This paper is concerned with the optimal dimensioning problem in which the layoutof a pipe network is given but several available diameters can be selected for each pipe. The purpose is to minimize total cost while satisfying certain restrictions. A new method is proposed, the main features of which are to treat the problem as a bilevel programming problem, then to simplify the lower level problem by conjugate duality theory and to handle the upper level problem by its piecewise linear and convex nature. Some numerical testing results are also presented.
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Zhang et al. (1996) studied this question.
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