Lidia Angulo-Meza

Alternative targets for data envelopment analysis through multi-objective linear programming: Rio de Janeiro Odontological Public Health System Case Study

In the last 10 years much has been written about the drawbacks of radial projection. During this time, many authors proposed methods to explore, interactively or not, the efficient frontier via non-radial projections. This paper compares three families of data envelopment analysis (DEA) models: the traditional radial, the preference structure and the multi-objective models. We use the efficiency analysis of Rio de Janeiro Odontological Public Health System as a background for comparing the three methods through a real case with one integer and one exogenous variable. The objectives of the study case are (i) to compare the applicability of the three approaches for efficiency analysis with exogenous and integer variables, (ii) to present the main advantages and drawbacks for each approach, (iii) to prove the impossibility to project in some regions and its implications, (iv) to present the approximate CPU time for the models, when this time is not negligible. We find that the multi-objective approach, although mathematically equivalent to its preference structure peer, allows projections that are not present in the latter. Furthermore, we find that, for our case study, the traditional radial projection model provides useless targets, as expected. Furthermore, for some parts of the frontier, none of the models provide suitable targets. Other interesting result is that the CPU-time for the multi-objective formulation, although its endogenous high complexity, is acceptable for DEA applications, due to its compact nature.In the last 10 years much has been written about the drawbacks of radial projection. During this time, many authors proposed methods to explore, interactively or not, the efficient frontier via non-radial projections. This paper compares three families of data envelopment analysis (DEA) models: the traditional radial, the preference structure and the multi-objective models. We use the efficiency analysis of Rio de Janeiro Odontological Public Health System as a background for comparing the three methods through a real case with one integer and one exogenous variable. The objectives of the study case are (i) to compare the applicability of the three approaches for efficiency analysis with exogenous and integer variables, (ii) to present the main advantages and drawbacks for each approach, (iii) to prove the impossibility to project in some regions and its implications, (iv) to present the approximate CPU time for the models, when this time is not negligible. We find that the multi-objective approach, although mathematically equivalent to its preference structure peer, allows projections that are not present in the latter. Furthermore, we find that, for our case study, the traditional radial projection model provides useless targets, as expected. Furthermore, for some parts of the frontier, none of the models provide suitable targets. Other interesting result is that the CPU-time for the multi-objective formulation, although its endogenous high complexity, is acceptable for DEA applications, due to its compact nature.

Joint carbon footprint assessment and data envelopment analysis for the reduction of greenhouse gas emissions in agriculture production

Operations management tools are critical in the process of evaluating and implementing action towards a low carbon production. Currently, a sustainable production implies both an efficient resource use and the obligation to meet targets for reducing greenhouse gas (GHG) emissions. The carbon footprint (CF) tool allows estimating the overall amount of GHG emissions associated with a product or activity throughout its life cycle. In this paper, we propose a four-step method for a joint use of CF assessment and Data Envelopment Analysis (DEA). Following the eco-efficiency definition, which is the delivery of goods using fewer resources and with decreasing environmental impact, we use an output oriented DEA model to maximize production and reduce CF, taking into account simultaneously the economic and ecological perspectives. In another step, we stablish targets for the contributing CF factors in order to achieve CF reduction. The proposed method was applied to assess the eco-efficiency of five organic blueberry orchards throughout three growing seasons. The results show that this method is a practical tool for determining eco-efficiency and reducing GHG emissions.

Evaluación de la eficiencia de las compañías aéreas brasileñas a través de un modelo híbrido de análisis envolvente de datos (DEA) y programación lineal multiobjetivo

El aumento creciente de la competitividad del sector de transporte aereo en los ultimos anos provoco un cambio en la dinamica del mercado, lo que ha llevado a las companias aereas a buscar nuevas estrategias para garantizar sus posiciones en el mercado. Este articulo tiene por objetivo hacer un analisis del desempeno de las companias aereas brasilenas, con relacion a su gestion operacional despues de la consolidacion de los cambios resultantes de la liberalizacion del sector en el ano 2005. La eficiencia de las empresas aereas se calcula a traves de la comparacion de los resultados obtenidos con el modelo del Analisis Envolvente de Datos (DEA) clasico con los indices de eficiencia calculados con base en el modelo multiobjetivo MCDEA-BCC, desarrollado para este estudio a partir del modelo MCDEA de Li e Reeves. Ademas este trabajo incluye la segmentacion de las empresas en agrupamientos y la identificacion de benchmarks, en la que se indican las companias con las mejores practicas gerenciales del sector aereo.

Studies of Some Duality Properties in the Li and Reeves Model

In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.

Condorcet Method with Weakly Rational Decision Makers: A Case Study in the Formula 1 Constructors’ Championship☆

Abstract The ordinal methods are widely used to establish rankings in sports competitions because sporting results are on an ordinal scale. However, these methods assume that the decision maker is highly rational and provide a full ranking. This paper analyses the case in which the decision maker is weakly rational. In this case, the decision maker respects the transitivity of preferences but not indifference. It also shows how to adapt the Condorcet method to deal with this situation, using the results of the 2013 Formula 1 Constructors’ World Championship.

Input redistribution using a parametric DEA frontier and variable returns to scale: The parabolic efficient frontier

Abstract In practical use of Data Envelopment Analysis (DEA), there are some cases that the resources used by each DMU can be shared with others or there can be a total limitation of resources to be used. In this way, DMUs may have to redistribute inputs to achieve the efficient frontier. One way to deal with this situation is to use the so-called parametric DEA, which dealt only with constant returns to scale. This paper proposes a method to determine a paraboloid frontier for the resource redistribution of DMUs, where the sum of one input among observed DMUs is constant. This extension of parametric DEA models deals with variable returns to scale. This paper also includes the mathematical demonstration of the variable returns to scale property of the parabolic frontier. To illustrate the use of the model we present numerical examples.In practical use of Data Envelopment Analysis (DEA), there are some cases that the resources used by each DMU can be shared with others or there can be a total limitation of resources to be used. I...