An extended aggregated ratio analysis in DEA

Abstract

Data Envelopment Analysis (DEA) and Ratio Analysis (RA) are two widely used methods for measuring units’ productivity and any other criteria that could be assessed based on the available input and output variables. A number of researchers have studied DEA and RA and noted the positive and negative differences between them. Aggregated ratio analysis (ARA) model, which provide an important linkage between DEA and RA theory, is equivalent to the CCR DEA model, and this equivalence property offers a great deal of opportunities for DEA to be interpreted and applied in different ways. This paper extends the results of ARA model and proposes an extended aggregated ratio analysis (EARA) model, similar as the development from CCR model to BCC model in DEA context. The proposed model can offer an insight into the characteristic of returns to scale, playing the corresponding role as BCC model does. The numerical example is revisited in the paper and the results are compared.

Keywords

Data Envelopment Analysis (DEA) / aggregated ratio analysis / efficiency evaluation / returns to scale

References

[1] Ali A.I., Lerme C.S., Seiford L.M.. Components of efficiency evaluation in data envelopment analysis. European Journal of Operational Research, 1995, 80(3): 462-473.

[2] Banker R.D., Charnes A., Cooper W.W.. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 1984, 30(9): 1078-1092.

[3] Bowlin W.F.. Financial analysis of civil reserve air fleet participants using data envelopment analysis. European Journal of Operational Research, 2004, 154(3): 691-709.

[4] Charnes A., Cooper W.W., Rhodes E.. Measuring the efficiency of decision making units. European Journal of Operational Research, 1978, 2(6): 429-444.

[5] Chen W.C., McGinnis L.F.. Reconciling ratio analysis and DEA as performance assessment tools. European Journal of Operational Research, 2007, 178(1): 277-291.

[6] Chen Y., Ali A.I.. Output-input ratio analysis and DEA frontier. European Journal of Operational Research, 2002, 142(3): 476-479.

[7] Chen Y., Li K.W., Xu H.Y., Liu S.F.. A DEA-TOPSIS method for multiple criteria decision analysis in emergency management. Journal of Systems Science and Systems Engineering, 2009, 18(4): 489-507.

[8] Cronje J.J.L.. Data Envelopment Analysis as a measure for technical efficiency measurement in banking — a research framework. Southern African Business Review, 2002, 6(2): 32-41.

[9] Despić O., Despić M., Paradi J.C.. DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of Productivity Analysis, 2007, 28(1): 33-44.

[10] Emrouznejad A., Amin G.R.. DEA models for ratio data: Convexity consideration. Applied Mathematical Modeling, 2009, 33(1): 486-498.

[11] Feroz E.H., Kim S., Raab R.L.. Financial statement analysis: a data envelopment analysis approach. Journal of the Operational Research Society, 2003, 54(1): 48-58.

[12] Gonzalez-Bravo M.I.. Prior-ratio-analysis procedure to improve data envelopment analysis for performance measurement. Journal of the Operational Research Society, 2007, 58(9): 1214-1222.

[13] Hollingsworth B., Smith P.. Use of ratios in data envelopment analysis. Applied Economics Letters, 2003, 10(11): 733-735.

[14] Holló, D. & Nagy, M. (2006). Bank efficiency in the enlarged European Union. MNB working papers

[15] Thanassoulis E., Boussofiane A., Dyson R.. A comparison of data envelopment analysis and ratio analysis as tools for performance assessment. Omega, International Journal of Management Science, 1996, 24(3): 229-244.

[16] Wu D., Liang L., Huang Z.M., Li S.. Aggregated ratio analysis in DEA. International Journal of Information Technology and Decision Making, 2005, 4(3): 369-384.