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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 853186, 15 pages
Research Article

Optimizing Operation of Water Supply Reservoir: The Role of Constraints

State Key Laboratory of Hydro-Science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

Received 22 October 2013; Revised 18 December 2013; Accepted 18 December 2013; Published 18 March 2014

Academic Editor: Yi-Kuei Lin

Copyright © 2014 Tongtiegang Zhao and Jianshi Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a mathematical analysis of water supply reservoir operation. The analysis illustrates one-stage, two-stage, and three-stage formulations of multiple-period reservoir operation depending on the effects of operational constraints. There is a one-stage model when storage capacity constraints are nonbinding. Release decisions depend on total water availability and exhibit equal marginal utilities. Binding upper (lower) storage capacity constraint blocks the effect of decreased (increased) water availability in the subsequent stages on release decisions in the preceding stages. When one storage capacity constraint is binding, multiple periods become two stages and a gap occurs between marginal utilities of water. When there are one upper and one lower binding storage capacity constraints, reservoir operation is characterized as a three-stage model. Effects of forecast uncertainty and ending storage on reservoir operation are affected by reservoir storage capacity. When the storage capacity constraints are nonbinding, the reservoir can regulate streamflow in an extended timeframe, and current release decision is affected by forecast uncertainty of total streamflow and ending storage. When the storage capacity constraints are binding, the reservoir can regulate streamflow only in a short timeframe, and current release decision is primarily affected by forecast uncertainty of streamflow in the current stage.