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)

The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: modelling and computational aspects

Determining the least distance to the efficient frontier for estimating technical inefficiency, with the consequent determination of closest targets, has been one of the relevant issues in recent Data Envelopment Analysis literature. This new paradigm contrasts with traditional approaches, which yield furthest targets. In this respect, some techniques have been proposed in order to implement the new paradigm. A group of these techniques is based on identifying all the efficient faces of the polyhedral production possibility set and, therefore, is associated with the resolution of a NP-hard problem. In contrast, a second group proposes different models and particular algorithms to solve the problem avoiding the explicit identification of all these faces. These techniques have been applied more or less successfully. Nonetheless, the new paradigm is still unsatisfactory and incomplete to a certain extent. One of these challenges is that related to measuring technical inefficiency in the context of oriented models, i.e., models that aim at changing inputs or outputs but not both. In this paper, we show that existing specific techniques for determining the least distance without identifying explicitly the frontier structure for graph measures, which change inputs and outputs at the same time, do not work for oriented models. Consequently, a new methodology for satisfactorily implementing these situations is proposed. Finally, the new approach is empirically checked by using a recent PISA database consisting of 902 schools

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

Improvement Least-Distance Measure Model with Coplanar DMU on Strong Hyperplanes

Technique of Data Envelopment Analysis (DEA) involves methods conducted for desirable objective management of Decision Making Unit (DMU) that is same increasing of efficiency level. Data envelopment analysis furthermore determines the efficiency level, provides situation, removes inefficiency with evaluated benchmarking information. In this paper the use of the improvement Least-Distance measure with relation previous model by coplanar DMU, is proposed for computational dissipation at assess distance on these interior combinations, for determination the shortest projection from a considered unit to the strongly efficient production frontier. Therefore locate nearest path to improvement efficiency the evaluated DMU

The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: modelling and computational aspects

Determining the least distance to the efficient frontier for estimating technical inefficiency, with the consequent determination of closest targets, has been one of the relevant issues in recent Data Envelopment Analysis literature. This new paradigm contrasts with traditional approaches, which yield furthest targets. In this respect, some techniques have been proposed in order to implement the new paradigm. A group of these techniques is based on identifying all the efficient faces of the polyhedral production possibility set and, therefore, is associated with the resolution of a NP-hard problem. In contrast, a second group proposes different models and particular algorithms to solve the problem avoiding the explicit identification of all these faces. These techniques have been applied more or less successfully. Nonetheless, the new paradigm is still unsatisfactory and incomplete to a certain extent. One of these challenges is that related to measuring technical inefficiency in the context of oriented models, i.e., models that aim at changing inputs or outputs but not both. In this paper, we show that existing specific techniques for determining the least distance without identifying explicitly the frontier structure for graph measures, which change inputs and outputs at the same time, do not work for oriented models. Consequently, a new methodology for satisfactorily implementing these situations is proposed. Finally, the new approach is empirically checked by using a recent PISA database consisting of 902 schools

A data-driven decision support framework for DEA target setting:an explainable AI approach

The intention of target setting for Decision-Making Units (DMUs) in Data Envelopment Analysis (DEA) is to perform better than their peers or reach a reference efficiency level. However, most of the time, the logic behind the target setting is based on mathematical models, which are not achievable in practice. Besides, these models are based on decreasing/increasing inputs/outputs that might not be feasible based on DMU's potential in the real world. We propose a data-driven decision support framework to set actionable and feasible targets based on vital inputs-outputs for target setting. To do so, DMUs are classified in their corresponding Efficiency Frontier (EF) levels based on multiple EFs approach and a machine learning classifier. Then, the vital inputs-outputs are determined using an Explainable Artificial Intelligence (XAI) method. Finally, a Multi-Objective Counterfactual Explanation is developed based on DEA (MOCE-DEA) to lead DMU in reaching the reference EF by adjusting actionable and feasible inputs-outputs. We studied Iranian hospitals to evaluate the proposed framework and presented two cases to demonstrate its mechanism. The results show that the performance of the DMUs is improved to reach the reference EF for studied cases. Then, a validation was conducted with the primal DEA model to show the robust improvement of DMUs after adjusting their original value based on the generated solutions by the proposed framework. It demonstrates that the adjusted values can also improve DMUs' performance in the primal DEA model.</p

A data-driven decision support framework for DEA target setting:an explainable AI approach

