A motivation for probabilistic balancing rule models used for real-time reservoir operations: Newsboy problem approach

The Probabilistic Balancing Rule (PBR) model addresses the problem of real-time (daily) reservoir system operations by defining the optimal set of release decisions as those which minimize the maximum non-exceedence probability values, for the respective decisions, within a specified forecast horizon. In contrast, penalty-based models define the optimal decisions as those which result in the minimum number of penalty points for non-ideal operations, within a given forecast horizon. In this paper a theoretical motivation is provided for Probabilistic Balancing Rule models. the design and results of a broad-based test of the PBR models and penalty-based models is provided elsewhere by the authors. The analytical motivation for the PBR model follows from the inventory problem known as the Newsboy or Christmas Tree problem. For a simple single reservoir system, the real-time operations problem is shown to be a Newsboy problem whose optimal solution can be found by solving the PBR model. For more complex system operation problems including hydroelectric energy production, water supply, flood damage mitigation, low flow augmentation and water quality improvement, the PBR model may be a close approximation of the real-time operations problem posed in the context of the Newsboy problem when marginal probability distribution functions of the decisions or control variables are used.