A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

Data envelopment analysis is a linear programming-based operations research technique for performance measurement of decision-making units. In this paper, we investigate data envelopment analysis from a multiobjective point of view to compute both the efficient extreme points and the efficient facets of the technology set simultaneously. We introduce a dual multiobjective linear programming formulation of data envelopment analysis in terms of input and output prices and propose a procedure based on objective space algorithms for multiobjective linear programmes to compute the efficient frontier. We show that using our algorithm, the efficient extreme points and facets of the technology set can be computed without solving any optimization problems. We conduct computational experiments to demonstrate that the algorithm can compute the efficient frontier within seconds to a few minutes of computation time for real-world data envelopment analysis instances. For large-scale artificial data sets, our algorithm is faster than computing the efficiency scores of all decision-making units via linear programming

X-Efficiency of Innovation Processes: Concept and Evaluation based on Data Envelopment Analysis

This paper investigates X-(in)efficiency of innovation processes in Small and Medium-sized Enterprises (SMEs). We have adopted the following approach: (a) we provide both a concept of X-(in)efficiency and a model of innovation processes for each SME; (b) from this model we evaluate both the dimensions of the innovation processes and the X-(in)efficiency of these processes using a variant of the Data Envelopment Analysis (DEA) model; (c) finally, we characterize X-inefficiency by using techniques of exploratory analysis derived from an empirical analysis. Our approach has been applied to regional SMEs in Normandy (France) with a representative random sample of 80 innovative businesses. The results show the existence of X- inefficiency in the innovation processes of SMEs in 71% of cases. This X-inefficiency arises primarily from the difficulties that entrepreneurs face in implementing the interacting rules and standards of exploitation and exploration activities

An MOLP based procedure for finding efficient units in DEA models

Data envelopment analysis, Multiple objective linear programming, Linear programming,