Uncertainty exists in the estimates of benefits and costs for any proposed water resource project. An approach is presented for the treatment of this uncertainty and its incorporation into the benefit-cost ratio. The method is based on subjective estimates of "most likely," "upper," and "lower" values for individual components of benefits and costs and estimates of the correlation coefficients between these components. The method is approximate but has the advantage of not requiring a computer for its application. The main errors introduced by the approach are analyzed and are shown to be relatively small. Finally, a case study is presented to demonstrate application of the method.
INTRODUCTIONThe benefit-cost ratio is a commonly used economic criterion for the comparison of alternative water resource projects [James and Lee, 1971]. Clearly, the economic benefits and costs of any proposed water resource project cannot be predicted with total precision due to a number of factors, including the following: (1) the randomness in hydrologic processes such as rainfall, runoff, and evaporation (these affect the crop yields due to irrigation, flood control benefits, etc.); (2) the uncertainty in future population growth, which affects the estimated benefits due to water supply, recreation, and flood control; (3) uncertainty in the community demand functions for water supply and recreation; (4) limited data records; (5) uncertainty in engineering cost estimates due to variations in foundation conditions, delays in construction, and variable productivity.As is noted by Goicoechea et al. [1982b], the U.S. Water Resources Council has produced a project evaluation procedure [U.S. Water Resources Council, 1979] to assist in the analysis of risk and uncertainty in water resources planning. As yet, no complete methodology exists for treating this problem.Goicoechea et al. [1982b] have highlighted some of the issues associated with this area by identifying sources of risk and uncertainty in water resources planning and by outlining a probabilistic approach to benefit-cost analysis. The Goicoechea et al. approach involves identifying a probability distribution for each benefit and cost component of the project. These distributions will usually be subjective and will be based on "expected," "optimistic," and "pessimistic" estimates of the relevant value. It is further assumed that all components are statistically independent, an assumption which is questioned by Goldman [19833. If the individual components are normally distributed, an analytical expression can be derived for the resulting benefit-cost ratio. Another expression applies if the underlying benefit and cost components all have gamma distributions.
One practical difficulty in using the Giocoechea et al.[198263 procedure is the need to use computer programs to compute the cumulative distributions of the benefit-cost ratio. This is required for numerical integration (in the case of normally distributed benefits and costs) or evaluation of the gamma function (if all benefi...