Capital Cost Minimization of Drainage Networks

This paper presents and compares three mathematical programming models for the optimization of drainage networks. The three models are based on two extensions of linear programming: separable-convex and mixed- integer programming. The first produces a continuous range of diameters while the second limits the solution to discrete commercially available sizes. It is shown that while the first can be formulated with pipes flowing full, the second must allow for partial flow. A solution which combines the use of both of these techniques can produce a minimum cost system with partially-full flows and commercially available diameters. This solution requires less computer time than those based strictly on mixed-integer programming. An example seven-link drainage network is designed by the three proposed methods and the results are reported in the paper.