Malmquist Productivity Index with Grey Data

  •  Kenan Oruc    


Malmquist Productivity Index (MPI) is widely used method to measure the productivity changes of Decision Making Units (DMUs) between two time periods. Although the conventional MPI requires accurate data, in many real life conditions the input and output data of DMUs usually involve uncertainty and only lower and upper bounds of data could be obtained. Grey (number) theory is one of the theories which are used for describing uncertainty. A grey number, with both a lower and upper bounds, is called an interval grey number. The purpose of this paper is to measure the productivity changes under uncertainty conditions based on the interval grey number theory. In the paper, new grey MPI models are proposed to measure productivity changes of DMUs which have interval data. A numerical example is provided to illustrate the application of the proposed models. Results of the numerical example show us that the proposed models are easy to handle and applicable for real life problems.

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