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An inexact fuzzy parameter two-stage stochastic programming model for irrigation water allocation under uncertainty

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Abstract

In this study, an inexact two-stage stochastic programming model is developed, which can provide an effective linkage between conflicting economic benefits and the associated penalties attributed to the violation of the predefined policies. The developed model was applied to irrigation water allocation optimization system in Minqin County, Gansu province, China. Three different water demands (high, middle, and low) were considered. Fuzzy parameters in the inexact two-stage stochastic programming model were introduced to account for fuzzy events that exist in the irrigation water allocation optimizing system. As the result, the optimal water allocation plans, both from surface water and groundwater, were obtained at different flow levels and different α-cut levels of Minqin County. The final results were expert to make great contributions in helping local managers to make decisions on allocating irrigation water more effectively under uncertainty.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (No. 91125017, 41271536, 71071154), National High Technology Research and Development Program of China (863 Program) (No. 2011AA100502), the Government Public Research Funds for Projects of Ministry of Agriculture (No. 201203077) and Ministry of Water Resources (No. 201001060, and 201001061).

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Authors and Affiliations

  1. Centre for Agricultural Water Research in China, China Agricultural University, Tsinghuadong Street No.17, Beijing, 100083, People’s Republic of China

    M. Li, P. Guo, S. Q. Fang & L. D. Zhang

  2. Environmental Science and Engineering Program, University of Northern British Columbia, Prince George, BC, V2N 4Z9, Canada

    P. Guo

  3. College of Water Conservancy, Hydropower and Architecture Engineering, Yunnan Agricultural University, Kunming, 650201, China

    L. D. Zhang

Authors
  1. M. Li
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  2. P. Guo
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  3. S. Q. Fang
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  4. L. D. Zhang
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Corresponding author

Correspondence to P. Guo.

Appendix

Appendix

t:

Water resources type, t = 1 is surface water, t = 2 is groundwater

n:

Irrigation area

h:

Flow levels, h = 1 is low level, h = 2 is middle level, h = 3 is high level

W ± tn :

Water application target (water resources type t) for irrigation area n, (104 m3) (decision variable of the first stage)

C ± tn :

The cost for irrigation area n per unit of water application target (water resources type t) (RMB ¥/104 m3)

S ± tnh :

The shortage of water by which the water allocation target (W ± tn ) is not met under inflow q ± tnh (104 m3) (decision variable of the second stage)

L ± tn :

The reduction of net benefit (penalty) for irrigation area n when per unit of water(surface water and groundwater) not delivered (RMB ¥/104 m3)

p tnh :

The probabilities of inflow q ± tnh

Q ± tn :

The available water supply (water resources type t) for irrigation area n at initial stages (104 m3)

q ± tnh :

The water from other resources (water resources type t) for irrigation area n under inflow probabilities p tnh (104m3)

\( \mathop {C_{tn} }\limits^{\sim } \) :

The cost for irrigation area n per unit of Water application target (water resources type t) (RMB ¥/104 m3) (fuzzy number)

\( \mathop {L_{tn} }\limits^{\sim } \) :

The reduction of net benefit (penalty) for irrigation area n when per unit of water (surface water and groundwater) not delivered (RMB ¥/104 m3) (fuzzy number)

\( \mathop {Q_{tn} }\limits^{\sim } \) :

The available water supply (water resources type t) for irrigation area n at initial stages (104 m3) (fuzzy number)

\( \mathop {q_{tnh} }\limits^{\sim } \) :

The available water supply (water resources type t) for irrigation area nr under inflow probabilities p tn h (104 m3) (fuzzy number)

α:

The fuzzy degree of membership level

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Li, M., Guo, P., Fang, S.Q. et al. An inexact fuzzy parameter two-stage stochastic programming model for irrigation water allocation under uncertainty. Stoch Environ Res Risk Assess 27, 1441–1452 (2013). https://doi.org/10.1007/s00477-012-0681-y

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