Socially-Optimal and Nash Pareto-Based Alternatives for Water Allocation under Uncertainty: an Approach and Application

This study has proposed a methodology by enhancing an interactive algorithm to multi-objective optimization problems with interval parameters, in an attempt to reach the tradeoff between quality and reliability of the resultant optimum solutions. The earlier algorithm could turn into a prolonged procedure that deals with several players with different aspirations at different reliability, or risk, levels under non-deterministic conditions. Hence, it is not a pertinent approach to solve problems of water allocation between competing parties. The enhanced methodology aims to alleviate the burdens of the procedure and generate a unique set of solutions (i.e., near-Pareto-optimal alternatives), instead of a myriad of compromise solution sets. We have investigated a real-world hydro-environmental problem, the allocation of water between Dorudzan-Korbal irrigation networks and Bakhtegan Lake in Fars Province, Iran to assess feasibility of this methodology. In order to reach a consensus concerning the stakeholders’ individual preferences, we identified the compromise alternatives from the obtained sets of non-dominated solutions by taking advantage of various social choice rules and the Nash bargaining model. The results demonstrated that the developed methodology could incorporate the risk of system constraints violations (i.e., planning reliability under uncertainty) into the process of approximating the optimal tradeoff set of solutions. It also gave policymakers a chance to acquire perception into the potentially best compromise for land and water allocation schemes regarding the preference profiles of the involved interest groups.