| A model was developed to evaluate the issue of water supply sustainability. The model considers multiple project objectives using a genetic algorithm (GA) procedure. It is written in the code language Visual Basic for Applications (VBA 6.3) and operates in the environment of a Microsoft ExcelRTM workbook. The multiple project objectives incorporated in the program are: minimize water supply cost, minimize net groundwater withdrawal, and maximize water supply for growth. The decision variables, each expressed in terms of model zone (up to 10) and/or time (years), include population growth rate, reduction in residential water use rate, and water import volume. The GA employed in the code uses a strategy whereby evolutionary pressure is exerted not during parent selection, but rather by competition between offspring and their parents using the criteria of domination and possession of current global optima in one or more objective functions. The program uses single-objective GA subroutines, optimizing each objective separately, to develop a very good first trial population. The program also incorporates a cost function for the non-use value of groundwater, which was derived during this research using Hotelling's exhaustible resource theory.; The model was applied to the Prescott (Arizona) Active Management Area (AMA), where groundwater supplies are limited and currently being heavily over-utilized, and rapid population growth is projected to greatly increase water demand in the near future. Model results indicate that the factor values used in the groundwater cost function have a pronounced effect upon future decisions regarding water supply. Implicitly assuming zero as the non-use value for groundwater results in large aquifer depletion over time, while moderate to high values produce a much smaller withdrawal or even a net replenishment, with correspondingly higher reliance on imported water. The model results also indicate this in terms of higher unit growth costs ({dollar}/AF) in situations where a positive value is assigned to the cost of groundwater depletion. |
