COST ESTIMATES FROM STOCHASTIC GEOMETRIC PROGRAMS

Geometric programming was initially developed for solving certain nonlinear optimization problems in engineering design and has since been cited for its design-oriented insights. More recently, geometric programming has been recognized as a mathematical tool for estimating and bounding the costs of engineering design projects characterized by stochastic parameters. Heretofore, these estimating and bounding techniques have been applicable only to design problems with posynomial-type formulations.; This dissertation extends the cost estimating theories of earlier writers to stochastic optimization problems of signomial form with both positive and negative term coefficients. The results indicate that optimal-design cost tends to be described by a normal or log-normal probability distribution depending on the insight available to the designer. Estimates of the statistical moments of optimal cost are also possible. As illustration, the civil engineering design of a diaphragm-cell cofferdam is considered under stochastic conditions. Cost estimates of the optimal design are obtained from statistical descriptions of (1) the unit costs of a cofferdam's two principal components: sheet piling and fill; and (2) the anticipated damage cost should overtopping occur.