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Optimal design of water distribution networks for fuzzy demands

Future water demands being difficult to predict with any certainty are considered herein as fuzzy demands and modelled by trapezoidal possibility distribution function as was done by Xu and Goulter. The fuzzy linear programming model as formulated by Xu and Goulter for minimum cost design of water distribution networks is modified by including loop-head loss constraints in the form of path-head loss constraints. This maintains hydraulic consistency in the network for critical demands and provides network design in a single iteration. Initially, the path concept is used to decide flow directions in various links and also for assuming flow distribution for fuzzy demands. Fuzzy nodal pressure head constraints for the assumed flow distribution are converted to crisp constraints. The proposed method is applied to an example network taken from the literature and the results are compared with those obtained by Xu and Goulter. The modified linear programming model avoids iterative procedure and also provides a cheaper solution.