Potential Optimality of Pareto Optima

AbstractIn this paper the notion of potential optimality without an assumption that a value function exists is used to investigate multicriterial optimization problems. Our results show that the notions of potential optimality and strong Pareto optimality (weak Pareto optimality, properly Pareto optimality) are equivalent for special forms of objective functions which are increasing with respect to strong Pareto relation (weak Pareto relation)

A linear programming approach to efficiency evaluation in nonconvex metatechnologies

The notions of metatechnology and metafrontier arise in applications of data envelopment analysis (DEA) in which decision making units (DMUs) are not sufficiently homogeneous to be considered as operating in the same technology. In this case, DMUs are partitioned into different groups, each operating in the same technology. In contrast, the metatechnology includes all DMUs and represents all production possibilities that can in principle be achieved in different production environments. Often, the metatechnology cannot be assumed to be a convex set. In such cases benchmarking a DMU against the common metafrontier requires implementing either an enumeration algorithm and solving a linear program at each of its steps, or solving an equivalent mixed integer linear program. In this paper we show that the same task can be accomplished by solving a single linear program. We also show that its dual can be used for the returns-to-scale characterization of efficient DMUs on the metafrontier

DEA Models with Production Trade-offs and Weight Restrictions

The final publication is available at Springer via http://dx.doi.org/10.1007/978-1-4899-7553-9There is a large literature on the use of weight restrictions in multiplier DEA models. In this chapter we provide an alternative view of this subject from the perspective of dual envelopment DEA models in which weight restrictions can be interpreted as production trade-offs. The notion of production trade-offs allows us to state assumptions that certain simultaneous changes to the inputs and outputs are technologically possible in the production process. The incorporation of production trade-offs in the envelopment DEA model, or the corresponding weight restrictions in the multiplier model, leads to a meaningful expansion of the model of production technology. The efficiency measures in DEA models with production trade-offs retain their traditional meaning as the ultimate and technologically realistic improvement factors. This overcomes one of the known drawbacks of weight restrictions assessed using other methods. In this chapter we discuss the assessment of production trade-offs, provide the corresponding theoretical developments and suggest computational methods suitable for the solution of the resulting DEA models

The hybrid returns-to-scale model and its extension by production trade-offs: an application to the efficiency assessment of public universities in Malaysia

Most applications of data envelopment analysis (DEA) employ standard constant or variable returns-to-scale models. In this paper we suggest that these models may sometimes underutilize our knowledge of the underlying production process. For example, in the context of higher education considered in the reported application, individual universities often maintain a certain student-to-staff ratio which points that there should be an approximately proportional relationship between students and staff, at least in the medium to long run.Adifferent example is an observation that the teaching of postgraduate students generally requires more resources than the teaching of the same number of undergraduate students. In order to incorporate such information in a DEA model, we propose a novel approach that combines the recently developed hybrid returns-to-scale DEA model with the use of production trade-offs. The suggested approach leads to a better-informed model of production technology than the conventional DEA models. We illustrate this methodology by an application to Malaysian public universities. This approach results in a tangibly better efficiency discrimination than would be possible with the standard DEA models

Preface: International conference on data envelopment analysis—DEA40, 16–18 April 2018

info:eu-repo/semantics/publishedVersio

Production trade-offs in models of data envelopment analysis with ratio inputs and outputs: an application to schools in England

In applications of data envelopment analysis (DEA), the inputs and outputs representing environmental and quality characteristics of the production process are often stated in the form of percentages, ratios and averages, collectively referred to as ratio measures. It is known that the conventional variable and constant returns-to-scale (VRS and CRS) DEA models cannot correctly incorporate such ratio inputs and outputs. This problem has been addressed by the development of Ratio-VRS and Ratio-CRS (R-VRS and R-CRS) models suitable for the incorporation of both volume and ratio inputs and outputs. Such models may, however, depending on the application, lack sufficient discriminatory power. In this paper we address this issue by developing a further extension of the R-VRS and R-CRS models (the latter with the most common fixed type of ratio inputs and outputs) by allowing the specification of production trade-offs between volume inputs and outputs, and, similarly, between ratio measures. As in the case of conventional VRS and CRS models in which the role of production trade-offs is well understood, the specification of such trade-offs in the R-VRS and R-CRS production technologies leads to their controlled expansion and results in improved efficiency discrimination of the resulting DEA models. We illustrate the application of the proposed methodology by the assessment of efficiency of a large sample of secondary schools in England

Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture

This paper was accepted for publication in the journal Omega and the definitive published version is available at http://dx.doi.org/10.1016/j.omega.2015.01.015In this paper we consider the use of data envelopment analysis (DEA) for the assessment of efficiency of units whose output profiles exhibit specialisation. An example of this is found in agriculture where a large number of different crops may be produced in a particular region, but only a few farms actually produce each particular crop. Because of the large number of outputs, the use of conventional DEA models in such applications results in a poor efficiency discrimination. We overcome this problem by specifying production trade-offs between different outputs, relying on the methodology of Podinovski (2004). The main idea of our approach is to relate various outputs to the production of the main output. We illustrate this methodology by an application of DEA involving agricultural farms in different regions of Turkey. An integral part of this application is the elicitation of expert judgements in order to formulate the required production trade-offs. Their use in DEA models results in a significant improvement of the efficiency discrimination. The proposed methodology should also be of interest to other applications of DEA where units may exhibit specialization, such as applications involving hospitals or bank branches

The hybrid returns-to-scale model and its extension by production trade-offs: an application to the efficiency assessment of public universities in Malaysia

The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-015-1854-0Most applications of data envelopment analysis (DEA) employ standard constant or variable returns-to-scale (CRS or VRS) models. In this paper we suggest that these models may sometimes underutilize our knowledge of the underlying production process. For example, in the context of higher education considered in the reported application, individual universities often maintain a certain student-to-staff ratio which points that there should be an approximately proportional relationship between students and staff, at least in the medium to long run. A different example is an observation that the teaching of postgraduate students generally requires more resources than the teaching of the same number of undergraduate students. In order to incorporate such information in a DEA model, we propose a novel approach that combines the recently developed hybrid returns-to-scale DEA model with the use of production trade-offs. The suggested approach leads to a better-informed model of production technology than the conventional DEA models. We illustrate this methodology by an application to Malaysian public universities. This approach results in a tangibly better efficiency discrimination than would be possible with the standard DEA models

Eco-efficiency measurement and material balance principle:an application in power plants Malmquist Luenberger Index

Incorporating Material Balance Principle (MBP) in industrial and agricultural performance measurement systems with pollutant factors has been on the rise in recent years. Many conventional methods of performance measurement have proven incompatible with the material flow conditions. This study will address the issue of eco-efficiency measurement adjusted for pollution, taking into account materials flow conditions and the MBP requirements, in order to provide ‘real’ measures of performance that can serve as guides when making policies. We develop a new approach by integrating slacks-based measure to enhance the Malmquist Luenberger Index by a material balance condition that reflects the conservation of matter. This model is compared with a similar model, which incorporates MBP using the trade-off approach to measure productivity and eco-efficiency trends of power plants. Results reveal similar findings for both models substantiating robustness and applicability of the proposed model in this paper