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

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