Integrated Model of Water Optimal Allocation with a Cooperative Game Approach Case Study: Shahid Rajaee Dam

Population growth and water resource constraints make optimal operation of available resources important. Considering the utility of the stakeholders and the physical limitations of the problem, the optimal allocation of water resources is, therefore, necessary. Among the proposed strategies, the game theory is one of the methods used to improve water resources management. Also, in order to achieve the optimal and fair allocation, a model and method should be selected in accordance to the conditions. Our main purpose was to study the optimal water allocation from the dam reservoir by increasing the overall profitability of the system through forming a coalition as well as increasing the profits of each water users participated in the coalition. Increase in profits will be possible without the need for any additional costs and only with the change in the operation management. Integration of Genetic Algorithm optimization model with Shapley Crisp game theory can be considered as the innovation of this research work applied to optimally allocate water from Shahid Rajaee Dam reservoir to downstream needs.

In this study, a new methodology based on crisp Shapley games is developed for optimal water allocation from the dam reservoir. First, the standard operation policy was used to determine the volume of available water. Then, the optimization model of the Genetic Algorithm was employed for initial allocation considering an equity criterion. The Crisp Cooperative Game Theory was then applied for secondary optimization of water allocation among stakeholders. The possible coalitions for increasing the overall system profits were formed using the Shapley method and the profits of each coalition were then calculated. Finally, the Shapley's value relationship was used to reassign profits to players in order to encourage them to participate in the grand coalition. This study was carried out on Shahid Rajaee dam located in 45 kilometers southwest of Sari in Tajan basin. This dam mainly supplies agricultural and drinking water. Rice and citrus production were the largest and second largest water consumer, respectively.

In this study, the monthly amount of water released from Shahid Rajaee Dam reservoir was determined by using standard utilization policy and then the amount of initial allocation to downstream dam needs was calculated using genetic algorithm optimization model. Then, by using the players' profit coefficient and the amounts allocated from the implementation of the genetic algorithm model, the initial profit values were calculated for each stakeholder. Employing the Shapley Crisp method, the amounts of water allocated to each player and their corresponding economic benefits were obtained for the grand and two-player coalition. The results showed that the grand coalition had more benefits than the binary coalitions as well as the initial allocation. At this step, the Shapley value relationship was used to reallocate the profits among the players. After allocating water to three participants based on different coalitions, since the fair share of each was obtained in the first step, payments must be made between the players in order to be fair. The player who receives more water share determined at the first step must pay money to other players receiving water less than their fair share. The method proposed for the 18 years statistical period was used to allocate water among the stakeholder. According to the findings, the formation of a grand coalition increases overall system profit without the need for any additional costs and only with revising the operation management.

In this research, an integrated model of optimization was developed using Genetic Algorithm and Shapley Crisp Cooperative Game Approach. The amount of financial payments among the stakeholders in the coalition was also determined based on the Shapely value. Constituent coalitions show the management impacts on water policy and demand management in the studied area. The best results were obtained when players formed a grand coalition. In other words, by participating in the grand coalition and reallocation of water and profits among players, the overall system profits will increase by 10 % and the profits of players cultivating rice, citrus and other agricultural products will rise by 6, 16 and 15 %, respectively, as compared with the condition the players do not participate in the grand coalition and water allocation is only done using the Genetic Algorithm. Therefore, the water allocation should be based on a grand coalition requiring the cooperation and participation of all stakeholders. The results indicate that this method can be applied to allocate resources equitably. It can be also used to solve social conflicts among decision-makers.