Development of an Optimization Model for Water Resources Allocation under Uncertain Conditions (Case study: Marand Watershed)

Given the limited available water resources, the conflict-laden issues of water allocation have become a challenging issue for planners and water consumers. The existence of different types of uncertainties and climate change conditions in the water resources systems intensify the complexity of the optimal allocation process of water resources in the agricultural field. Therefore, In the present study, it is tried to optimally allocate water resources in Marand watershed by developing a mathematical planning model that is capable of dynamics and uncertainty conditions both in the parameters of objective functions and in constraints.

In this study, an uncertainty-based interactive multi-stage stochastic programming (UIMSP) approach is proposed by incorporating the fractile criterion method and chance-constrained programming within a multi-stage decision-making framework for agricultural water resource management in various planning horizon. A two-period scenario tree with different probabilities for violating constraints (α) and various satisfactory levels of the objective function (β) were selected.

The results indicates that the minimum and maximum benefits of the system are [46.6, 983.6] × 1010 (Rials) and [699.7, 1483.1] × 1010 (Rials) when α=0.01  and , β=0.9 , respectively. In addition, an increase in satisfactory levels of the objective function (β) led to a gradual decrease in both upper and lower bound of the total net benefits at each given probability level of violating constraint (α), while any change in probability of constraint violation (α) resulted in creating a significant change in the system profits. Also, the results of the UIMSP model show that water scarcity is observed in different scenarios due to insufficient water resources in Marand watershed. However, according to the results, in the second period, despite the decrease in the amount of water available, the amount of water shortage has decreased with increasing irrigation efficiency. For example, under medium flow level, the amount of surface and groundwater shortages in the first period is 43.6% and 32.5%, respectively, while it is reduced by [36.9, 24.5] and [24.5, 0] percent in the second period.

The results can help decision-makers examine potential interactions between risks related to the stochastic objective function and constraints. Also, increasing irrigation efficiency and upgrading irrigation systems are among the main strategies that can provide an economic benefit to farmers while reducing environmental damage.