Network Flow Optimization Model for Basin-Scale Water Supply Planning

Nien-Sheng Hsu
Associate Professor, Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan, ROC. E-mail: nsshue@ce.ntu.edu.tw

Ker-Wei Cheng
Graduate Student, Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan, ROC.

Traditionally, both simulation and optimization models are used for basin-wide water resources planning and management. Simulation models analyze the results from various stipulated alternatives and then check for feasibility and optimality. It is inherently a trial-anderror approach and optimality is not assured. The major advantages of using a simulation model are that the model is easy to operate and it generally requires minimum computer time and storage. On the other hand, optimization models minimize or maximize a given objective function subject to the imposed set of constraints; thus the solution obtained is feasible and optimal. However, for large-scale water resources systems, this approach may become infeasible because of the dimensionality problem. In recent years, improvements in both computer capability and algorithm efficiency make the optimization models more attractive.

This paper develops a generalized network flow optimization model for long-term supply-demand analysis for basin-wide water resources planning. A set of nodes and arcs are used to form the network, and the decision variables are reservoir storage and water supply for public and agricultural uses. The objective function to be minimized is formed by summing the products of the decision variables multiplied by their corresponding cost coefficients. The constraints of the model include continuity equations, reservoir operation rule curves, reduced water supply due to water shortage, and evaporation losses from reservoirs. The formulated network model has losses in the transshipment and is solved by an efficient embedded generalized network solver (EMNET). The developed model is applied to a river basin located in the northern part of Taiwan. To analyze the characteristics of the model, the results obtained from the optimization model are compared with those obtained from a well-calibrated simulation model. The comparison shows that the water shortage computed by the optimization model is smaller than that computed by the simulation model. The developed model is then used to analyze future water supply-demand conditions for the area.

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