Models for Capacity Planning of Water Systems

Several models are reported in the technical literature for deciding the optimal capacity of water systems. Many require use of numerical techniques and the computer for solution. Simple approximating equations are presented for calculating the optimal design periods of two models particularly relevant to sanitary engineering; one pertains to capacity expansions and the other to initial construction where facilities have not yet been built. The principal contribution of this paper is a model for determining the optimal waiting period prior to constructing new systems; an approximating equation is presented for the optimality conditions to avoid use of numerical methods. Model assumptions are appropriate for both economically advanced and developing countries. The penalty cost of not satisfying demands is shown to be a key model parameter; a method is presented for inputting its value. Numerical examples are included.