A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

Ehrgott, M. and Hasannasab, M. and Raith, A. (2019) A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis. Journal of Multi-Criteria Decision Analysis, 26 (3-4). pp. 187-198. ISSN 1057-9214

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Abstract

Data envelopment analysis is a linear programming-based operations research technique for performance measurement of decision-making units. In this paper, we investigate data envelopment analysis from a multiobjective point of view to compute both the efficient extreme points and the efficient facets of the technology set simultaneously. We introduce a dual multiobjective linear programming formulation of data envelopment analysis in terms of input and output prices and propose a procedure based on objective space algorithms for multiobjective linear programmes to compute the efficient frontier. We show that using our algorithm, the efficient extreme points and facets of the technology set can be computed without solving any optimization problems. We conduct computational experiments to demonstrate that the algorithm can compute the efficient frontier within seconds to a few minutes of computation time for real-world data envelopment analysis instances. For large-scale artificial data sets, our algorithm is faster than computing the efficiency scores of all decision-making units via linear programming.