عنوان مقاله [English]
Background and Objectives: Considering the existence of uncertainty in the data of water resource problems, it has become more essential to design a reliable water resource allocation model under uncertainty. Due to multi-dimensional nature of optimal water allocation problem, considering multiple conflicting objectives within the optimization models is inevitable. The aim of this study is to provide a quantity-quality optimization model in which not only balance the economic and environmental objectives, but also remain robust in the face of existing uncertainties.
Materials and Methods: The nominal model of the study was constructed using the objectives of maximizing the income of the entire system and minimizing pollution load entered to the river. It was applied to the Dez-Karoon river system as a case study. By taking the uncertainties of river flow and water demands into account, the nominal model was promoted to a robust multi-objective optimization model using the Bertsimas and Sim's approach. The sensitivity of the robust model to changes in uncertainty levels and the probability of constraint violation was investigated. The ɛ-constraint method was used to solve the problem and the nominal model was applied to assess the results of the developed model. Among optimal solutions set, Knee point of the Pareto front of was selected as the solution of the problem.
Results: Application of developed model into the case study demonstrates its ability in quickly finding the exact solution of the problem. Comparing the optimal solution of knee points showed that hedging the optimization model against uncertainties via considering the uncertainty level and violation probability of 0.1, requires the decrease in operating the river water from 8301.5 to 7368.9 MCM/year and adjustment of the economic income from 1,636,808 to 1,365,693 million Rial/year in comparison with the nominal model. Under such a condition in which prevents the failure of supplying water under a given level of risk, the pollution load discharged into the river will decrease from 53,949 to 48,505 ton/ year. The results illustrate that without adding extra complexity into the nominal model, it can be immunized against uncertainties via the robust approach. By determining the uncertainty level and the probability of constraint violation, the decision maker is able to select the robustness level of the water resource allocation model and therefore, explore tradeoff among the values of the objectives and reliability of the system.
Conclution: The results demonstrate the satisfactory, high reliability and flexibility of the proposed robust model. Accordingly, the provided linear model of this study may be used as a user-friendly tool in the decision making process for optimal allocation of water resources.