Water Distribution System Design under Uncertainties

A chance constrained model is presented for the minimum cost design of water distribution networks. This methodology attempts to account for the uncertainties in required demands, required pressure heads, and pipe roughness coefficients. The optimization problem is formulated as a nonlinear progmmmhg model which is solved using a generalized reduced gradient method. Details of the mathematical model formulation are presented along with example applications. Results illustrate that uncertainties in future demands, pressure head requirements, and pipe roughness can have significant effects on the optimd network design and cost. There is currently no universally accepted definition or measure of the reliability of water distribution systems. In general, reliability is defined as the probability that a system performs its mission within specified limits for a given period of time in a specified environment. Over the past two decades, there have been many models developed for the analysis and the minimum cost design of water distribution networks (e.g., Alperovit~ and Shamir 1977; Quindry et al. 1981; Morgan and Goulter 1986; Lansey and Mays 1987). Only a very few models have been reported that attempt to consider the reliability of the water distribution network and the various components. Coals and Goulter (1985) presented three approaches by which the probability of failure of individual pipes can be related to a measure of the overall system reliability in a linear programming minimum cost design procedure. No models explicitly consider the uncertainties in demands, pressure heads, and pipe roughness. The real issue of water distribution system reliability concems the ability of the system to supply the demands at the nodes or demand points within the system at required minimum pressures. The conventional design process for water distribution systems is a trial and emor procedure that attempts to fmd a design that represents a least-cost solution that can satisfy demands. These trial and error methods make no attempt to analyze or define any reliability aspects of the designed system and have no guarantee that the Asst. Prof., School of Civ. Engrg., Oklahoma State Univ., Stillwater, OK 74078; fol;merly, Res. Asst., Dept. of Civ. Engrg., The Univ. of Texas, Austin, TX 78712. Res. Engr., Chinese Res. Acad. of Envir. Sci., Beijing, Peoples Republic of China; formerly Res. Asst., Center for Res. in Water Resow., The Univ. of Texas, Austin, Tx. Dir., Center for Res. in Water Resow. and Engrg., Foundation Endowed Prof., Dept. of Civ. Engrg., The Univ. of Texas, Austin, TX. 4 A ~ ~ ~ ~ . Prof., Dept. of Statistics, and Wyoming Water Res. Center, Univ. of Wyoming, Laramie, WY 82071. Note. Discussion open until February 1, 1990. To extend the closing date one month, a written request must be fded with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on October 27, 1987. This paper is part of the Journal of Water Resources Phnning and Management, Vol. 115, No. 5, September, 1989. BASCE, ISSN 0733-9496/89/ OOO5-0630/$1 .OO + $. 15 per page. Paper No. 23875. I