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

Abstract

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.

Entropy as an Objective Function of Optimization Multimodal Transportations

“…The task of finding a solution through many criteria and many parameters has found a wide response in the scientific literature. In particular, Ehrgott's work is often referred to [1,2]. The classic article [1] rightly points out the complexity of optimization problems and proposes an application of the heuristic approach as a forced solution.…”

“…The heuristic approach by definition does not give significant relevance to the proposed solutions. The article [2] proposes double multi-objective linear programming to simplify the calculation of optimization problems by their linearization. It should also be borne in mind that the approach [2] is proposed to avoid the use of classical optimization methods.…”

“…The article [2] proposes double multi-objective linear programming to simplify the calculation of optimization problems by their linearization. It should also be borne in mind that the approach [2] is proposed to avoid the use of classical optimization methods. This was taken into account when developing the mathematical approach proposed by the authors.…”

An iterative vertex enumeration method for objective space based vector optimization algorithms

“…Recall that DEA is used to compute the efficiency of decision-making units (DMUs) with common inputs and outputs (for a review, see [10,11]), and it has many application areas including, banking, healthcare, energy and environmental sciences, agriculture, see for instance the survey papers [20,30]. In [16], Ehrgott, Hasannasab and Raith proposed an algorithm in order to generate the extreme points and facets of the efficient frontier of data envelopment analysis (DEA) problems using the geometric duality theory for linear multiobjective optimization problems (MOPs). Accordingly, instead of relying on solving a linear program for each DMU as many other DEA solution approaches from the literature do, their algorithm is based on solving online VEPs in each iteration and does not solve any LP.…”

“…Accordingly, instead of relying on solving a linear program for each DMU as many other DEA solution approaches from the literature do, their algorithm is based on solving online VEPs in each iteration and does not solve any LP. It is demonstrated in [16] that their algorithm is computationally comparable with the standard DEA approach for some real life problems and it is faster than that for large-scale artificial data sets for which the percentage of efficient DMUs is rather small.…”