数据不确定的鲁棒数据包络分析方法(英文)

本文研究了输出参数不确定的数据包络分析(DEA)模型.利用鲁棒优化方法,建立了一个鲁棒DEA模型,通过数值试验表明了该模型在有效性评价和排序方面的可靠性.本文的模型可处理分布未知的不确定数据,与已有的只考虑对称分布不确定参数的模型相比,适用范围更广.     

A new robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.     

Sensitivity and stability analysis in fuzzy data envelopment analysis

As a useful management and decision tool, data envelopment analysis (DEA) has become a pop area of research. One of the topics of interests in DEA is sensitivity and stability analysis of decision making units (DMUs). Due to the uncertainty of the data in real life, this paper will give some DEA models in fuzzy environment. It is followed by a series analysis of sensitivity and stability for all DMUs. Finally a numerical example will be presented to give an illustration of the sensitivity and stability analysis.     

A robust data envelopment analysis model with different scenarios

Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company.     

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.     

Context-based competition strategy and performance analysis with fixed-sum outputs: an application to banking sector

In the prior literature on performance measurement of firms with fixed-sum outputs, an equilibrium-efficient frontier is constructed. This paper shows that a single equilibrium-efficient frontier needs a significant trade-off between efficient and inefficient firms, and this may be impossible in practical applications. We develop a data envelopment analysis (DEA) model to construct multiple equilibrium-efficient frontiers in the presence of fixed-sum outputs. The approach uses context-dependent DEA that refers to a DEA approach where a set of firms are assessed against a particular assessment context. Numerical examples are used to illustrate the applicability of the approach.     

Benchmarking the operating efficiency of Asia container ports

The aim of this paper is to explore the operating efficiency, the scale efficiency targets, and the variability of DEA efficiency estimates of Asian container ports. This study applies data envelopment analysis (DEA) with the traditional DEA model, most productive scale size concept, returns to scale approach, and bootstrap method to assess the operating performance, set scale efficient targets, and determine efficiency rankings of Asian container ports. The results of this study can provide port managers with insights into resource allocation, competitive advantages, as well as optimization of the operating performance. The potential applications and strengths of DEA in assessing the Asian container ports are highlighted.     

A survey of data envelopment analysis in energy and environmental studies

Data envelopment analysis has gained great popularity in energy and environmental (E&E) modeling in recent years. In this paper, we present a literature survey on the application of data envelopment analysis (DEA) to E&E studies. We begin with an introduction to the most widely used DEA techniques, which is followed by a classification of 100 publications in this field. The main features observed are summarized. Issues related to the selection of DEA models in E&E studies are discussed.     

Sensitivity analysis of efficient units in the presence of non-discretionary inputs

Discretionary models of data envelopment analysis (DEA) 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 discusses and reviews the use of super-efficiency approach in data envelopment analysis (DEA) sensitivity analyses when some inputs are exogenously fixed. Super-efficiency data envelopment analysis (DEA) model is obtained when a decision making unit (DMU) under evaluation is excluded from the reference set. In this paper by means of modified Banker and Morey’s (BM hereafter) model [R.D. Banker, R. Morey, Efficiency analysis for exogenously fixed inputs and outputs, Operations Research 34 (1986) 513–521], in which the test DMU is excluded from the reference set, we are able to determine what perturbations of discretionary data can be tolerated before frontier DMUs become nonfrontier.     

Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis

It has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units. This paper proposes a new methodology for ranking decision making units (DMUs). The new methodology ranks DMUs by imposing an appropriate minimum weight restriction on all inputs and outputs, which is decided by a decision maker (DM) or an assessor in terms of the solutions to a series of linear programming (LP) models that are specially constructed to determine a maximin weight for each DEA efficient unit. The DM can decide how many DMUs to be retained as DEA efficient in final efficiency ranking according to the requirement of real applications, which provides flexibility for DEA ranking. Three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between DMUs, particularly DEA efficient units.     

Sensitivity analysis of DEA models for simultaneous changes in all the data

In data envelopment analysis (DEA) efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for the basic DEA models, such as, those proposed by Charnes, Cooper and Rhodes (CCR), Banker, Charnes and Cooper (BCC) and additive models, when variations in the data are simultaneously considered for all DMUs. By means of modified DEA models, in which the specific DMU under examination is excluded from the reference set, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalises the usual sensitivity analysis approach developed in which perturbations of the data are only applied to the test DMU while all the remaining DMUs remain fixed. In our framework data are allowed to vary simultaneously for all DMUs across different subsets of inputs and outputs. We study the relations of the infeasibility of modified DEA models employed and the robustness of DEA models. It is revealed that the infeasibility means stability. The empirical applications demonstrate that DEA efficiency classifications are robust with respect to possible data errors, particularly in the convex DEA case.     

Duality in data envelopment analysis under constant returns to scale

This paper explores duality in models of data envelopment analysis(DEA) for assessing the productive efficiencies of organizationalunits where efficient production is characterized by constantreturns to scale. The paper identifies dualityof the spacesin which efficiency is measured and discusses the practicalimplications of duality in DEA.     

