The design of water distribution systems has received a great deal of attention in the last three decades because of its importance to industrial growth and its crucial role in society for community health, firefighting capability, and quality of life. The cost of installing a water distribution system is typically in the tens of millions of dollars. These systems also account for the largest costs in the municipal maintenance budgets. Furthermore, existing systems are being burdened by increasing urban development and water use. All these factors cause the pipe sizing decisions to be a critical task in designing a cost effective water distribution system that is capable of handling the demand and satisfying the minimum pressure head and hydraulic redundancy requirements.

A number of research efforts have focused on the least cost pipe sizing decision, each of them generating improved solutions for several standard test problems from literature, but so far, very little work has been done to test the quality of these solutions. In this thesis, two lower bounding schemes are proposed to evaluate the quality of these solutions. These lower bounding schemes make use of the special concave-convex nature of the nonlinear frictional loss terms. We show that the first is a dual to Eiger et al.’s [1994] bounding procedure while the second method produces far tighter lower bounds with comparable ease. Results on applying these lower bounding schemes to some standard test problems from literature are presented.

The second lower bounding scheme is then embedded in a branch-and-bound procedure along with an upper bounding scheme by suitably restricting the flows at each node of the search tree. By branching successively, we attempt to narrow the gap from optimality to generate near optimal solutions to the least cost pipe sizing problem. This results in a comprehensive reduced cost network design that satisfies all pressure and flow requirements for realistically sized problems. The proposed method is applied to standard test problems from the literature. It is hoped that this method will provide a useful tool for city engineers to design a cost effective water distribution system that meets specified hydraulic requirements.