A Mathematical Programming Approach to Public Water Project Portfolio Selection

Abstract

MATHEMATICAL programming techniques were used in this dissertation to develop and test a public water resources project selection model. Selection and scheduling of annual portfolios of projects were accomplished of the projects which the Tennessee Valley Authority (TVA) had considered during the 1965-1973 planning period. Discounted benefit and cost flow concepts were utilized in quantifying the models which utilized linear programming (LP), integer programming (IP), and integer goal programming (GP) techniques.The programming approaches were compared to the present approach-individual project selection based on maximum benefit-cost ratio (BCR). The LP and IP portfolio solutions differed from the BCR solution due to the complexity of the water resources problem considered and because of the inadequacy of the BCR as a criterion. And IP was deemed superior to LP because the large number of fractional projects rendered the LP solution of little practical value.Long-term budget level determination was facilitated through analysis of LP dual variables and by using parametric (LP) programming. The IP technique was not suited to this problem because of the near-meaningless dual variables (IP), and because the IP technique consumes too much computational time for the parametric programming problem.Individual project scheduling techniques were developed by analyzing the dual variables of the LP solution. The dual variable represents the marginal cost of not including the particular project during a certain year. The LP dual variables were also analyzed with regard to political or social factors which caused the forced acceptance of a particular project. The effects on the optimum net present value (NPV) gave guidance as to the better year to implement the forced projects.Multiple objectives-economic (national and regional) and environmental improvement-were incorporated into the IP model by use of the GP approach. It was found especially important to use IP instead of LP because the LP-GP projects were found to be extremely fractional in portfolio acceptance. The GP approach involves "satisficing" the several goals rather than maximizing (or minimizing) one goal. The objectives were quantified in both monetary and physical terms, i.e., river miles lost, shoreline gained, area inundated, kilowatts gained, etc. Because more than one goal was formally considered, this represented a significant advance for quantitative decision making of water resources problems.The results of two programming approaches, IP maximizing NPV and GP, were then compared to the TVA result in terms of project selection and scheduling, portfolio NPV attained, and degree of goal attainment. The following is an example of the differing results: * A dissertation completed at the University of Georgia in 1973. 1593

A portfolio approach to public water project decision making

“…Such factors would include certain political and environmental constraints. These additional considerations could be especially appropriate incorporated in a goal programing portfolio approach [Neely, 1974].…”

“…The case study [Neely, 1974] applying the portfolio approach consisted of 33 projects and subprojects which were considered by the TVA between 1965 and 1974. The benefit s and costs were unadjusted TVA data.…”

“…The set of LP dual variables corresponding to the budget set is interpreted as the increase in the objective function, NPV, which results from a unitary increase in each annual budget value. Therefore the budget corresponding to the year with a relatively low dual variable should be shifted to a year with a higher dual variable to increase NPV [Neely, 1974]. The IP dual variables corresponding to each project/year are not interpreted in the same manner as the LP dual variables.…”

Planning and Selecting Multiobjective Projects by Goal Programming1

“…Budget planning can ,be enhanced using LP (Neely 1974) and GP techniques. The budgetary constraints (2) and (3) can be stated as goals instead of constraints (Lee and Lerro 1974).…”

“…With the many quantitative inputs necessary t o make the separate economic, environmental and political subdecisions, independently, the final decision is often quite subjective and often confused or delayed. The results have been shown to provide neither an appropriate mix nor to maximize either environmental or economic objectives (Neely 1974). A planning approach which recognizes a simultaneous solution for obtaining multiple objectives is essential to achieve some better level of efficiency in project planning and construction.…”