Abstract: Controlling the flood limit water levels of a reservoir by stages is an effective approach to raising flood water utilization rates. In this study, by dividing flood season into different stages using the circular distribution method, we determine benefit index sets and risk index sets for a staged control of the limit water levels, and construct a multi-objective collaborative decision-making model that can coordinate conflicts between risk and benefit. Then, we calculate a utility function for each index set, determine a payoff function and a reachable utility set, and solve for the ideal Nash negotiation solution using a nonlinear programming method. And by the theory of pattern recognition, an optimal scheme can be determined; a certain preference for risk or benefit can be realized using the current situation point as the basis for benefit-risk negotiation decision and then adjusting this point. In a case study of the Xianghongdian Reservoir, we adopt a condition of risk and benefit valued equally, and obtain the optimal flood control levels of 126.5 m and 127.0 m for pre-flood and post-flood stages, respectively. It shows that by raising the risk at the corresponding risk status point, a risk preference in pre-flood stage can be realized, resulting in a greater value of the risk payoff function and thus a lower optimal limit water level. Similarly, by raising the benefit at this point, a preference for benefit in post-flood season can be realized with a greater value of the benefit payoff function and a higher optimal limit water level.

Key words: flood season staging, circular distribution method, multi-objective decision, flood limit water level, Nash negotiation solution