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A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis
Author(s) -
Ehrgott Matthias,
Hasannasab Maryam,
Raith Andrea
Publication year - 2019
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.1684
Subject(s) - data envelopment analysis , linear programming , efficient frontier , mathematical optimization , computer science , set (abstract data type) , computation , extreme point , multi objective optimization , data set , point (geometry) , envelopment , algorithm , mathematics , artificial intelligence , portfolio , geometry , combinatorics , financial economics , economics , programming language
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.