An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem

Abstract

This paper presents an algorithm using sensitivity analysis to solve a linear two-stage optimization problem. The underlying theory rests on a set of first order optimality conditions that parallel the Kuhn-Tucker conditions associated with a one-dimensional parametric linear program. The solution to the original problem is uncovered by systematically varying the parameter over the unit interval and solving the corresponding linear program. Finite convergence is established under nondegenerate assumptions. The paper also discusses other solution techniques including branch and bound and vertex enumeration and gives an example highlighting their computational and storage requirements. By these measures, the algorithm presented here has an overall advantage. Finally, a comparison is drawn between bicriteria and bilevel programming, and underscored by way of an example.