A Semi-Infinite Programming Model In Data Envelopment Analysis

Abstract

Abstract We consider a model for data envelopment analysis with infinitely many decision-making units. The determination of the relative efficiency of a given decision-making unit amounts to the solution of a semi-infinite optimization problem. We show that a decision-making unit of maximal relative efficiency exists and that it is 100% efficient. Moreover, this decision-making unit can be found by calculating a zero of the semi-infinite constraint function. For the latter task we propose a bi-level algorithm. We apply this algorithm to a problem from chemical engineering and present numerical results Keywords: Data Envelopment AnalysisMulti-Objective ProgrammingSemi-Infinite ProgrammingBi-Level OptimizationChemical EngineeringPareto Efficiency ∗Corresponding author Supported in part by Alexander von Humboldt-Stiftung and by US-Air Force Office of Scientific Research under grant F49620-98-1-0329 ∗Corresponding author Supported in part by Alexander von Humboldt-Stiftung and by US-Air Force Office of Scientific Research under grant F49620-98-1-0329 Notes ∗Corresponding author Supported in part by Alexander von Humboldt-Stiftung and by US-Air Force Office of Scientific Research under grant F49620-98-1-0329