Factors In Data Envelopment Analysis Research Articles

A robust DEA model in the presence of uncertain integer-valued parameters

PurposeUncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors.Design/methodology/approachThis research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model.FindingsIn this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities.Originality/valueThis study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

Using Data Analytics to Improve Nursing Home Quality.

There exists an array of quality performance measures for nursing homes. They can confuse consumers, administrators, and government regulators. Our methodology provides a unified multidimensional evaluation. To present a methodology to perform a multidimensional assessment of each nursing home within any specified group of nursing homes to aid policy makers, administrators, and consumers with a clear, easy-to-interpret evaluation of a nursing home quality performance. We use data envelopment analysis (DEA) to integrate several quality measures into a comprehensive benchmarking model. We present statewide results comparing DEA performance scores with the Five-Star rating using data from New York State (NYS) Department of Health. In total, 212 of the 526 nursing homes performed as well as possible. Public nursing homes are most likely to lie on the frontier and have the highest average performance scores. The relationship between the DEA-based performance scores and the NYS Five-Star quality ratings is very weak. DEA is a comprehensive methodology for measuring nursing home quality. The DEA factor performance scores provide detailed information for individual nursing homes, enabling administrators to benchmark their facility's quality performance and to focus quality improvement efforts more effectively.

Measuring the Efficiency of Community Colleges Using Super Efficiency Approach for the Case of Non-discretionary Factors in Data Envelopment Analysis with Sensitivity Analysis

Malaysian community colleges play a significant role in achieving Malaysia's vision to be a developed country in 2020. For this reason, their efficiency should appropriately be measured. However, their efficiency measurement using a conventional data envelopment analysis (DEA) model is not appropriate since some of their inputs; e.g., entrant and enrolment students are non-discretionary while a part of output of their graduate employability is discretionary. This paper thus proposes an alternative approach of super efficiency slack-based measure for the case of non-discretionary factors in DEA. The proposed approach was used to evaluate the efficiency of 25 main campuses of Malaysian community colleges from 2012 to 2013. The results support the decision maker of Malaysian community colleges to discriminate and rank efficient and inefficient community colleges in the presence of both super efficiency and non-discretionary factors. The significance of inputs-outputs on efficiency status was tested by sensitivity analysis.

Measuring the efficiency of community colleges using super efficiency approach for the case of non-discretionary factors in data envelopment analysis with sensitivity analysis

Measuring the efficiency of community colleges using super efficiency approach for the case of non-discretionary factors in data envelopment analysis with sensitivity analysis

The desirable input of undesirable factors in data envelopment analysis

Recent papers have provided a number of overviews in connection with the fast growing literature on bad outputs in Data Envelopment Analysis (DEA), such as defective products, emissions and waste. However, there does not seem to exist any comprehensive overview of the opposite phenomenon, particularly not regarding DEA, namely of bads as undesirable objects or factors which are desirable input (flow) into transformation processes, e.g. into waste incineration. Moreover, the terms ‘bad input’ and ‘(un-)desirable input/factor’ are not clearly defined. We use a purely preference-based notion for the desirability of inputs and outputs. A systematic literature search reveals only 22 DEA articles which explicitly address the (desirable) input of bads as original undesirable factors, i.e. as input into the first stage of a single- or multi-stage process. Their detailed analysis shows that current approaches are based on two core ideas involving various efficiency measures. Only four papers deal with real applications of original undesirable factors, namely waste water treatment. Moreover, those disposability assumptions for DEA models often critically discussed in relation to bad outputs (e.g. weak disposability) are not used in these papers, presumably because the processes modelled are themselves disposal processes. Finally, we exemplarily demonstrate how DEA models with bads as inputs (and outputs) can be systematically derived from a decision-theoretic generalization of DEA methodology proposed in the literature.

