Abstract
This paper presents the adjusted spherical frontier model (ASFM), a parametric data envelopment analysis (DEA) model for input allocation. Following a common principle from other solutions found in the literature, ASFM considers that the process of allocating the new input is fair if it ends in such a way that all decision-making units will become DEA-CCR efficient. ASFM's main assumption is the spherical shape of the efficiency frontier. It is because of that assumption that ASFM is called a parametric DEA model. Numeric examples are presented showing that, within the context of sensitivity analysis, ASFM reaches more coherent results than other models found in the literature. This numeric evidence leads to a theorem which formally states this more coherent behaviour. The proof of this theorem is included in this paper.
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References
Asmild M, Paradi JC and Pastor JT (2009). Centralized resource allocation BCC models. Omega 37: 40–49.
Avellar JVG, Milioni AZ and Rabello TN (2007). Spherical frontier DEA model based on a constant sum of inputs. J Opl Res Soc 58: 1246–1251.
Banker RD, Charnes A and Cooper WW (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Mngt Sci 30: 1078–1092.
Beasley JE (2003). Allocating fixed costs and resources via data envelopment analysis. Eur J Opl Res 147: 198–216.
Charnes A and Cooper WW (1985). Preface to topics in data envelopment analysis. Ann Opns Res 2: 59–94.
Charnes A, Cooper WW and Rhodes E (1978). Measuring the efficiency of decision making units. Eur J Opl Res 2: 429–444.
Cook WD and Kress M (1999). Characterizing an equitable allocation of shared costs: A DEA approach. Eur J Opl Res 119: 652–661.
Cook WD and Zhu J (2005). Allocation of shared costs among decision making units: A DEA approach. Comput Opns Res 32: 2171–2178.
Cooper W, Seiford LM and Tone K (2000). Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. Kluwer Academic: Boston.
EMS 1.3 (2007). Efficiency measurement system DEA software. available at http://www.wiso.uni-dortmund.de/lsfg/or/scheel/ems/, accessed 15 March.
Estellita Lins MP, Gomes EG, Soares de Mello JCCB and Soares de Mello AJR (2003). Olympic ranking based on a zero sum gains DEA model. Eur J Opl Res 148: 312–322.
Farrell MJ and Fieldhouse M (1962). Estimating efficient production functions under increasing returns to scale. JR Stat Soc 120: 252–267.
Freitas GM (2008). Estudo da variação dos produtos como conseqüência da inclusão ou alteração de insumos em DEA. Master's Thesis, Instituto Tecnológico de Aeronáutica.
Gomes EG and Estellita Lins MP (2008). Modelling undesirable outputs with zero sum gains data envelopment analysis. J Opl Res Soc 59: 616–623.
Korhonen P and Syrjänen M (2004). Resource allocation based on efficiency analysis. Mngt Sci 50 (8): 1134–1144.
Lozano SA and Villa G (2004). Centralized resource allocation using data envelopment analysis. J Prod Anal 22: 143–161.
Lozano SA and Villa G (2005). Centralized DEA models with the possibility of downsizing. J Opl Res Soc 56 (4): 357–364.
Lozano SA, Villa G and Adenso-Diaz B (2004). Centralised target setting for regional recycling operations using DEA. Omega 32: 101–110.
Milioni AZ and Silva RC (2010). Parametric DEA models with weight constraints. Annals of EURO 2010, Lisbon, Portugal, p 69.
Milioni AZ, Freitas GM and Avellar JVG (2008). Fairly sharing a new total fixed input variable with parametric DEA. Annals of IFORS, Johannesburg, South Africa, p 67.
Milioni AZ, Avellar JVG, Gomes EG and Soares-de-Mello JCCB (2011). An ellipsoidal frontier model: Allocating input via parametric DEA. Eur J Opl Res Soc 209: 113–121.
Takeda E (2000). An extended DEA model: Appending an additional input to make all DMUs at least weakly efficient. Eur J Opl Res 125: 25–33.
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Guedes, E., Milioni, A., de Avellar, J. et al. Adjusted spherical frontier model: allocating input via parametric DEA. J Oper Res Soc 63, 406–417 (2012). https://doi.org/10.1057/jors.2011.42
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DOI: https://doi.org/10.1057/jors.2011.42