A robust optimization approach to overall profit efficiency with data uncertainty: application on bank industry

Abstract

ABSTRACTIn this paper, we consider a framework of data envelopment analysis (DEA) to measure the overall profit efficiency of decision-making units (DMUs) subject to inputs and outputs uncertainty. Under uncertain conditions, classic methods can lead to unrealistic solutions in practice. In this work, robust optimization is proposed to incorporate uncertainty into measuring the overall profit efficiency. In a robust optimization model, it is supposed that uncertain parameters belong to a specified set with a solution that is efficient for all possible uncertainty outcomes while it is not optimal for a given value of the parameters. We show that the overall profit efficiency score may not always occur in an optimistic case and the decision maker can obtain the overall profit efficiency score corresponding to a value in the uncertainty set. The results of the experiment on bank data show that a robust overall profit efficiency score provides a significant improvement in the performance, as the uncertainty increases.Abbreviations: DEA: data envelopment analysis; DMUs: decision-making units; CRS: constant returns to scale; VRS: variable returns to scale; ROP: robust optimization problem; RC: robust counterpart; ROPE: robust overall profit efficiency; OOPE: optimistic overall profit efficiency; GAMS: generalized algebraic modeling system