Generalized DEA: an approach for supporting input/output factor determination in DEA

Purpose The determination of input and output factors is a well-known source of pitfalls when applying data envelopment analysis (DEA). The purpose of this paper is to contribute to overcome the respective problems of input/output factor determination related to factor selection, dual-role factors and undesirable factors. Design/methodology/approach The problems of input/output factor determination are discussed from a goal-oriented perspective, shedding a new light on the role of input/output factors in DEA. This is exemplified by the case of measuring pharmacy stores’ efficiency concerning their goal of customer retention. Findings The findings suggest to applying a generalized DEA (GDEA). The three steps of this approach include the development of a system of objectives, the derivation of corresponding performance criteria as well as the construction of cost and benefit functions. These functions build the basis for GDEA models, of which one is exemplarily described and applied to the customer retention case. Research limitations/implications While traditional DEA implicitly assumes linear cost and benefit functions, GDEA requires to explicitly specifying these functions. In doing so, the approach contributes to solve the problem of factor selection, the problem of dual-role factors and the problem of undesirable factors. Practical implications For determining input/output factors in a consistent and transparent manner, it is recommended to apply GDEA in practical benchmarking studies. Originality/value GDEA integrates well-known concepts of multi-criteria decision making into traditional DEA. The new approach helps to cope with the challenges of input/output factor determination in DEA.

Decision Tree Analysis for Selection of Factors in DEA: An Application to Banks in India

The body of research assessing the technical efficiency of decision-making units (DMUs) with a special reference to Indian banking sector suggests that a majority of these studies have employed data envelopment analysis (DEA) for measuring technical efficiency with two-input/two-output or three-input/three-output or models with several combinations of various input and output factors. In almost all the cases, the choice of input and output factors was based on the judgement of the researchers. They lack the rigorous justification pertaining to the appropriateness of or the efficacy of such input– output factors to measure the true technical efficiency of the DMUs. This study evaluates 11 select DEA models representing the intermediary approach with various input–output factors and investigates the relationship between the computed efficiency scores and a single performance measure of DMUs by using decision tree (DT) analysis. The objective is to find a better criterion using a scientific method of input–output selection to effectively assess the true efficiency of the DMUs. The article analyzes the relative efficiency scores of 57 DMUs (representing private, public and foreign scheduled commercial banks) from 11 different variable returns to scale (VRS) DEA models with input orientation. The results indicate that 2 out of the 11 models are the most appropriate to measure relative efficiency when intermediary approach is considered to evaluate the banks. This leads to the conclusion that the management of the banks in our study should focus their efforts and resources on the input–output factors from these two models to improve efficiency and increase profitability.

An evaluation of energy-environment-economic efficiency for EU, APEC and ASEAN countries: Design of a Target-Oriented DFM model with fixed factors in Data Envelopment Analysis

This paper aims to offer an advanced assessment methodology for sustainable national energy-environment-economic efficiency strategies, based on an extended Data Envelopment Analysis (DEA). The use of novel efficiency-improving approaches based on DEA originates from the so-called Distance Friction Minimisation (DFM) method. To design a feasible improvement strategy for low-efficiency DMUs, we develop here a Target-Oriented (TO) DFM model. However, in many real-world cases input factors may not be flexibly adjusted in the short run. In this study, we integrate the TO-DFM model with a fixed (inflexible) factor (FF) approach to cope with such more realistic circumstances. Super-efficiency DEA is next used in our comparative study on the efficiency assessment of energy-environment-economic targets for the EU, APEC and ASEAN (A&A) countries, employing appropriate data sets from the years 2003 to 2012. We consider two inputs (primary energy consumption and population) and two outputs (CO2 and GDP), including a fixed input factor (viz. population). On the basis of our DEA analysis results, EU countries appear to exhibit generally a higher efficiency than A&A countries. The above-mentioned TO-DFM-FF projection model is able to address realistic circumstances and requirements in an operational sustainability strategy for efficiency improvement in inefficient countries in the A&A region.

Multi-dimensional Nondiscretionary Factors in Data Envelopment Analysis: A Slack-Based Measure

Various extension using data envelopment analysis (DEA) are available in the literature for performance measurement in public sector. The existence of multiple non- discretionary factors in DEA based public sector models leads to overestimation of the efficiency. This paper proposes a two-step procedure to handle non-discretionary factors in DEA models. In the first step, the multiple non-discretionary factors are transformed into a single artificial factor and then, using a slack-based model the performance assessment is done. To highlight the comparison, an analysis using simulated data is performed. The results show that the proposed two-stage approach is relatively better than existing approaches when we apply the slack based measure of efficiency.

