Abstract
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.
Highlights
Data Envelopment Analysis (DEA) is a nonparametric method to measure the relative efficiencies of enterprises (Decision Making Units-DMUs) which use multiple inputs in order to produce multiple outputs
The aim of this paper is to propose grey Malmquist Productivity Index (MPI) models for DMUs with interval grey data
Three different approaches are held by using grey whitenization functions
Summary
Data Envelopment Analysis (DEA) is a nonparametric method to measure the relative efficiencies of enterprises (Decision Making Units-DMUs) which use multiple inputs in order to produce multiple outputs. Fare et al (1992) combined ideas on the measurement of efficiency from Farrell (1957) and the measurement of productivity from Caves et al (1982) to construct a MPI directly from input and output data using DEA (Chen & Ali, 2004). The aim of this paper is to propose grey MPI models for DMUs with interval grey data. Interval grey input and output data are whitenized by using equal weight whitenization and equal weight mean whitenization functions.
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