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

Aplicación del ACP al análisis de índices de eficiencia DEA del sistema bibliotecario

En este trabajo fin de grado se analizarán las eficiencias del conjunto de bibliotecas españolas de titularidad estatal dados unos inputs y outputs, durante el año 2020. Este análisis de la eficiencia se realizará mediante el uso del DEA, análisis envolvente de datos. Debido a que se medirá la eficiencia en cada centro para todos los escenarios, que son cada una de las posibles combinaciones de inputs y outputs, obteniendo diferentes resultados, se utilizará ACP, análisis de componentes principales, para obtener una medida global de eficiencia, obteniendo un ranking de las bibliotecas y eliminando el efecto que se genera a partir de la elección de unos determinados inputs/outputs. Se estudiarán e interpretarán todos los resultados que se obtengan de estos análisis previos y se obtendrán las conclusiones de este proyecto.In this dissertation, the efficiencies of the set of Spanish state-owned libraries will be analyzed, given some inputs and outputs, during the year 2020. This efficiency analysis will be carried out using DEA, data envelopment analysis. Because the efficiency will be measured in each center for all the scenarios, which are each one of the possible combinations of inputs and outputs, obtaining different results, PCA, principal component análisis, will be used to obtain a global measure of efficiency, obtaining a ranking of the libraries and eliminating the effect generated by the choice of certain inputs/outputs. All the results obtained from these previous analyzes will be studied and interpreted and the conclusions of this project will be obtained.Departamento de Estadística e Investigación OperativaGrado en Estadístic