The intention of target setting for Decision-Making Units (DMUs) in Data Envelopment Analysis (DEA) is to perform better than their peers or reach a reference efficiency level. However, most of the time, the logic behind the target setting is based on mathematical models, which are not achievable in practice. Besides, these models are based on decreasing/increasing inputs/outputs that might not be feasible based on DMU's potential in the real world. We propose a data-driven decision support framework to set actionable and feasible targets based on vital inputs-outputs for target setting. To do so, DMUs are classified in their corresponding Efficiency Frontier (EF) levels based on multiple EFs approach and a machine learning classifier. Then, the vital inputs-outputs are determined using an Explainable Artificial Intelligence (XAI) method. Finally, a Multi-Objective Counterfactual Explanation is developed based on DEA (MOCE-DEA) to lead DMU in reaching the reference EF by adjusting actionable and feasible inputs-outputs. We studied Iranian hospitals to evaluate the proposed framework and presented two cases to demonstrate its mechanism. The results show that the performance of the DMUs is improved to reach the reference EF for studied cases. Then, a validation was conducted with the primal DEA model to show the robust improvement of DMUs after adjusting their original value based on the generated solutions by the proposed framework. It demonstrates that the adjusted values can also improve DMUs' performance in the primal DEA model.</p

Evaluación de la eficiencia de la Superliga de Voleibol 2013/14

La eficiencia, entendida como la relación entre inputs y outputs, ha sido evaluada para numerosos deportes como el fútbol, baloncesto, tenis o béisbol. Sin embargo, en el ámbito del voleibol no se han realizado estudios de este tipo. Por ello, en este trabajo se evalúa la eficiencia de los equipos masculinos y femeninos de la Superliga española de voleibol. A nivel individual, se evalúa la eficiencia de los jugadores (masculinos y femeninos) de voleibol diferenciando entre posición defensiva y ofensiva. Para ello, se hace uso de un modelo análisis envolvente de datos radial bajo orientación output y rendimientos constantes a escala. En un análisis de segunda etapa se verifica que no hay diferencias estadísticamente significativas en la eficiencia de los jugadores internacionales y no internacionales. Así mismo, se puede concluir que dentro de las posiciones defensivas, los jugadores/as líberos son más eficientes que los receptores. Por el contrario, en las posiciones ofensivas (central, opuesto y atacante) las diferencias de eficiencia no son significativas

Embedding eWOM into efficiency DEA modelling: an application to the hospitality sector

This paper develops and tests an innovative DEA model in the hospitality sector, by originally embedding online customer ratings among the outputs of the model. Based on a sample of 268 independent hotels located in Rome (Italy), we test a eWOM-informed DEA model and find that the introduction of online ratings among the outputs of the model significantly affects the assessment of hotels’ efficiency regardless of hotel category. The efficiency rankings generated by the DEA models embedding eWOM are radically different compared to those resulting from DEA models exclusively based on financial variables. The number of hotels improving their position in the efficiency rankings is lower than the number of hotels decreasing in the ranking. However, the average efficiency variation is positive and higher for 2- and 3- stars hotels than for 4- and 5- stars hotels. Implications for researchers in hospitality and tourism, managers and practitioners are discussed

Análisis de la Eficiencia y Productividad de la Superliga de Voleibol

La eficiencia, entendida como el buen aprovechamiento de los inputs para obtener outputs, ha sido evaluada en numerosos deportes como el fútbol, baloncesto, tenis o béisbol. Sin embargo, en el ámbito del voleibol no se han realizado estudios de este tipo. Por ello, en este trabajo se analiza la eficiencia de los equipos masculinos y femeninos de la Superliga española de voleibol. Para ello, se hace uso de un modelo análisis envolvente de datos por etapas (DEA Network) bajo orientación output y rendimientos constantes a escala. En un segundo análisis evaluamos el cambio en la productividad mediante el indicador de Luenberger. Se puede concluir que sólo los primeros equipos clasificados son eficientes y que existen indicios de que los resultados deportivos están relacionados con la eficiencia. En cuanto al cambio en la productividad existen grandes diferencias entre la Superliga Masculina y Femenina. En el primer caso, en general se ha producido un empeoramiento tecnológico y sólo los equipos que han tenido una gran mejora en su eficiencia han mejorado su productividad. En la Superliga Femenina todos los equipos han experimentado una mejora tecnológica, sin embargo, sólo algunos equipos han mejorado su productividad