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

Methods of critical value reduction for type-2 fuzzy variables and their applications

A type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space; it is an appropriate tool for describing type-2 fuzziness. This paper first presents three kinds of critical values (CVs) for a regular fuzzy variable (RFV), and proposes three novel methods of reduction for a type-2 fuzzy variable. Secondly, this paper applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops a new class of generalized credibility DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA model into its equivalent parametric programming problem, in which the parameters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers. Finally, one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed DEA model.     

Cost,Revenue and Profit Efficiency Models in Generalized Fuzzy Data Envelopment Analysis

One of the most important information given by data envelopment analysis models is the cost, revenue and profit efficiency of decision making units (DMUs). Cost efficiency is defined as the ratio of minimum costs to current costs, while revenue efficiency is defined as the ratio of maximum revenue to current revenue of the DMU. This paper presents a framework where data envelopment analysis (DEA) is used to measure cost, revenue and profit efficiency with fuzzy data. In such cases, the classical models cannot be used, because input and output data appear in the form of ranges. When the data are fuzzy, the cost, revenue and profit efficiency measures calculated from the data should be uncertain as well. Fuzzy DEA models emerge as another class of DEA models to account for imprecise inputs and outputs for DMUs. Although several approaches for solving fuzzy DEA models have been developed, numerous deficiencies including the $\alpha$-cut approaches and types of fuzzy numbers must still be improved. This scheme embraces evaluation method based on vector for proposed fuzzy model. This paper proposes generalized cost, revenue and profit efficiency models in fuzzy data envelopment analysis. The practical application of these models is illustrated by a numerical example.     

E-DEA: Enhanced data envelopment analysis

Data envelopment analysis (DEA) has enjoyed a wide range of acceptance by researchers and practitioners alike as an instrument of performance analysis and management since its introduction in 1978. Many formulations and thousands of applications of DEA have been reported in a considerable variety of academic and professional journals all around the world. Almost all of the formulations and applications have basically centered at the concept of “relative self-evaluation”, whether they are single or multi-stage applications. This paper suggests a framework for enhancing the theory of DEA through employing the concept of “relative cross-evaluation” in a multi-stage application context. Managerial situations are described where such enhanced-DEA (E-DEA) formulations had actually been used and could also be potentially most meaningful and useful.     

Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach

Designing a supply chain network (SCN) is an important issue for organizations in competitive markets. In this paper, a novel robust SCN that considers the efficiencies and costs simultaneously is proposed. In order to estimate the efficiency of the producers and distributors, data envelopment analysis (DEA) model is incorporated into SCN. Moreover, to handle the uncertainty in data, a scenario-based robust optimization approach is applied. The proposed model finds out the efficient location of producers and distributors and determines the amount of purchases from each supplier in uncertain conditions. To illustrate the application of the proposed model, a numerical example is solved and results are analyzed.     

Dominance stochastic models in data envelopment analysis

In this paper stochastic models in data envelopment analysis (DEA) are developed by taking into account the possibility of random variations in input-output data, and dominance structures on the DEA envelopment side are used to incorporate the modelbuilder's preferences and to discriminate efficiencies among decision making units (DMUs). The efficiency measure for a DMU is defined via joint dominantly probabilistic comparisons of inputs and outputs with other DMUs and can be characterized by solving a chance constrained programming problem. Deterministic equivalents are obtained for multivariate symmetric random errors and for a single random factor in the production relationships. The goal programming technique is utilized in deriving linear deterministic equivalents and their dual forms. The relationship between the general stochastic DEA models and the conventional DEA models is also discussed.     

Measuring the performance of manufacturing firms with super slacks based model of data envelopment analysis: An application of 500 major industrial enterprises in Turkey

Data envelopment analysis (DEA) is a mathematical programming technique which has a wide application area. There are many applications of DEA to measure firms’ performance. Balance sheet data is frequently used in order to measure performance of firms through DEA. So it is the characteristic of balance sheets that assets and liabilities amount to the same value. When the data for inputs and outputs are selected from both assets and liabilities sections of the balance sheet, it is important that more attention be paid to the analysis since values assigned to inputs and outputs could be included in assets and liabilities at the same time. Such a situation could create problems concerning the conclusions drawn as a result of analysis.     

Duality,efficiency computations and interpretations in imprecise DEA

Data envelopment analysis (DEA) has proven to be a useful tool for assessing efficiency or productivity of organizations which is of vital practical importance in managerial decision making. While DEA assumes exact input and output data, the development of imprecise DEA (IDEA) broadens the scope of applications to efficiency evaluations involving imprecise information which implies various forms of ordinal and bounded data possibly or often occurring in practice. The primary purpose of this article is to characterize the variable efficiency in IDEA. Since DEA describes a pair of primal and dual models, also called envelopment and multiplier models, we can basically consider two IDEA models: One incorporates imprecise data into envelopment model and the other includes the same imprecise data in multiplier model. The issues of rising importance are thus the relationships between the two models and how to solve them. The groundwork we will make includes a duality study, which makes it possible to characterize the efficiency solutions from the two models and link with the efficiency bounds and classifications that some of the published IDEA studies have done. The other purposes are to present computational aspects of the efficiency bounds and how to interpret the efficiency solutions. The computational method developed here extends the previous IDEA method to effectively incorporate a more general form of strict ordinal data and partial orders in its framework, which in turn overcomes some drawbacks of the previous approaches. The interpretation of the resulting efficiency is also important but we have never seen it before.