Abstract
Data Envelopment Analysis (DEA) is a well-known methodology for estimating technical efficiency from a set of inputs and outputs of Decision Making Units (DMUs). This paper is devoted to computational aspects of DEA models when the determination of the least distance to the Pareto-efficient frontier is the goal. Commonly, these models have been addressed in the literature by applying unsatisfactory techniques, based essentially on combinatorial NP-hard problems. Recently, some heuristics have been introduced to solve these situations. This work improves on previous heuristics for the generation of valid solutions. More valid solutions are generated and with lower execution time. A parameterized scheme of metaheuristics is developed to improve the solutions obtained through heuristics. A hyper-heuristic is used over the parameterized scheme. The hyper-heuristic searches in a space of metaheuristics and generates metaheuristics that provide solutions close to the optimum. The method is competitive versus exact methods, and has a lower execution time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aigner DJ, Chu SF (1968) On estimating the industry production function. Am Econ Rev 58:826–839
Aigner DJ, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econ 6:21–37
Almeida F, Giménez D, López-EspÃn JJ, Pérez-Pérez M (2013a) Parameterized schemes of metaheuristics: basic ideas and applications with genetic algorithms, scatter search and GRASP. IEEE Trans Syst Man Cybern 43(3):570–586
Almeida F, Giménez D, López-EspÃn JJ (2013b) A parameterized shared-memory scheme for parameterized metaheuristics. J Supercomput 58(3):292–301
Amirteimoori A, Kordrostami S (2010) A Euclidean distance-based measure of efficiency in data envelopment analysis. Optimization 59:985–996
Ando K, Kai A, Maeda Y, Sekitani K (2012) Least distance based inefficiency measures on the Pareto-efficient frontier in DEA. J Oper Res Soc Jpn 55(1):73–91
Aparicio J, Pastor JT (2013) A well-defined efficiency measure for dealing with closest targets in DEA. Appl Math Comput 219:9142–9154
Aparicio J, Pastor JT (2014a) On how to properly calculate the Euclidean distance-based measure in DEA. Optimization 63(3):421–432
Aparicio J, Pastor JT (2014b) Closest targets and strong monotonicity on the strongly efficient frontier in DEA. Omega 44:51–57
Aparicio J, Ruiz JL, Sirvent I (2007) Closest targets and minimum distance to the Pareto-efficient frontier in DEA. J Prod Anal 28:209–218
Aparicio J, Mahlberg B, Pastor JT, Sahoo BK (2014a) Decomposing technical inefficiency using the principle of least action. Eur J Oper Res 239:776–785
Aparicio J, Borras F, Ortiz L, Pastor JT (2014b) Benchmarking in healthcare: an approach based on closest targets. In: Emrouznejad A, Cabanda E (ed) Managing service productivity. International series in operations research & management science, vol 215, Springer, Berlin, pp 67–91
Baek C, Lee J (2009) The relevance of DEA benchmarking information and the least-distance measure. Math Comput Model 49:265–275
Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage Sci 30:1078–1092
Benavente C, López-EspÃn JJ, Aparicio J, Pastor JT, Giménez D (2014) Closets targets, benchmarking and data envelopment analysis: a heuristic algorithm to obtain valid solutions for the shortest projection problem. In: 11th international conference on applied computing
Briec W (1997) Minimum distance to the complement of a convex set: duality result. J Optim Theory Appl 93(2):301–319
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444
Charnes A, Cooper WW, Golany B, Seiford L, Stutz J (1985) Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J Econ 30:91–107
Cherchye L, Van Puyenbroeck T (2001) A comment on multi-stage DEA methodology. Oper Res Lett 28:93–98
