Skip to main content
Log in

Negative data in DEA: a directional distance approach applied to bank branches

  • Theoretical Paper
  • Published:
Journal of the Operational Research Society

Abstract

This paper is drawn from the use of data envelopment analysis (DEA) in helping a Portuguese bank to manage the performance of its branches. The bank wanted to set targets for the branches on such variables as growth in number of clients, growth in funds deposited and so on. Such variables can take positive and negative values but apart from some exceptions, traditional DEA models have hitherto been restricted to non-negative data. We report on the development of a model to handle unrestricted data in a DEA framework and illustrate the use of this model on data from the bank concerned.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3

Similar content being viewed by others

References

  • Farrell MJ (1957). The measurement of productive efficiency. J R Stat Soc Ser A 120: 253–281.

    Article  Google Scholar 

  • Charnes A, Cooper WW and Rhodes E (1978). Measuring efficiency of decision making units. Eur J Opl Res 2: 429–444.

    Article  Google Scholar 

  • Drake L and Howcroft B (1995). Measuring the relative efficiency of the selling function: an application of data envelopment analysis to UK bank branches. Working Paper No. 89/95, Loughborough University Banking Centre, UK.

  • Howcroft JB and Beckett A (1993). Change in the UK bank branch networks: a customer perspective. Service Ind J 13: 267–288.

    Article  Google Scholar 

  • Howcroft JB (1992). Contemporary issues in UK bank delivery systems. Int J Service Ind M 3(1): 39–56.

    Article  Google Scholar 

  • Howland A (2000). The evolution of the bank branch. Canadian Banker 6: 25–29.

    Google Scholar 

  • Cook WD, Hababou M and Tuenter HJH (2000). Multicomponent efficiency measurement and shared inputs in data envelopment analysis: an application to sales and service performance in bank branches. J Prod Anal 14: 209–224.

    Article  Google Scholar 

  • Cook WD and Hababou M (2001). Sales performance measurement in bank branches. Omega Int J Mngt Sci 29: 299–307.

    Article  Google Scholar 

  • Pastor JT (1994). How to discount environmental effects in DEA: an application to bank branches. Working Paper No. 011/94, Depto. De Estadistica e Investigacion Operativa, Universidad de Alicante, Spain.

  • Lovell CAK (1995). Measuring the macroeconomic performance of the Taiwanese economy. Int J Prod Econ 39: 165–178.

    Article  Google Scholar 

  • Seiford ML and Zhu J (2002). Modeling undesirable factors in efficiency evaluation. Eur J Opl Res 142: 16–20.

    Article  Google Scholar 

  • Charnes A et al (1985). Foundations of data envelopment analysis for Pareto–Koopmans efficient empirical production functions. J Econ 30: 91–107.

    Article  Google Scholar 

  • Ali AI and Seiford LM (1990). Translation invariance in data envelopment analysis. Opns Res Lett 9: 403–405.

    Article  Google Scholar 

  • Lovell CAK and Pastor JT (1995). Units invariant and translation invariant DEA models. Opns Res Lett 18: 147–151.

    Article  Google Scholar 

  • Pastor JT (1996). Translation invariance in data envelopment analysis: a generalisation. Ann Opns Res 66: 93–102.

    Article  Google Scholar 

  • Thrall RM (1996). The lack of invariance of optimal dual solutions under translation. Ann Opns Res 66: 103–108.

    Article  Google Scholar 

  • Banker RD, Charnes A and Cooper WW (1984). Source models for estimating technical and scale inefficiencies in data envelopment analysis. Mngt Sci 30: 1078–1092.

    Article  Google Scholar 

  • Chambers RG, Chung Y and Färe R (1996). Benefit and distance functions. J Econ Theory 70: 407–419.

    Article  Google Scholar 

  • Chambers RG, Chung Y and Färe R (1998). Profit, directional distance functions, and Nerlovian efficiency. J Optim Theory Appl 98: 351–364.

    Article  Google Scholar 

  • Coelli T (1998). A multi-stage methodology for the solution of orientated DEA models. Opns Res Lett 23: 143–149.

    Article  Google Scholar 

  • Frei FX and Harker PT (1999). Projections onto efficient frontiers: theoretical and computational extensions to DEA. J Prod Anal 11: 275–300.

    Article  Google Scholar 

  • Cherchye L and van Puyenbroeck T (2001). A comment on multi-stage DEA methodology. Opns Res Lett 28: 93–98.

