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A semi-infinite programming model in data envelopment analysis

Andreas Jess, Hubertus Th. Jongen, Luka Neralic and Oliver Stein

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.

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