Cobb CW, Douglas PH (1928) A theory of production, vol 18, issue 1. In: The American economic review, supplement, papers and proceedings of the fortieth annual meeting of the American economic association, pp 139–165
Cooper WW, Park KS, Pastor JT (1999) RAM: a range adjusted measure of inefficiency for use with additive models, and relations to others models and measures in DEA. J Prod Anal 11:5–42
Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer Nijhoff Publishing, Boston
Farrel MJ (1957) The measurement of productive efficiency. J Roy Stat Soc Ser A (General) 120(3):253–290
Frei FX, Harker PT (1999) Projections onto efficient frontiers: theoretical and computational extensions to DEA. J Prod Anal 11:275–300
Fukuyama H, Maeda Y, Sekitani K, Shi J (2014a) Input-output substitutability and strongly monotonic p-norm least-distance DEA measures. Eur J Oper Res 237:997–1007
Fukuyama H, Masaki H, Sekitani K, Shi J (2014b) Distance optimization approach to ratio-form efficiency measures in data envelopment analysis. J Prod Anal 42:175–186
Fukuyama H, Hougaard JL, Sekitani K, Shi J (2016) Efficiency measurement with a nonconvex free disposal hull technology. J Oper Res Soc (in press)
González E, Alvarez A (2001) From efficiency measurement to efficiency improvement: the choice of a relevant benchmark. Eur J Oper Res 133:512–520
González M, López-EspÃn JJ, Aparicio J, Giménez D, Pastor JT (2015) Using genetic algorithms for maximizing technical efficiency in data envelopment analysis. Procedia Comput Sci 51(2015):374–383
González M, López-EspÃn JJ, Aparicio J, Gimenéz D (2016) Implementing the principle of least action in data envelopment analysis: a parameterized scheme of metaheuristics. Working Paper, University Miguel Hernandez of Elche
Jahanshahloo GR, Hosseinzadeh Lotfi F, Zohrehbandian M (2005) Finding the piecewise linear frontier production function in data envelopment analysis. Appl Math Comput 163:483–488
Jahanshahloo GR, Lotfi FH, Rezai HZ, Balf FR (2007) Finding strong defining hyperplanes of production possibility set. Eur J Oper Res 177:42–54
Jahanshahloo GR, Vakili J, Mirdehghan SM (2012) Using the minimum distance of DMUs from the frontier of the PPS for evaluating group performance of DMUs in DEA. Asia-Pac J Oper Res 29(2):1250010
Koopmans TC (1951) Analysis of production as an efficient combination of activities. In: Koopmans TC (ed) Activity analysis of production and allocation. John Wiley, New York
López-EspÃn JJ, Aparicio J, Giménez D, Pastor JT (2014) Benchmarking and data envelopment analysis. An approach based on metaheuristics. Procedia Comput Sci 29:390–399
Lozano S, Villa G (2005) Determining a sequence of targets in DEA. J Oper Res Soc 56:1439–1447
Meeusen W, van den Broeck J (1977) Efficiency estimation from Cobb-Douglas production functions with composed error. Int Econ Rev 18:435–444
Pastor JT, Aparicio J (2010) The relevance of DEA benchmarking information and the least-distance measure: comment. Math Comput Model 52:397–399
Pastor JT, Ruiz JL, Sirvent I (1999) An enhanced DEA Russell graph efficiency measure. Eur J Oper Res 115:596–607
Portela MCS, Borges PC, Thanassoulis E (2003) Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies. J Prod Anal 19:251–269
Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130:498–509
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this chapter
Cite this chapter
Aparicio, J., Gonzalez, M., Lopez-Espin, J.J., Pastor, J.T. (2016). A Parameterized Scheme of Metaheuristics to Solve NP-Hard Problems in Data Envelopment Analysis. In: Aparicio, J., Lovell, C., Pastor, J. (eds) Advances in Efficiency and Productivity. International Series in Operations Research & Management Science, vol 249. Springer, Cham. https://doi.org/10.1007/978-3-319-48461-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-48461-7_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48459-4
Online ISBN: 978-3-319-48461-7
eBook Packages: Economics and FinanceEconomics and Finance (R0)