Revisiting dual-role factors in data envelopment analysis: derivation and implications

Data Envelopment Analysis (DEA) is a mathematical programming method to evaluate relative performance. Typical DEA studies consider a production process transforming inputs to outputs. In some cases, however, some factors can be both inputs and outputs simultaneously and are termed dual-role factors. For example, research funding can be an input that strengthens a university's academic performance and the actual funds can be an output. This article investigates the problem of how to incorporate dual-role factors in DEA. Rather than proposing an ad hoc evaluation model directly, this article considers the concept of “joint technology,” two individual production processes acting in common by summarizing the intuitive thinking. The efficiency evaluation models, based on variant assumptions, thus can be axiomatically derived, validated, and extended. How to determine the input/output tendency of a dual-role factor based on the evaluating results is shown and explained from different aspects. It is concluded that the tendency is a property on the projected boundary, not the data point itself.

ENVIRONMENTAL EFFICIENCY OF CHINESE PAPER MILLS ALONG HUAI RIVER: A DATA ENVELOPMENT ANALYSIS (DEA) BASED STUDY

To deal with the undesirable factors in Data Envelopment Analysis (DEA), a non-linear DEA model was previously developed for a paper production system, where the desirable outputs are increased and the undesirable outputs are decreased for efficiency improvement. To convert the proposed non-linear model into a linear one, a linear approximation to the non-linear constraint is used and an approximate efficiency score is obtained. In this paper, we propose a new method to solve the non-linear programming problem and calculate the efficiency scores accurately, in which a second-order cone programming (SOCP) is defined and applied to transfer the non-linear programming model into a linear one. We applied the proposed model to measure the environmental performance of 30 paper mills along the Huai River in China. It was found that the efficiency scores obtained by our model is obvious different with the ones by approximate models.

Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

In the last decade, ranking units in data envelopment analysis (DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. Also, some of these data may be known only in terms of ordinal relations. While the models developed in the past are interesting and meaningful, they didn't consider both undesirable and ordinal factors at the same time. In this research, we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models. This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units (DMUs) with undesirable and ordinal data. For this purpose, we transform the ordinal data into definite data, and then we consider each undesirable input and output as desirable output and input, respectively. Finally, an application that shows the capability of the proposed method is illustrated.

Revisiting Dual-Role Factors in DEA: Derivation and Implications

Data Envelopment Analysis (DEA) is a mathematical programming method to evaluate relative performance. Typical DEA studies consider a production process transforming inputs to outputs. In some cases, however, some factors can be both inputs and outputs simultaneously, and are termed dual-role factors. For example, research funding can be an input that strengthens a university’s academic performance and the actual funds can be an output. This paper investigates the problem of how to incorporate dual-role factors in DEA. Rather than proposing an ad hoc evaluation model directly, we propose a joint technology by summarizing the intuitive thinking. The efficiency evaluation models, based on variant assumptions, thus can be axiomatically derived, validated and extended. We show how to determine the input/output tendency of a dual-role factor based on the evaluating results and explained from different aspects. We conclude that the tendency is a property on the projected boundary, not the data point itself.

Qualitative factors in data envelopment analysis: A fuzzy number approach

Qualitative factors are difficult to mathematically manipulate when calculating the efficiency in data envelopment analysis (DEA). The existing methods of representing the qualitative data by ordinal variables and assigning values to obtain efficiency measures only superficially reflect the precedence relationship of the ordinal data. This paper treats the qualitative data as fuzzy numbers, and uses the DEA multipliers associated with the decision making units (DMUs) being evaluated to construct the membership functions. Based on Zadeh’s extension principle, a pair of two-level mathematical programs is formulated to calculate the α-cuts of the fuzzy efficiencies. Fuzzy efficiencies contain more information for making better decisions. A performance evaluation of the chemistry departments of 52 UK universities is used for illustration. Since the membership functions are constructed from the opinion of the DMUs being evaluated, the results are more representative and persuasive.

An Efficiency-Based Multicriteria Strategic Planning Model for Ambulatory Surgery Centers

Ambulatory surgery centers (ASCs) provide a low-cost alternative to traditional inpatient care. In addition, with health care reform imminent, it is likely that many currently uninsured people will soon acquire health care coverage, significantly increasing the demand for health services. ASCs are among the providers that can expect to see a substantial amount of this new pent-up demand and, therefore, ASCs are likely to continue their current growth into the foreseeable future. Those ASCs that plan accordingly by optimizing procedure mix and volume will benefit most from the increased demand. We propose a two-stage efficiency-based multicriteria decision model to guide an ASC in identifying its optimal procedure mix. The first stage uses Data Envelopment Analysis (DEA) to calculate the efficiency of each procedure based on the resources required to perform the procedure, the revenue it generates, and its risk of complications. The second stage uses the DEA factor efficiency scores in a bottleneck program to optimize the mix of procedures while satisfying the ASC's resource and operational constraints. The criteria are to (1) maximize reimbursement while (2) minimizing the total number of complications. We demonstrate the approach using a data set based in part on data from an actual ASC.

