Application of Interactive Interval Linear Programming for Optimal Water and Crop Area Allocation Considering Virtual Water Content and Socio-economic Factors (Case study: Dorudzan-Korbal Plain)

One of the key issues in the practical planning for water resources is the existence of uncertain factors. One of the approaches for decision making under such circumstances is interval programming. The aim of the study is to develop an interactive optimization model for water and crop area allocation. The developed model comprises four objectives that take into account socio-economic factors, the virtual water content of crops, and meeting environmental water requirements. For solving the model, four crop area scenarios (assumptions) were considered. Results showed that by raising the level of satisfaction threshold on the constraints, the amount of water allocated to each water user is declined. So that from the satisfaction level of 0.65 to the level of complete satisfaction, the model allocates only the minimum amount of water (40 MCM) to meet the environmental water needs. Based on considered scenarios for solving the model, the largest cultivation areas are allocated to wheat and maize for autumn and spring cultivations, respectively. Solving the model in the absence of upper bound for crop areas revealed that the greatest difference between optimal crop area and the highest cultivation area happened was belong to rice with 2777 and 5821.6 hectares in Dorudzan and Korbal districts, respectively. The main advantage of the developed model in the present study is the linear formulation as well as its ability to deal with uncertain parameters. Outcomes of the model provide information required for the assessment of risk and reliability of planning options for water allocation.