Xu et al. (2026) A Bellman equation-based unified framework for evaluating and optimizing reservoir hedging rules: Incorporating inflow temporal dependence and non-stationary environments

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-08-17
• Authors: Ximeng Xu, Chao Ma, Haixing Gou
• DOI: 10.1016/j.jhydrol.2026.136264

Research Groups

State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, Tianjin, China; School of Civil Engineering, Tianjin University, Tianjin, China.

Short Summary

This study develops a unified framework for evaluating and optimizing reservoir hedging rules by incorporating inflow temporal dependence and non-stationary environments using the Bellman equation. The framework supports both the evaluation and optimization of hedging rules.

Objective

• Investigate the limitations of traditional hedging rule (HR) formulations, including predetermined differentiable utility functions, temporally independent inflows, and stationary environments.
• Develop a unified framework for evaluating and optimizing HRs based on the Bellman equation.

Study Configuration

• Spatial Scale: Reservoir operation at the local to regional scale.
• Temporal Scale: Short-term (daily to weekly) to long-term (seasonal to annual).

Methodology and Data

• Models used: Markov decision process, Bellman expectation equation, and Bellman optimality equation.
• Data sources: Numerical experiments and theoretical analysis.

Main Results

• The unified framework supports both the evaluation and optimization of HRs.
• Key properties of the optimal value function, including monotonicity, concavity, and convergence, are derived.
• Time-varying HRs and two-dimensional HRs are obtained for non-stationary environments and Markovian inflow cases, respectively.

Contributions

• This study addresses the limitations of traditional HR formulations by incorporating inflow temporal dependence and non-stationary environments.
• The unified framework provides a quantitative criterion for rule comparison and supports both the evaluation and optimization of HRs.

Funding

• This research was supported by the State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University.

Citation

@article{Xu2026Bellman,
  author = {Xu, Ximeng and Ma, Chao and Gou, Haixing},
  title = {A Bellman equation-based unified framework for evaluating and optimizing reservoir hedging rules: Incorporating inflow temporal dependence and non-stationary environments},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.136264},
  url = {https://doi.org/10.1016/j.jhydrol.2026.136264}
}