A slacks-based measure of efficiency for the case of exogenously fixed factors

Standard data envelopment analysis (DEA) models assume that all inputs and outputs can be varied at the discretion of management or other users. In any realistic situation, however, there may exist “exogenously fixed” or non-discretionary factors that are beyond the control of a DMU’s management, which also need to be considered. This paper proposes a slacks-based measure (SBM) of efficiency in the presence of non-discretionary factors in data envelopment analysis. This scalar measure deals directly with the discretionary input excess and the discretionary output shortfall of the decision making units (DMUs) concerned. The new measure has a close connection with the measure proposed by Banker and Morey (1986). We then apply this measure to a real world data set.

Modeling undesirable factors in data envelopment analysis

Data envelopment analysis is a mathematical programming technique for identifying efficient frontiers for peer decision making units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. In the current paper, we present a data envelopment analysis (DEA) model in which can be used to improve the relative performance via increasing undesirable inputs and decreasing undesirable outputs.

Dual-role factors in data envelopment analysis

This paper presents a methodology for dealing with performance evaluation settings where factors can simultaneously play both input and output roles. Model structures are developed for classifying Decision-Making Units (DMUs) into three groups according to whether such a factor is behaving like an output, an input, or is in equilibrium, neither wanting to lose or gain any of the factors. We connect these ideas to those involving increasing, decreasing and constant returns to scale. Examples of factors that play this dual-role are: trainees in organizations, such as nurses, medical students, and doctoral students; awards to scholars or university departments; certain revenue—generating transactions in banks, and so on. We apply the model to the analysis of a set of university departments. In some settings, a dual-role factor may be one that can be reallocated, such as would be the case when DMUs are managed by a central authority. We develop the appropriate model structures to permit such a reallocation. We present two such structures, with the first involving reallocation from an existing allocation, and the second, a zero-base allocation.

Non-discretionary and discretionary factors and scale in data envelopment analysis

This paper discusses the interpretation of exogenously fixed, non-discretionary factors in data envelopment analysis (DEA) and suggests a generalised model for incorporating different types of inputs and outputs in DEA. The paper first compares two approaches to the inclusion of continuous non-discretionary factors in a one-stage model, one introduced by Banker and Morey [Operat. Res. 34 (4) (1986) 513–521] and the other by Lovell [TOP 2 (1994) 175–248] and Ruggiero [Eur. J. Operat. Res. 90 (1996) 553–565]. The approaches are compared theoretically, on the basis of axiomatic systems, and empirically, on the basis of examples and simulated data. The key difference is that some models require non-discretionary factors to be scale independent, i.e. indices, and some require them to be scale dependent, i.e. volume measures. Also, the returns to scale properties vary depending on the manner in which non-discretionary factors are treated. In practice, we may want to utilise the properties of the different models simultaneously. A generalised DEA model allowing for this possibility is presented.

Data Envelopment Analysis with Preference Structure

It is important to consider the decision making unit (DMU)'s or decision maker's preference over the potential adjustments of various inputs and outputs when data envelopment analysis (DEA) is employed. On the basis of the so-called Russell measure, this paper develops some weighted non-radial CCR models by specifying a proper set of ‘preference weights’ that reflect the relative degree of desirability of the potential adjustments of current input or output levels. These input or output adjustments can be either less or greater than one; that is, the approach enables certain inputs actually to be increased, or certain outputs actually to be decreased. It is shown that the preference structure prescribes fixed weights (virtual multiplier bounds) or regions that invalidate some virtual multipliers and hence it generates preferred (efficient) input and output targets for each DMU. In addition to providing the preferred target, the approach gives a scalar efficiency score for each DMU to secure comparability. It is also shown how specific cases of our approach handle non-controllable factors in DEA and measure allocative and technical efficiency. Finally, the methodology is applied with the industrial performance of 14 open coastal cities and four special economic zones in 1991 in China. As applied here, the DEA/preference structure model refines the original DEA model's result and eliminates apparently efficient DMUs.