Multi-water conjunctive optimal allocation based on interval-parameter two-stage Fuzzy-stochastic programming

Abstract: Rapid population growth and economy development has led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an interval-parameter two-stage Fuzzy-stochastic optimization model was developed for dispatching the underground and surface water systems for different crops in Hong Xinglong irrigation of China under the conditions of uncertainty and complexity. In the model, the maximal system benefit was regarded as the objective function and 3 methods of probability density function, discrete intervals and fuzzy sets were introduced into the two-stage linear programming framework to resolve uncertain issues. The model allocated a predefined water to crops in the first stage, according to benefit and punishment for water shortage condition to adjust the water supply in the second stage, making the system reach the balance of systems benefit and the risk of punishment, the process of water allocation for multiple corps was simulated, meanwhile, the allocation of water from various sources was optimized. Because inflows water was of obvious probability characteristics in irrigation area, the model took into account of the random of inflow, and assumed that the probability of occurrence for high, middle and low levels were 0.2, 0.6 and 0.2. Since the quantity of stream flows, water requirement of crop and available water supply were uncertain, and uncertainties might also exist in system benefits and costs, the uncertain parameters of above-mentioned were described by interval variables. The available water in the irrigation area was represented by fuzzy sets based on credibility theory. The different probabilities, discrete interval number and fuzzy sets together were used to build the irrigation multi-water resource, multi-crop water distribution model. The model was solved by the method of linear programming, the optimal distribution scheme of water was achieved and the maximum benefit was 1 355.144×106-2 371.792×106 RMB. It could reflect not only uncertainties in water resources system, but also provide an effective linkage between conflicting economic benefits and the associated penalties attributed to the violation of the predefined water distribution target. Meanwhile, the results were presented in the forms of interval number, proving a more broad decision space for decision makers. Moreover, the results indicated that farmer planted a large number of high-yield and high water consumption of crops such as rice and corn in irrigation area and single planting structure would lead to the risk of the decrease of crop production in dry year, the model was valuable for supporting the adjustment or justification of the existing irrigation patterns and identify a desired water allocation plan for agricultural irrigation under uncertainty. Compared with the other traditional two-stage model, this model had advantages: 1) it considered uncertain factors as much as possible, made the model more close to actual condition; 2) The model effectively relieved groundwater pressure of water supply by utilizing surface water and groundwater; 3) The model results would suggest managers reducing planting area of high water consumption crops; 4) Water resources management by system benefit would stimulate employee enthusiasm; and 5) The model data was relatively easy to access.