Rights statement: This is the peer reviewed version of the following article: Ehrgott, M, Hasannasab, M, Raith, A. A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis. J Multi‐Crit Decis Anal. 2019; 26: 187– 198. https://doi.org/10.1002/mcda.1684 which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1002/mcda.1684 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis
AU - Ehrgott, M.
AU - Hasannasab, M.
AU - Raith, A.
N1 - This is the peer reviewed version of the following article: Ehrgott, M, Hasannasab, M, Raith, A. A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis. J Multi‐Crit Decis Anal. 2019; 26: 187– 198. https://doi.org/10.1002/mcda.1684 which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1002/mcda.1684 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
PY - 2019/8/28
Y1 - 2019/8/28
N2 - 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.
AB - 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.
KW - data envelopment analysis
KW - duality
KW - efficient frontier
KW - linear programming
KW - multiobjective optimization
KW - objective space algorithm
U2 - 10.1002/mcda.1684
DO - 10.1002/mcda.1684
M3 - Journal article
VL - 26
SP - 187
EP - 198
JO - Journal of Multi-Criteria Decision Analysis
JF - Journal of Multi-Criteria Decision Analysis
SN - 1057-9214
IS - 3-4
ER -