 2, pp. 1–22, 1968.
  • E. C. Kipkorir and D. Raes, “Transformation of yield response factor into Jensen's sensitivity index,” Irrigation and Drainage Systems, vol. 16, no. 1, pp. 47–52, 2002.
  • G. P. Tsakiris, “A method for applying crop sensitivity factors in irrigation scheduling,” Agricultural Water Management, vol. 5, no. 4, pp. 335–343, 1982.
  • J. Ma, Z. Ding, W. M. Edmunds, J. B. Gates, and T. Huang, “Limits to recharge of groundwater from Tibetan plateau to the Gobi desert, implications for water management in the mountain front,” Journal of Hydrology, vol. 364, no. 1-2, pp. 128–141, 2009.
  • Y. Qu, S. Ma, and W. Qu, “water resources transformation and development and use model in the arid area of northwest china,” Journal of Desert Research, vol. 18, no. 4, pp. 299–307, 1988.
  • L. Yao, S. Feng, X. Mao, Z. Huo, S. Kang, and D. A. Barry, “Coupled effects of canal lining and multi-layered soil structure on canal seepage and soil water dynamics,” Journal of Hydrology, vol. 430-431, pp. 91–102, 2012. \endinput