A Parallel Application of Matheuristics in Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a non-parametric methodology for estimating technical efficiency and benchmarking. In general, it is desirable that DEA generates the efficient closest targets as benchmarks for each assessed unit. This may be achieved through the application of the Principle of Least Action. However, the mathematical models associated with this principle are based fundamentally on combinatorial NP-hard problems, difficult to be solved. For this reason, this paper uses a parallel matheuristic algorithm, where metaheuristics and exact methods work together to find optimal solutions. Several parallel schemes are used in the algorithm, being possible for them to be configured at different stages of the algorithm. The main intention is to divide the number of problems to be evaluated in equal groups, so that they are resolved in different threads. The DEA problems to be evaluated in this paper are independent of each other, an indispensable requirement for this algorithm. In addition, taking into account that the main algorithm uses exact methods to solve the mathematical problems, different optimization software has been evaluated to compare their performance when executed in parallel. The method is competitive with exact methods, obtaining fitness close to the optimum with low computational time.J. Aparicio and M. González thank the financial support from the Spanish ‘Ministerio de Economía, Industria y Competitividad’ (MINECO), the ‘Agencia Estatal de Investigacion’ and the ‘Fondo Europeo de Desarrollo Regional’ under grant MTM2016-79765-P (AEI/FEDER, UE)

A parameterized scheme of metaheuristics with exact methods for determining the Principle of Least Action in Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a nonparametric methodology for estimating technical efficiency of a set of Decision Making Units (DMUs) from a dataset of inputs and outputs. This paper is devoted to computational aspects of DEA models under the application of the Principle of Least Action. This principle guarantees that the efficient closest targets are determined as benchmarks for each assessed unit. Usually, these models have been addressed in the literature by applying unsatisfactory techniques, based fundamentally on combinatorial NPhard problems. Recently, some heuristics have been developed to partially solve these DEA models. This paper improves the heuristic methods used in previous works by applying a combination of metaheuristics and an exact method. Also, a parameterized scheme of metaheuristics is developed in order to implement metaheuristics and hybridations/combinations, adapting them to the particular problem proposed here. In this scheme, some parameters are used to study several types of metaheuristics, like Greedy Random Adaptative Search Procedure, Genetic Algorithms or Scatter Search. The exact method is included inside the metaheuristic to solve the particular model presented in this paper. A hyperheuristic is used on top of the parameterized scheme in order to search, in the space of metaheuristics, for metaheuristics that provide solutions close to the optimum. The method is competitive with exact methods, obtaining fitness close to the optimum with low computational timeJ. Aparicio and M. González thank the financial support from the Spanish ‘Ministerio de Economa, Industria y Competitividad’ (MINECO), the ‘Agencia Estatal de Investigacion’ and the ‘Fondo Europeo de Desarrollo Regional’ under grant MTM2016-79765-P (AEI/FEDER, UE).Additionally, D. Giméenez thanks the financial support from the Spanish MINECO, as well as by European Commission FEDER funds, under grant TIN2015-66972-C5-3-R

Management Quality Measurement: Using Data Envelopment Analysis (DEA) Estimation Approach for Banks in Brazil

While the quality of a bank's management is generally acknowledged to be a key contributor to a financial institutional failure, it is usually not calculated for lack of an objective measure. This paper presents a new paradigm approach for quantifying a bank's managerial efficiency, using a data envelopment analysis (DEA) model that combines multiple inputs and outputs to compute a scalar measure of efficiency and management quality. The analysis of the largest 50 Brazilian banks over a twelve-year period from 1995 to 2006 shows significant differences in management quality scores between institutions. Hence, this new metric provides an important, but previously missing, modelling element for the early identification of troubled banks and can be used as a tool for off-site bank supervision in Brazil.Data Envelopment Analysis, DEA, Banks, Brazil

Sustainable educational supply chain performance measurement through DEA and Differential Evolution: a case on Indian HEI

Data envelopment analysis or DEA methodology is employed for assessing the relative efficiency of different homogeneous units. Through DEA one can analyze the areas which need more attention and can suggest measures for improving the performance of different sectors. Through this article, the authors have tried to analyze the relative efficiency of IITR (The Indian Institute of Technology Roorkee), a higher educational institute (HEI) in India. The efficiency of nineteen academic departments of IIT Roorkee is measured with respect to teaching and research. The novlty of the paper is twofold (1) the authiors have considered the environmental aspects (sustainability criteria) while measuring efficiency (2) Differential Evolution (DE) algorithm is employed in accordance with DEA on the fractional model generated for calculating efficiency

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Medición de la eficiencia y la productividad: Aspectos computacionales

