This study proposes a method of analyzing the error bound of optimal reservoir operation based on an inflow forecast with a limited horizon. This is a practical approach to real-world applications because current weather forecasts and climate predictions cannot necessarily achieve the “perfect forecast” required for optimal solutions. This study proposes a method to measure the error and error bound according to terminal stage boundary conditions, for which a theoretical convergence rate is derived. Our results suggest that convergence can be attained at a rate faster than the inverse of the extension of the study horizon. This demonstrates that the application of rolling horizons can improve the quality of decision making by exploiting available forecasts/information. When a perfect forecast is unavailable, the rolling decision procedure with regularly updated forecast information could help to avoid serious losses due to shortsighted policies.