The purpose of this paper is to derive the general optimality conditions of the commonly used operating policies for reservoirs in parallel with joint water demand, which are defined in terms of system-wide release rules and individual reservoir storage balancing functions. Following that, a new set of release rules for individual reservoirs are proposed in analytical forms by considering the optimality conditions for the balance of total water delivery utility and carryover storage value of individual reservoirs. Theoretical analysis indicates that the commonly used operating policies are a special case of the newly derived rules. The derived release rules are then applied to simulating the operation of a parallel reservoir system in northeastern China. Compared to the performance of the commonly used policies, some advantages of the proposed operation rules are illustrated. Most notably, less water shortage occurrence and higher water supply reliability are obtained from the proposed operation rules.

Hedging is widely used to mitigate severe water shortages in the operation of reservoirs during droughts. Rationing is usually instituted with one hedging policy, which is based only on one trigger, i.e., initial storage level or current water availability. It may perform poorly in balancing the benefits of a release during the current period versus those of carryover storage during future droughts. This study proposes a novel hedging rule to improve the efficiency of a reservoir operated to supply water, in which, based on two triggers, hedging is initiated with three different hedging sub-rules through a two-step approach. In the first step, the sub-rule is triggered based on the relationship between the initial reservoir storage level and the level of the target rule curve or the firm rule curve at the end of the current period. This step is mainly concerned with increasing the water level or not in the current period. Hedging is then triggered under the sub-rule based on current water availability in the second step, in which the trigger implicitly considers both initial and ending reservoir storage levels in the current period. Moreover, the amount of hedging is analytically derived based on the Karush–Kuhn–Tucker (KKT) conditions. In addition, the hedging parameters are optimized using the improved particle swarm optimization (IPSO) algorithm coupled with a rule-based simulation. A single water-supply reservoir located in Hubei Province in central China is selected as a case study. The operation results show that the proposed rule is reasonable and significantly improves the reservoir operation performance for both long-term and critical periods relative to other operation policies, such as the standard operating policy (SOP) and the most commonly used hedging rules.

Dynamic canal-system scheduling faces the fundamental challenge of determining the optimal reduction in the current period’s water allocation to reserve sufficient water for remaining periods, thereby hedging against potentially greater future water shortages. Although forecast information has been widely incorporated to address this hedging problem, its effectiveness is heavily dependent on forecast accuracy. Integrating abundant historical canal scheduling data with forecast information provides a promising pathway to improve scheduling performance, yet relevant studies remain limited. This study introduces the concept of Target Residual Lump-Sum Water Quota (TRLSWQ) for each time interval and develops a novel “Bi-level, Two-stage” (BT) model for dynamically updated canal-system scheduling that jointly leverages TRLSWQ and forecast information. The model defines clear canal scheduling rules and effectively adapts to the hierarchical structure in canal system scheduling. The model is applied to the summer–autumn irrigation scheduling of the Yongji main canal and six associated sub-canals in the Hetao Irrigation Area, Inner Mongolia, China. The results indicate that compared with the conventional model, the BT model reduces the total water shortage index of sub-canals from 40.81 to 31.44 (a decrease of 22.9%) and increases the utilization rate of the water quota from 89.3% to 92.9% (an increase of 3.9%). Furthermore, this study clarifies the mechanism of canal scheduling deviations caused by forecast errors: early-stage rainfall under-forecasting induces excessive early-stage allocation, leaving no water for later periods, whereas early-stage over-forecasting leads to withheld early allocation and unused residual lump-sum quota in later stages. The BT model effectively balances shortage risks between current and future periods and offers a practical and robust strategy for improving dynamic canal scheduling in irrigation districts.

It is hardly realistic to assume that, under all decision circumstances, followers will always choose a solution that leads to the worst upper-level objective functional value. However, this generally accepted concept of the pessimistic solution to the ill-posed bilevel programming problems may lead to the leader’s attitude being more pessimistic vis à vis his anticipation of the follower’s decision being non-antagonistic. It will result in a wrong pessimistic solution and a greater potential of cooperation space between the leader and the followers. This paper presents a new concept of a non-antagonistic pessimistic solution with four numerical examples for bilevel programming problems from a non-antagonistic point of view. We prove that the objective function value of the non-antagonistic pessimistic solution generally dominates or is equal to the objective functional value of the pessimistic solution and the rewarding solution, and the maximum potential space for leader-follower cooperation can be overestimated in a generally applied pessimistic solution. Our research extends the concept of the pessimistic solution. It also sheds light on the insights that the non-antagonistic pessimistic solution can describe the practical potential of cooperation space between the leader and followers in non-antagonistic circumstances.