Programa de Doctorado en Economía (DECiDE)The purpose of efficiency and productivity problems is based on evaluating whether the use of the resources available (inputs) by a company or public institution (in general, any decision-making unit) corresponds or not with the optimal way of operating in such a way as to generate the largest possible number of outputs. To carry out this type of calculations, several mathematical models have already been proposed in the specialized literature that can be used, all of which are based on Mathematical Programming problems, and, in particular, some of them correspond to Mixed Integer Linear Programming problems (MILP). These types of problems combine several types of variables, continuous and discrete, in the same mathematical model as well as numerous restrictions, depending on the nature of the problem; features that can make the resolution process somewhat difficult. In addition, it is worth noting that these problems tend to be combinatorial in practice (NP-hard). Throughout this work, the analysis and study will focus on a field within the area of Operations Research called Data Envelopment Analysis (DEA), whose main objective is the estimation of production frontiers and the measurement of productive efficiency. Different optimization models belonging to this field will be put to the test in this thesis from a purely computational perspective, being solved through different techniques, both 2 exact and approximate, analyzing the performance and the difficulty of the same. The main objective of this work does not lie in the development and modeling of new problems in the field of DEA, but in how to achieve optimal solutions in a reasonable time for certain problems of a combinatorial nature, given that being NP-hard type problems, as the size of the problem grows, so does the difficulty of obtaining optimal solutions, especially in a short time. At this point, we will focus on the study and design of approximation techniques, known in the literature as Metaheuristics, closely linked to Machine Learning or Artificial Intelligence methodologies. In addition to these methodologies, based on learning and improving the solutions obtained, parallelization techniques have also been incorporated, capable of efficiently reducing the time needed to obtain optimal solutions in complex problems.La finalidad de los problemas de eficiencia y productividad se basan en evaluar si el uso de los recursos (entradas o inputs, en inglés) disponibles por parte de una empresa o institución pública (en general, cualquier unidad tomadora de decisiones) se corresponde o no con la forma óptima de operar de dicha entidad, generando la mayor cantidad de salidas posible (outputs en inglés). Para llevar a cabo este tipo de cálculos, varios modelos matemáticos han sido ya planteados en la literatura especializada que pueden ser utilizados, teniendo en común todos ellos que están basados en problemas de Programación Matemática, y, en particular, algunos de ellos se corresponden con problemas de Programación Matemática Lineal Mixta (Mixed Integer Linear Programming en inglés – MILP). Este tipo de problemas combinan en un mismo modelo matemático varios tipos de variables, continuas y discretas, así como numerosas restricciones, dependiendo de la naturaleza del problema, siendo estas restricciones características que pueden hacer que el proceso de resolución resulte ser algo difícil. Además, cabe destacar la característica de que estos problemas suelen ser en la práctica de tipo combinatorio (NP-duros). A lo largo de este trabajo, el análisis y el estudio se va a centrar en un campo dentro del área de Investigación Operativa denominado Análisis Envolvente de Datos (Data Envelopment Analysis en inglés - DEA), cuyo principal objetivo es el de la estimación de fronteras de producción y la medición de la eficiencia productiva. Diferentes modelos de optimización pertenecientes a este ámbito serán puestos a prueba en esta tesis desde una perspectiva puramente computacional, siendo resueltos a través de diferentes técnicas, tanto exactas como de aproximación, analizando el rendimiento y la dificultad del mismo. El objetivo principal de este trabajo no reside en el desarrollo y modelado de nuevos problemas en el ámbito del DEA, sino en cómo conseguir soluciones óptimas y eficientes en un tiempo razonable para ciertos problemas de naturaleza combinatoria, dado que al ser problemas de tipo NP-duro, a medida que el tamaño del problema crece, también lo hace la dificultad de obtener soluciones óptimas, sobre todo en un tiempo reducido. En este punto, centraremos la atención en el estudio y diseño de técnicas de aproximación, conocidas en la literatura como Metaheurísticas, estando muy ligadas a metodologías de Machine Learning o Artificial Inteligence. Además de estas metodologías, basadas en el aprendizaje y la mejora de las soluciones obtenidas, también se han incorporado técnicas de paralelismo, capaces de reducir de forma eficiente el tiempo necesario para obtener soluciones óptimas en problemas complejos

Efficiency in Brazilian Refineries Under Different DEA Technologies

This paper aims to assess the environmental efficiency of refineries in the public sector with emphasis on generated effluents and water consumption in the production process. In order to conduct this research, the addressed method was quantitative with a qualitative approach to the environmental aspects of controllable and uncontrollable variables implemented in two classical models of Data Envelopment Analysis (DEA), considering only desirable outputs and two DEA models which include undesirable outputs. The sample consists of ten refineries considering the following as input variables: idleness percentage of the operating plant, the amount of water consumed; and the following as outputs: refinery production volume and generated effluents, desirable and undesirable, respectively, besides the uncontrollable variable, the refinery age. With the comparison result between the models, we observed the clear importance of the environmental variable for a more realistic analysis of the production process

Improving Green Computing in Business Intelligence by Measuring Performance of Reverse Supply Chains

Increasing attention has been given to greencomputing in Business Intelligence. This paper specificallyconsiders the measurement of performance in the reversesupply chain. That is because of the increasing value ofproducts and technology at the end of general direct supplychains as well as the impact of new green legislation. Unlikeforward supply chains, design strategies for reverse supplychains are relatively unexplored and underdeveloped.Meanwhile measuring supply chain performance is becomingimportant as the need for data in business intelligence systemsincreases and the understanding, collaboration and integrationincreases between supply chain members. It also helpscompanies to target the most profitable market segments oridentify a suitable service definition. This paper describes asynthesis of known theory concerning measuring performanceand assesses the state of the art. Strengths and gaps areidentified. Some initial results are presented for measuringsupply performance in reverse supply chains (using robustmethods) and are outlined future research needs

A hybrid egalitarian bargaining game-DEA and sustainable network design approach for evaluating, selecting and scheduling urban road construction projects

Selecting and scheduling urban road construction projects (URCPs) is inherently an Urban Network Design Problem (UNDP) with a complex decision making process. Recently some studies have focused on sustainable UNDP, using different mathematical methods. In this paper, first a new network data envelopment analysis (NDEA) model has been developed. Then, considering sustainability dimensions, by integrating data envelopment analysis (DEA), game theory and sustainable UNDP, a bi-level model has been proposed for selecting and scheduling URCPs. A meta-heuristic algorithm is proposed to solve the presented bi-level model. Different test instances are solved to show the acceptable performance of proposed algorithm in both solution quality and execution time. Afterwards, the proposed model is applied to study the problem of urban road construction projects selection in a real-world case study of urban transportation network of Isfahan city in Iran. The results show that by applying obtained solution the environmental and social performance of the network has been improved and the performance of the network is almost efficient in all evaluation periods