Input redistribution using a parametric DEA frontier and variable returns to scale: The parabolic efficient frontier

Abstract

In practical use of Data Envelopment Analysis (DEA), there are some cases that the resources used by each DMU can be shared with others or there can be a total limitation of resources to be used. In this way, DMUs may have to redistribute inputs to achieve the efficient frontier. One way to deal with this situation is to use the so-called parametric DEA, which dealt only with constant returns to scale. This paper proposes a method to determine a paraboloid frontier for the resource redistribution of DMUs, where the sum of one input among observed DMUs is constant. This extension of parametric DEA models deals with variable returns to scale. This paper also includes the mathematical demonstration of the variable returns to scale property of the parabolic frontier. To illustrate the use of the model we present numerical examples.

Keywords:

• Data envelopment analysis
• parametric DEA
• input redistribution
• parabolic frontier