Optimization of Gravity‐Fed Water Distribution Systems: Theory

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Abstract
A method is developed for the optimal design of multisource, looped, gravity‐fed water distribution systems subjected to a single loading pattern. The method is based on linear programming (LP) techniques and produces a locally optimal solution. Initially, design feasibility constraints are derived to check whether network design and therefore network optimization is feasible. Based on classical transportation problem principles, a theory is developed to formulate an LP problem for obtaining design paths from the source nodes to the demand nodes and thereby for obtaining the design distribution graph for the entire distribution system. Separate LP optimization models are then formulated to deal with the either the D‐specified condition in which the nonprimary links are of some minimum or specified diameter, or the Q‐specified condition in which the nonprimary links carry some minimum or specified discharge. The proposed method is illustrated through a design example in an accompanying paper dealing with application. General comments and limitations of the proposed method are also provided therein.

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