Inequality trends in health and future health risk among English children and young people, 1999-2009.

To investigate trends in health inequality among children and young people between 1999 and 2009, using outcomes consistent with the current NHS reforms

A Modified Super-Efficiency in the Range Directional Model

The range directional model (RDM) relaxes the assumption of non-negativity of inputs and outputs in the conventional data envelopment analysis (DEA) with the aim of evaluating the efficiency of a decision-making unit (DMU) when some data are negative. Although the concept of super-efficiency in the RDM contributes to enhancing discriminatory power, the formulated model may lead to the infeasibility problem for some efficient DMUs. In this paper, we modify the super-efficiency RDM (SRDM) model to overcome the infeasibility problem occurring in such cases. Our method leads to a complete ranking of the DMUs with negative data for yielding valuable insights that aid decision makers to better understand the findings from a performance evaluation process. The contribution of this paper is fivefold: (1) we detect the source of infeasibility problems of SRDM in the presence of negative data, (2) the proposed model in this study yields the SRDM measures regardless of feasibility or infeasibility of the model, (3) when feasibility occurs, the modified SRDM model results in the scores that are the same as the original model, (4) we differentiate the efficient units to improve discriminatory power in SRDM, and (5) we provide two numerical examples to elucidate the details of the proposed method

Benchmarking with network DEA in a fuzzy environment

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Benchmarking is a powerful and thriving tool to enhance the performance and profitabilities of organizations in business engineering. Though performance benchmarking has practically and theoretically developed in distinct fields such as banking, education, health and so on, supply chain benchmarking across multiple echelons that includes certain characteristics such as intermediate measure differs from other fields. In spite of incremental benchmarking activities in practice, there is the dearth of a unified and effective guideline for benchmarking in organizations. Amongst the benchmarking tools, data envelopment analysis (DEA) as a non-parametric technique has been widely used to measure the relative efficiency of firms. However, the conventional DEA models that are bearing out precise input and output data turn out to be incapable of dealing with uncertainty, particularly when the gathered data encompasses natural language expressions and human judgements. In this paper, we present an imprecise network benchmarking for the purpose of reflecting the human judgments with the fuzzy values rather than precise numbers. In doing so, we propose the fuzzy network DEA models to compute the overall system scale and technical efficiency of those organizations whose internal structure is known. A classification scheme is presented based upon their fuzzy efficiencies with the aim of classifying the organizations. We finally provide a case study of the airport and travel sector to elucidate the details of the proposed method in this study

A new efficiency evaluation approach with rough data: An application to Indian fertilizer

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In the world of chaos, nothing is certain. In such an unpredictable world, measuring the efficiency of any individual is inevitable. In a conventional data envelopment analysis (DEA) model, exact input and output quantity data are needed to measure the relative efficiencies of homogeneous decision-making units (DMUs). However, in many real-world applications, the exact knowledge of data might not be available. The rough set theory allows for handling this type of situation. This paper tries to construct a rough DEA model by combining conventional DEA and rough set theory using optimistic and pessimistic confidence values of rough variables, all of which help provide a way to quantify uncertainty. In the proposed method, the same set of constraints (production possibility sets) is employed to build a unified production frontier for all DMUs that can be used to properly assess each DMU's performance in the presence of rough input and output data. Besides, a ranking system is presented based on the approaches that have been proposed. In the presence of uncertain conditions, this article investigates the efficiency of the Indian fertilizer supply chain for over a decade. The results of the proposed models are compared to the existing DEA models, demonstrating how decision-makers can increase the supply chain performance of Indian fertilizer industries

Data Envelopment Analysis Models with Ratio Data: A revisit

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The performance evaluation of for-profit and not-for-profit organisations is a unique tool to support the continuous improvement process. Data envelopment analysis (DEA) is literally known as an impeccable technique for efficiency measurement. However, the lack of the ability to attend to ratio measures is an ongoing challenge in DEA. The convexity axiom embedded in standard DEA models cannot be fully satisfied where the data set includes ratio measures and the results obtained from such models may not be correct and reliable. There is atypical approach to deal with the problem of ratio measures in DEA, in particular when numerators and denominators of ratio data are available. In this paper, we show that the current solutions may also fail to preserve the principal properties of DEA as well as to instigate some other flaws. We also make modifications to explicitly overcome the flaws and measure the performance of a set of operating units for the input-and output orientations regardless of assumed technology.Finally, a case study in the education sector is presented to illustrate the strengths and limitations of the proposed approach

The role of multiplier bounds in fuzzy data envelopment analysis

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The non-Archimedean epsilon ε is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of ε can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach

Measurement of Returns-to-Scale using Interval Data Envelopment Analysis Models

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkThe economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterized by intervals. For instance, the heat losses of the combined production of heat and power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study

Fuzzy Efficiency Measures in Data Envelopment Analysis Using Lexicographic Multiobjective Approach

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature

An extended multiple criteria data envelopment analysis model

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries

Efficiency Evaluation in Two-stage Data Envelopment Analysis under a Fuzzy Environment: A Common-Weights Approach

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Data envelopment analysis (DEA) has been genuinely known as an impeccable technique for efficiency measurement. In practice, since many production systems such as broadcasting companies, banking and R&D activities include two processes connected in series, we have need of utilizing two-stage DEA models to identify the sources of inefficiency and explore in turn appropriate options for improving performance. The lack of the ability to generate the actual weights is not only an ongoing challenge in traditional DEA models, it can have serious repercussion for the contemporary DEA models (e.g., two-stage DEA). This paper presents a common-weights method for two-stage structures that allows us to consider equality of opportunity in a fuzzy environment when evaluating the system efficiency and the component process efficiencies. The proposed approach first seeks upper bounds on factor weights and then determines a set of common weights by a single linear programming problem. We illustrate the approach with a data set taken from the literature