    Article  Google Scholar 

  • Portela MCS, Borges P and Thanassoulis E (2003). Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies. J Prod Anal 19(2/3): 251–269.

    Article  Google Scholar 

  • Krivonozhko VE, Utkin OB, Volodin AV and Sablin IA (2001). Application of DEA approach to production units with some negative outputs. Paper Presented at OR43, University of Bath, UK, 4–6 September.

  • Färe R, Grosskopf S and Lovell AK (1994). Production Frontiers. Cambridge University Press: Cambridge, UK.

    Google Scholar 

  • Chen Y and Ali AI (2002). Output–input ratio analysis and DEA frontier. Eur J Opl Res 142: 476–479.

    Article  Google Scholar 

  • Allen K (1999). Dea in the ecological context — an overview. In: Westermann G (ed). Data Envelopment Analysis in the Service Sector. Gabler Edition Wissenschaft: Harzer, pp 203–235.

    Chapter  Google Scholar 

  • Dyckhoff H and Allen K (2001). Measuring ecological efficiency with data envelopment analysis. Eur J Opl Res 132: 312–325.

    Article  Google Scholar 

  • Chung Y, Färe R and Grosskopf S (1997). Productivity and undesirable outputs: a directional distance function approach. J Environ Mngt 51: 229–240.

    Article  Google Scholar 

  • Thanassoulis E (2001). Introduction to the Theory and Application of Data Envelopment Analysis: A Foundation Text with Intefrated Software. Kluwer Academic Publishers: Dordrecht.

    Book  Google Scholar 

  • Cooper WW, Park KS and Pastor JT (1999). RAM: a range measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J Prod Anal 11: 5–42.

    Article  Google Scholar 

  • Bogetoft P and Hougaard JL (1998). Efficiency evaluations based on potential (non-proportional) improvements. J Prod Anal 12: 233–247.

    Article  Google Scholar 

  • Asmild M, Hougaard JL, Kronborg D and Kvist HK (2003). Measuring inefficiency via potential improvements. J Prod Anal 19: 59–76.

    Article  Google Scholar 

  • Ali AI and Seiford LM (1993). The mathematical programming approach to efficiency analysis. In: Fried HO, Knox Lovell CA and Schmidt SS (eds). The Measurement of Production Efficiency: Techniques and Applications. Oxford University Press, New York, Oxford, pp 120–159.

    Google Scholar 

  • Cherchye L and van Puyenbroeck T (1999). Learning from input–output mixes in DEA: a proportional measure for slack-based efficient projections. Managerial Decis Econ 20: 151–161.

    Article  Google Scholar 

  • Cherchye L and van Puyenbroeck T (1999). Non-radial efficiency and semi-radial efficiency. In: Westermann G (ed). Data envelopment Analysis in the Service Sector. Gabler Edition Wissenschaft: Harzer, pp 51–64.

    Chapter  Google Scholar 

  • Charnes A, Haag S, Jaska P and Semple J (1992). Sensitivity of efficiency classifications in the additive model of data envelopment analysis. Int J Systems Sci 23: 789–798.

    Article  Google Scholar 

  • Briec W (1998). Hölder distance function and measurement of technical efficiency. J Prod Anal 11: 111–131.

    Article  Google Scholar 

  • Athanassopoulos AD, Soteriou AC and Zenios SA (2000). Disentangling within- and between-country efficiency differences of bank branches. In: Harker PT and Zenios SA (eds). Performance of Financial Institutions; Efficiency. Innovation and Regulation. Cambridge University Press, Cambridge, UK, pp 336–363.

    Google Scholar 

  • Golany B and Storbeck JE (1999). A data envelopment analysis of the operational efficiency of bank branches. Interfaces 29(3): 14–26.

    Article  Google Scholar 

  • Berger AN and Humphrey DB (1997). Efficiency of financial institutions: international survey and directions for future research. Eur J Opl Res 98: 175–212.

    Article  Google Scholar 

  • Banker RD and Morey RC (1986). Efficiency analysis for exogenously fixed inputs and outputs. Opns Res 34: 513–520.

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge the financial support of the Portuguese Foundation for Science and Technology, and the European Social Fund. The contents of the paper are the responsibility of the authors.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M C A Silva Portela.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Portela, M., Thanassoulis, E. & Simpson, G. Negative data in DEA: a directional distance approach applied to bank branches. J Oper Res Soc 55, 1111–1121 (2004). https://doi.org/10.1057/palgrave.jors.2601768

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/palgrave.jors.2601768

Keywords

Navigation