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)

New resonance approach to competitiveness interventions in lagging regions: the case of Ukraine before the armed conflict

Regional competitiveness is considered to be an alternative basis for the determination of regional interventions. However, the composite competitiveness indicator is quite sensitive to the weights of sub-indicators, no matter what methodology is being used. To avoid this uncertainty in the determination of regional interventions, we proposed a new non-compensatory resonance approach that is focused on the hierarchical coincidence between weaknesses of NUTS 1 and NUTS 2 regions measuring the extensive and intensive components of competitiveness. Such a coincidence, being perceived as a resonance effect, is supposed to increase the effectiveness of interventions triggering synergetic effects and stirring up local regional potentials. The components of competitiveness are obtained through synthesising DEA methodology and Hellwig's index, correspondingly focusing on the measurement of technical efficiency and resource level. In analysing Ukrainian regions, no correlation between resonance interventions and the composite competitiveness indicator or GDP per capita was found, pointing toward a completely different direction in resonance approach. In western Ukraine, the congestion of six NUTS 2 regions was defined as a homogeneous area of analogous resonance interventions focused on improving business efficiency.Web of Science171562

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

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

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

Efficiency of French football clubs and its dynamics

In the paper we evaluate the efficiency of French football clubs (Ligue 1) from 2004 to 2007 using Data Envelopment Analysis (DEA) with « Assurance Region ». Then, we study the dynamics of clubs’ performances. Contrary to previous works on other championships, best teams in competition or most profitable clubs are not the most efficient units in our sample. High average scores show that French First League is efficient. The first source of inefficiency in the Ligue 1 is linked to size problems and over-investments. Despite an average club performance stable over the period, we exhibit a deterioration of conditions in which clubs operate.Ligue 1, efficiency scores, Data Envelopment Analysis (DEA), Malmquist index, over-investment

Hospital Efficiency: An Empirical Analysis of District and Grant-in-Aid Hospitals in Gujarat

This study focuses on analysing the hospital efficiency of district level government hospitals and grant-in-aid hospitals in Gujarat. The study makes an attempt to provide an overview of the general status of the health care services provided by hospitals in the state of Gujarat in terms of their technical and allocative efficiency. One of the two thrusts behind addressing the issue of efficiency was to take stock of the state of healthcare services (in terms of efficiency) provided by grant-in-aid hospitals and district hospitals in Gujarat. The motivation behind addressing the efficiency issue is to provide empirical analysis of governments policy to provide grants to not-for-profit making institutions which in turn provide hospital care in the state. The study addresses the issue whether grant-in-aid hospitals are relatively more efficient than public hospitals. This comparison between grant-in-aid hospitals and district hospitals in terms of their efficiency has been of interest to many researchers in countries other than India, and no consensus has been reached so far as to which category is more efficient. The relative efficiency of government and not-for-profit sector has been reviewed in this paper. It is expected that the findings of the study would be useful to evaluate this policy and help policy makers to develop benchmarks in providing the grants to such institutions.

Complete Closest-Target Based Directional FDH Measures of Efficiency in DEA

In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invariant. In addition, we present effective enumeration algorithms to compute them. Our proposed measures have several practical advantages such as: (a) providing closest Pareto-efficient observed targets (b) incorporating the decision maker’s preference information into efficiency analysis and (c) being flexible in computer programming. We illustrate the newly developed approach with a real world data set