Extention of Malmquist Productivity Index using Targeted Trade-offs in Data Envelopment Analysis

Document Type : Research Paper



If an external evaluation of decision making units (DMUs) is available based on some bachground information of them, we can estimate it using some defined trade-offs in DEA models. In this paper, we firstly select optimal combination of trade-offs to maximize correlation between external and internal evaluation of DMUs and then we set up the targeted trade-off production possibility set by using the selected optimal trade-offs. Considering this PPS as a based technology in the Malmquist index, we can extend the malmquist productivity index. In the following, a new factor as “external evaluation factor” is introduced so we can present new decompositions of Malmquist index. Finally, using a numerical example we illustrate the extended Malmquist index and its decompositions


Alirezaee, M.R. & Afsharian, M. (2010). Improving the discrimination of data envelopment analysis models in multiple time periods. International Transactions in Operational Research, 17(5), 667–679.
Alirezaee, M.R. & Boloori, F. (2012). Proportional production trade-offs in DEA, Asia-pacific journal of operational research, 29(6), 1317-1334.
Alirezaee, M.R. & Rafiee Sani, M.R. (2010). A Development on AHP/DEA Methodology for Ranking Decision Making Units. Journal of industrial management, 2(5), 83-102. (in Persian)
Alirezaee, M.R. & Rafiee Sani, M.R. (2014). Trade-off Selection by Generalized Trade-Off Data Envelopment Analysis. Journal of industrial management, 6(3), 555-572. (in Persian)
Banker, R.D., Charnes, A. & Cooper, W.W. (1984). Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 30(9), 1078–1092.
Caves, D.C., Christensen, L. R. & Dievert, W.E. (1982). The economic theory of index number and the measurement of input, output, and productivity. Econometrica, 50(6), 1393–1414.
Charnes, A., Cooper, W.W. & Rhodes, E., (1978). Measuring the efficiency of the decision making units. European Journal of Operational Research, 2(6), 429–444.
Fare, R., Grosskopf, S., Lindgren, B. & Roose, P. (1992). Productivity change in Swedish analysis pharmacies 1980–1989: a nonparametric Malmquist approach. Journal of Productivity Analysis, 3(1), 85–102.
Fare, R., Grosskopf, S., Norris, M. & Zhang, A. (1994). Productivity growth, technical progress, and efficiency changes in industrial country. The American Economic Review, 84(1), 66–83.
Khosravi, M. & Shahroodi, K. (2014). Applying Network DEA Model in Evaluating Efficiency of Power Transmission Sector, in Iran Electricity Industry. Journal of industrial management, 6(2), 263-282. (in Persian)
Mahmoudabadi, M.Z., Taheri Mehrjardi, M.H., Mahdavian, A. (2014). Evaluation of R&D Activities in Iran: Data Envelopment Analysis Approach. Journal of industrial management, 6(1), 55-74. (in Persian)
Malmquist, S. (1953). Index numbers and indifferent surfaces. Trabajos de Estadistica, 4(2): 209–242.
Momeni, M., Rostami Malkhalifeh, M., Razavi, S.M. & Keykhosro, Y. (2014). Group Ranking of Bank Units According to Data Envelopment Analysis Approach. Journal of industrial management, 6(1), 181-196. (in Persian)
Podinovski, V.V. & Bouzdine Chameeva, T. (2013). Weight Restrictions and Free Production in Data Envelopment Analysis. Operations Research, 61(2), 426-437.
Podinovski, V.V. (2004). Production trade-offs and weight restrictions in data envelopment analysis. The Journal of the Operational Research Society, 55(4), 1311–1322.
Podinovski, V.V. (2007). Improving data envelopment analysis by the use of production trade-offs. TheJournal of the Operational Research Society, 58(7), 1261–1270.