Marginal values and returns to scale for nonparametric production frontiers

We present a unifying linear programming approach to the calculation of various directional derivatives for a very large class of production frontiers of data envelopment analysis (DEA). Special cases of this include different marginal rates, the scale elasticity and a spectrum of partial and mixed elasticity measures. Our development applies to any polyhedral production technology including, to name a few, the conventional variable and constant returns-to-scale DEA technologies, their extensions with weight restrictions, technolo gies with weakly disposable undesirable outputs and network DEA models. Furthermore, our development provides a general method for the characterization of returns to scale (RTS) in any polyhedral technology. The new approach effectively removes the need to develop bespoke models for the RTS characterization and calculation of marginal rates and elasticity measures for each particular technology

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 (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

Implications of the PPSMI policy for the performance of Malaysian secondary schools in mathematics and science subjects

The introduction of the Teaching and Learning Mathematics and Science Subjects in English (PPSMI) policy to change the medium of instruction in mathematics and science subjects from Bahasa Melayu to English has raised many debates on the effectiveness of the policy and the ability of the schools, teachers and pupils to adapt to the new medium of instruction. This study evaluates the implications of the PPSMI policy for the school performance in mathematics and science subjects. The school performances before and after the implementation of the policy were assessed and compared according to school types, states, and locations by developing an advanced technique in measuring school efficiency based on hybrid returns to scale (HRS) data envelopment analysis (DEA). A new methodology of measuring change in performance over time based on the Malmquist index was also developed to measure the difference in performance before and after the implementation of the policy. The aim of developing the methodologies is to provide an alternative assessment of the implications of the PPSMI policy for the school performance in mathematics and science subjects thus helping the Ministry of Education Malaysia to decide on the direction of the PPSMI policy. The HRS DEA model is a new extension in DEA based on the concept of selective proportionality in the relationship of input-output variables. It gives a better estimate compared to the original convex models, the constant returns to scale (CRS) and the variable returns to scale (VRS), when some of the inputs and outputs have proportional relationship while others do not. In this study, an HRS-based DEA model utilising 10 inputs and 8 outputs was developed to assess the efficiency of schools from three states i.e. Kedah, Penang, and Perlis. The schools comprise of three different types i.e. the national, fully residential, and religious school-types. The efficiency was also assessed by using the CRS and VRS models to compare the results. The Malmquist index is a popular productivity index for measuring efficiency over time. The Malmquist index can be calculated from the CRS-based or the VRS-based DEA efficiency scores. This study developed a new productivity index called the HRS-based Malmquist index. This is similar to the VRS-based Malmquist index but the calculation of the index is based on the efficiency scores from the HRS DEA model. The efficiency scores and Malmquist indices of schools in different categories (i.e. school-types, states, and locations) were tested for significant difference by using nonparametric statistical tests. Nonparametric statistical tests were used due to the nonparametric nature of DEA. The statistical tests used in this study are Mann-Whitney U Test and Kruskal-Wallis Test to look at independent samples such as samples from different school-types, and Wilcoxon Signed Ranks Test and Friedman's Two-Way Analysis of Variance to examine dependent samples such as the difference in performance before and after the implementation of the policy

MS Excel based Software Support Tools for Decision Problems with Multiple Criteria

AbstractDecision making in real practice is usually connected with multiple criteria. Multiple criteria decision making (MCDM) and data envelopment analysis models, even they solve different problem classes, belong to the most often used modeling techniques in this field. Their wider using is often limited by availability of appropriate software tools. The paper presents two freeware software systems that are available for downloading on the author's web pages. The first system is DEA Excel Solver and the second one is Sanna – application for multi-criteria evaluation of alternatives. DEA Excel Solver covers basic DEA models and uses internal MS Excel optimization solver. The application includes standard envelopment models with constant and variable returns to scale including super-efficiency models. Sanna is a simple MS Excel based application for multi-criteria evaluation of alternatives using several important MCDM methods (WSA, ELECTRE I and III, ORESTE, PROMETHEE, TOPSIS, and MAPPAC)

The Use of Parametric and Non Parametric Frontier Methods to Measure the Productive Efficiency in the Industrial Sector. A Comparative Study

Parametric frontier models and non-parametric methods have monopolised the recent literature on productive efficiency measurement. Empirical applications have usually dealt with either one or the other group of techniques. This paper applies a range of both types of approaches to an industrial organisation setup. The joint use can improve the accuracy of both, although some methodological difficulties can arise. The robustness of different methods in ranking productive units allows us to make an comparative analysis of them. Empirical results concern productive and market demand structure, returns-to-scale, and productive inefficiency sources. The techniques are illustrated using data from the US electric power industry.Productive efficiency; parametric frontiers; DEA; industrial sector

Analyzing the accuracy of variable returns to scale data envelopment analysis models

