APPLICATION OF MATHEMATICAL PROGRAMMING FOR OPTIMAL INVESTMENT, WATER SUPPLY AND PRICING DECISIONS FOR RURAL WATER SYSTEMS IN OKLAHOMA

Scope and Method of Study. The purpose of this research was to provide information for the planning and management of rural water systems in Oklahoma. The objective was to demonstrate an improved planning model by incorporating intertemporal and attitudinal correlates with decisions on rural water supply investments. This was accomplished by first reviewing theory on demand and supply of public goods. Second, the economics of water demand and supply were analyzed. Empirical results are presented for aggregate water demand by rural system. Investment and operation and maintenance cost functions were estimated for a sample of systems. Growth in terms of the number of water tap connections was estimated over a 16 year period. Third, a mathematical programming model (mixed integer) was developed and applied for determining optimum timing and size of investment and optimum pricing of water. The parameters estimated in the water demand and supply functions were used in the model as decision criteria. Fourth, the model results were analyzed under varying conditions of system growth, discount rate and size of system.;Findings and Conclusions. Rural water systems have characteristics of public goods--all who wish to connect must be considered. Consumers of rural water services in Oklahoma are price sensitive--the estimated price elasticity of demand is -0.58. Water supply shows significant economies of scale in both investment and operation and maintenance costs. Under conditions of marginal cost pricing, these findings show close interrelationships among water price, consumption and supply. Rural water systems in Oklahoma have grown at an average annual rate of eight percent. Thus, growth of water systems together with economies of scale in water supply support the proposition that excess capacity should be considered in optimal capacity design. Substantial increased benefits are shown for optimal model results relative to actual results. Based upon the findings of this study the following decision criteria are proposed: (1) price-sensitive consumer behavior should be considered in decisions of capacity design and price, (2) existence of economies of scale in water supply are important for capacity design, (3) predictions of growth are highly important in planning optimal capacity, and (4) these criteria should be considered simultaneously in making global optimal water supply decisions.