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TopData Envelopment Analysis
Data Envelopment Analysis (DEA) is a non-parametric approach for identifying relative efficiency of Decision Making Units (DMUs) that are producing multiple outputs using multiple inputs. DEA does not require any assumption about the functional form. The efficiency of a DMU is measured relative to all other units with the simple restriction that all DMUs lie on or below an efficient frontier (Cooper et al., 2006). A production possibility set, containing ‘all input-output correspondences which are feasible in principle including those observed units being assessed’, is constructed (Thanassoulis, 2001). Hence, DEA determines the efficiently performing units in relation to each other and benchmark the other units relative to the efficient units in the defined production possibility set through the calculation of efficiency scores. Therefore, the efficiency scores for the units performing efficiently relative to other units are obtained as one and those units take place on the efficient frontier. The DMUs scoring less than one are identified as inefficient with respect to all other units in terms of input and output variables and remain outside the efficient frontier. The efficiency score of each decision unit is obtained by solving a pair of mutually dual linear programs that are based on either the envelopment or the multiplier DEA model. The linear programming model maximises (or minimizes) the objective function that is formulated as output-oriented (or input-oriented) form. For further information and various DEA modelling issues, the reader is referred to Thanassoulis (2001) and Cooper et al. (2006).
Key Terms in this Chapter
Performance Measurement: A tool that is used to describe improvement and change in business environment. This concept is related with the measurement and improvement of efficiency to a great extent.
Malmquist Productivity Index (MPI): A measure of productivity change overtime. It contains information about the source of productivity change evident through decompositions into frontier shift and efficiency change components.
Adjacent Malmquist Index (AMI): A general type of MPI measure that shows the productivity change of single decision making unit overtime. For any individual decision making unit, it can be calculated through the relative efficiency scores of the unit relative to the frontiers.
Global Malmquist Index (GMI): A specific type of MPI measure that represents an aggregated measure of productivity change for the whole sample. This can be basically interpreted as the geometric mean of the frontier differences observed by all units.
Data Envelopment Analysis (DEA): A non-parametric linear programming based approach for identifying relative efficiency of decision making units that are producing multiple outputs using multiple inputs.
Efficiency: The use of the fewest inputs (resources) to produce the most outputs (products or services).
Linear Programming (LP): A mathematical method for determining best decisions that minimise or maximise the given objective in view of some restrictions. It is a specific case of mathematical programming where the objective and constraints are represented as linear relationships of decisions.
Decision Making Units (DMUs): Entities responsible for converting inputs into outputs. They are operational units of an organization or organizations themselves, which typically perform similar functions.