Data ‎E‎nvelopment Analysis and Malmquist Index for Measuring Productivity of Inefficient ‎DMUs

Document Type : Research Paper

Authors

1 Department of Mathematics, Sari Branch, Islamic Azad University, Sari, ‎Iran‎

2 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, ‎Iran‎.

3 Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, ‎Iran

Abstract

Data envelopment analysis (DEA), is a non-parametric mathematical programming technique to evaluate the efficiency of a set of homogeneous decision-making units (DMUs), so that DMUs are evaluated into two groups, efficient and inefficient. According to the staggering costs in order to managing DMUs or organizations, maintaining some loss-making organizations are not cost-effective. Therefore, one of the concerns of managers in the discussion related to the financial problems of organizations is the maintenance or merger or elimination of inefficient organizations (inefficient DMUs). However, this article focuses on the performance of inefficient units. Therefore, we measure the productivity of inefficient DMUs using the revised Malmquist productivity index (MPI) to make a decision based on the maintenance or merger or elimination of these DMUs by decision makers (DMs).

Keywords


 [1] R. D. Banker, A. Charnes, W. W. Cooper, Some Methods for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis, Management Science 30 (1984) 1078-1092.
[2] S. A. Berg, F. R. Forsund, F. S. Jansen, Malmquist indices of Productivity growth during the deregulation of Norwegian banking,
Scandinavian Journal of economics 14 (1992) 211-228.
[3] A. Camanho, R. Dyson, Data envelopment analysis and Malmquist indices for measuring group performance,
J Prod Anal 26 (2006) 35-49.
[4] D. W. Caves, L. R. Christensen, W. E. Diewert, The economic theory of index numbers and the measurement of input, output and productivity,
Econometrica 50 (1982) 1393-1414.
[5] A. Charnes, W. W. Cooper, Preface to topics in data envelopment analysis,
Annals of Operations Research 2 (1985) 59-94.
[6] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units,
European Journal of Operational Research 2 (1978) 429-440.
[7] H. David Sherman, R. Timothy, Do bank mergers have hidden or foregone value? Realized and unrealized operating synergies in one bank merger,
European Journal of Operational Research 168 (2006) 253-268.
[8] O. Despic, M. Despic, J. C. Paradi, DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications,
Journal of Productivity Analysis 28 (2007) 33-44.
[9] R. Fare, S. Grosskopf, C. A. K. Lovell, Production Frontiers, Cambridge University Press, Cambridge, (1994a).
[10] R. Fare, S. Grosskopf, B. Lindgren, P. Ross, Productivity developments in Swedish hospitals: A Malmquist output index approach,
Boston, (1994b).
[11] R. Fare, S. Grosskopf, R. R .Russell, Index numbers: essays in honour of sten
 Malmquisit, Kluwer Academic Publishers, Dordreicht, (1998).
[12] R. Fare, C. A. K. Lovell, Measuring the technical efficiency of production,
J. Econ Theory 19 (1978) 150-162.
[13] R. Fare, M. Norris, S. Grosskopf, Z. Zhang, Productivity growth, Technical progress, and efficiency change in industrialized counties,
American Economic Review 84 (1994) 66-83.
[14] M. J. Farrell, The measurement of productive efficiency,
Journal of Royal Statistical Society, Series A (1957) CXX:253-281.
[15] S. Malmquist, Index numbers and indifference surfaces,
Trabajos de Estadistica, Trabajos de Estadistica 4 (1953) 209-242.
[16] M. R. Mozaffari, J. Gerami, J. Jablonsky, Relationship between DEA models without explicit inputs and DEA-R models,
Central European Journal of Operations Research 22 (2014) 1-12.
[17] M. R. Mozaffari, F. Dadkhah, J. Jablonsky, P. F. Wanke, Finding efficient surfaces in DEA-R models,
Applied Mathematics and Computation 386 (2020) 125-135.
[18] M. Tavallaaee, M. R. Alirezaee, Applied decompositions of Malmquist, cost Malmquist, and allocation Malmquist indices by considering changes in cost efficiency and technology,
Journal of Industrial and Systems Engineering 13 (2021) 41-60.
[19] C. K. Wei, L. C. Chen, R. K. Li, C. H. Tsai, Using the DEA-R model in the hospital industry to study the pseudo-inefficiency problem,
Expert Systems with Applications 38 (2011) 2172-2176.
[20] C. K. Wei, L. C. Chen, R. K. Li, C. H. Tsai, Exploration of efficiency underestimation of CCR model: Based on medical sectors with DEA-R model,
Expert Systems with Applications 38 (2011) 3155-3162.