The data envelopment analysis (DEA) model is extensively used to estimate efficiency, but no study has determined the DEA model that delivers the most precise estimates. To address this issue, we advance the Monte Carlo simulation-based data generation process proposed by Kohl and Brunner (2020). The developed process generates an artificial dataset using the Translog production function (instead of the commonly used Cobb Douglas) to construct well-behaved scenarios under variable returns to scale (VRS). Using different VRS DEA models, we compute DEA efficiency scores with artificially generated decision-making units (DMUs). We employ five performance indicators followed by a benchmark value and ranking as well as statistical hypothesis tests to evaluate the quality of the efficiency estimates. The procedure allows us to determine which parameters negatively or positively influence the quality of the DEA estimates. It also enables us to identify which DEA model performs the most efficiently over a wide range of scenarios. In contrast to the widely applied BCC (Banker-Charnes-Cooper) model, we find that the Assurance Region (AR) and Slacks-Based Measurement (SBM) DEA models perform better. Thus, we endorse the use of AR and SBM models for DEA applications under the VRS regime

Does Expansion Cause Congestion? The Case of the Older British Universities, 1994 to 2004

This paper examines whether the rapid growth in the number of students in British universities in recent years has led to congestion, in the sense that certain universities’ output could have been higher if this expansion had been less rapid. The focus of the paper is on 45 older universities that were in existence prior to 1992. The analysis covers the period 1994/5 to 2003/4. Several alternative methods of measuring congestion are examined and, to check the sensitivity of the results to different specifications, three alternative DEA models are formulated. The results indicate that congestion was present throughout the decade under review, and in a wide range of universities, but whether it rose or fell is uncertain, as this depends on which congestion model is used. A crucial point here is whether one assumes constant or variable returns to scale. Nonetheless, all models point to a rise in congestion between 2001/2 and 2003/4, and this may well be a result of the rapid growth that occurred in this period. All models also record a sharp drop in mean technical efficiency in 2003/4. A possible explanation of the absence of a clear-cut trend in congestion is that the student : staff ratio in these universities was relatively stable in the decade under review, rising only gently from 2000/1 onwards.British universities; congestion; DEA

Comparative evaluation of public universities in Malaysia using data envelopment analysis

Applications of Data Envelopment Analysis (DEA) for the assessment of performance of universities have been widely reported in the literature. Often the number of universities under the assessment is relatively small compared to the number of performance measures (inputs and outputs) used in the analysis, which leads to a low discriminating power of DEA models on efficiency scores. The main objective of this thesis is the development of improved DEA models that overcome the above difficulty, using a sample of public universities in Malaysia as an illustrative application. The proposed new approach combines the recently introduced Hybrid returns to scale (HRS) model with the use of additional information about the functioning of universities stated in the form of production trade-offs. The new model developed in this thesis, called Hybrid returns to scale model with trade-offs (HRSTO), is applied to a sample of eighteen universities, which is considered to be a very small sample for the DEA methodology. Our results show that, in contrast with standard DEA models, the new model is perfectly suitable for such samples and discriminates well between good and bad performers. The proposed combined use of HRS model with production trade-offs is a novel methodology that can be used in other applications of DEA. Overall, the thesis makes several contributions of the theory and practice of DEA. First, for the first time, it is shown that the higher education sector satisfies the assumptions and can be modelled using the proposed HRSTO model. Second, also for the first time, it is shown that production trade-offs can be assessed for such applications and the methodology of their assessment has been developed and used in the thesis. Third, it is demonstrated that the HRSTO model significantly improves the discriminating power of analysis compared to standard DEA models, which is particularly important for small data sets. Fourth, it is concluded that the HRS model is further improved if production trade-offs are used. Fifth, by experimenting with different specific values of production trade-offs, it is shown that even the most conservative estimates of trade-offs notably improve the model. Finally, our results contribute to the more general discussion of the performance of universities in Malaysia and identification of the best performers among them

Some Computational Issues in Data Envelopment Analysis

This paper reflects the author\u27s experiences in developing various DEA software, including models such as CCR, BCC, general returns to scale, categorical inputs and outputs and different systems. All the software deals with the dual side of the original CCR model and no non-Archimedian small number is used

An evaluation of the world\u27s major airlines\u27 technical and environmental performance

This study is the first to use bootstrapped data envelopment analysis (DEA) models under variable returns to scale in order to examine both the environmental and technical efficiency of airlines. Using the regional classification of the International Air Transport Association (IATA), we chose 48 of the world\u27s major full-service and low-cost carriers from six different regions, and then estimated their performance over the period 2007- 2010. Our empirical results show that many of the most technically efficient airlines are from China and North Asia, while many of the most environmentally efficient airlines are from Europe. We also found that although the number of environmentally oriented full-service airlines is increasing, low-cost carriers are still more environmentally oriented. Our findings also show that almost all the low-cost carriers are technically operating under increasing returns to scale in all the studied years. However, this result was quite the opposite of what we found for the largest airlines