基于C~2R模型的广义链式网络DEA模型

传统网络DEA方法是将传统DEA方法评价过程中的"黑箱"打开,考虑输入到输出的中间环节,对生产过程中的各个环节分别评价。传统网络DEA方法获得的是相对于有效决策单元评价的结果,但有时可能要相对于非有效决策单元或者非决策单元进行评价,传统网络DEA方法无法解决该类问题。为此给出相对于非有效决策单元或者非决策单元进行评价的基于C~2R模型的广义链式网络DEA模型,并探讨相关性质.     

Ranking ranges in cross-efficiency evaluations

The existence of alternate optima for the DEA weights may reduce the usefulness of the cross-efficiency evaluation, since the ranking provided depends on the choice of weights that the different DMUs make. In this paper, we develop a procedure to carry out the cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into consideration all the possible choices of weights that all the DMUs can make, and yields for each unit a range for its possible rankings instead of a single ranking. This range is determined by the best and the worst rankings that would result in the best and the worst scenarios of each unit across all the DEA weights of all the DMUs. This approach might identify good/bad performers, as those that rank at the top/bottom irrespective of the weights that are chosen, or units that outperform others in all the scenarios. In addition, it may be used to analyze the stability of the ranking provided by the standard cross-efficiency evaluation.     

Dominance relations and ranking of units by using interval number ordering with cross-efficiency intervals

This paper proposes an approach to the cross-efficiency evaluation that considers all the optimal data envelopment analysis (DEA) weights of all the decision-making units (DMUs), thus avoiding the need to make a choice among them according to some alternative secondary goal. To be specific, we develop a couple of models that allow for all the possible weights of all the DMUs simultaneously and yield individual lower and upper bounds for the cross-efficiency scores of the different units. As a result, we have a cross-efficiency interval for the evaluation of each unit. Existing order relations for interval numbers are used to identify dominance relations among DMUs and derive a ranking of units based on the cross-efficiency intervals provided. The approach proposed may also be useful for assessing the stability of the cross-efficiency scores with respect to DEA weights that can be used for their calculation.     

A DEA based procedure for the selection of subgroups

Data Envelopment Analysis (DEA) is a nonparametric technique originally conceived for efficiency analysis of a set of units. The main characteristic of DEA based procedures is endogenous determination of weighting vectors, i.e., the weighting vectors are determined as variables of the model. Nevertheless, DEA’s applications have vastly exceeded its original target. In this paper, a DEA based model for the selection of a subgroup of alternatives or units is proposed. Considering a set of alternatives, the procedure seeks to determine the group that maximizes overall efficiency. The proposed model is characterized by free selection of weights and allows the inclusion of additional information, such as agent’s preferences in terms of relative importance of the variables under consideration or interactions between alternatives. The solution is achieved by computing a mixed-integer linear programming model. Finally, the proposed model is applied to plan the deployment of filling stations in the province of Seville (Spain).     

DEA models for minimizing weight disparity in cross-efficiency evaluation

Cross-efficiency evaluation is a commonly used approach for ranking decision-making units (DMUs) in data envelopment analysis (DEA). The weights used in the cross-efficiency evaluation may sometimes differ significantly among the inputs and outputs. This paper proposes some alternative DEA models to minimize the virtual disparity in the cross-efficiency evaluation. The proposed DEA models determine the input and output weights of each DMU in a neutral way without being aggressive or benevolent to the other DMUs. Numerical examples are tested to show the validity and effectiveness of the proposed DEA models and illustrate their significant role in reducing the number of zero weights.     

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.     

Fixed cost and resource allocation based on DEA cross-efficiency

In many managerial applications, situations frequently occur when a fixed cost is used in constructing the common platform of an organization, and needs to be shared by all related entities, or decision making units (DMUs). It is of vital importance to allocate such a cost across DMUs where there is competition for resources. Data envelopment analysis (DEA) has been successfully used in cost and resource allocation problems. Whether it is a cost or resource allocation issue, one needs to consider both the competitive and cooperative situation existing among DMUs in addition to maintaining or improving efficiency. The current paper uses the cross-efficiency concept in DEA to approach cost and resource allocation problems. Because DEA cross-efficiency uses the concept of peer appraisal, it is a very reasonable and appropriate mechanism for allocating a shared resource/cost. It is shown that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency DEA-based iterative method is further extended into a resource-allocation setting to achieve maximization in the aggregated output change by distributing available resources. Such allocations for fixed costs and resources are more acceptable to the players involved, because the allocation results are jointly determined by all DMUs rather than a specific one. The proposed approaches are demonstrated using an existing data set that has been applied in similar studies.     

Finding common weights based on the DM's preference information

Data Envelopment Analysis (DEA) is basically a linear programming-based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach that we term as ‘preference common weights’, which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce a multiple objective linear programming model in which objective functions are input/output variables subject to the constraints similar to the equations that define production possibility set of standard DEA models. Then by using the Zionts–Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.     

Resource allocation for performance improvement

In this paper the problem of allocating resources among Decision Making Units is considered. This study covers the case in which several homogeneous units are operating under the supervision of a central unit. The resource allocation is carried out by the DM (central unit) in such a way that the overall performance of the system is improved. Performance is defined by means of a convex combination of the ratio of the efficiencies before and after the resource allocation. It is assumed that each unit is allowed to modify its resources within the current production possibility set. A novel model is proposed which aims at achieving the best performance of the system. The method is capable of dealing with some additional constraints, imposed by the DM. The model is illustrated by a simple numerical example and a real application.     

DEA cross-efficiency evaluation under variable returns to scale

Cross-efficiency evaluation in data envelopment analysis (DEA) has been developed under the assumption of constant returns to scale (CRS), and no valid attempts have been made to apply the cross-efficiency concept to the variable returns to scale (VRS) condition. This is due to the fact that negative VRS cross-efficiency arises for some decision-making units (DMUs). Since there exist many instances that require the use of the VRS DEA model, it is imperative to develop cross-efficiency measures under VRS. We show that negative VRS cross-efficiency is related to free production of outputs. We offer a geometric interpretation of the relationship between the CRS and VRS DEA models. We show that each DMU, via solving the VRS model, seeks an optimal bundle of weights with which its CRS-efficiency score, measured under a translated Cartesian coordinate system, is maximized. We propose that VRS cross-efficiency evaluation should be done via a series of CRS models under translated Cartesian coordinate systems. The current study offers a valid cross-efficiency approach under the assumption of VRS—one of the most common assumptions in performance evaluation done by DEA.     

Relationship between DEA models without explicit inputs and DEA-R models

Data envelopment analysis (DEA) is one of often used modeling tools for efficiency and performance evaluation of decision making units. Ratio DEA (DEA-R) is a group of novel mathematical models that combines standard DEA methodology and ratio analysis. The efficiency score given by standard DEA CCR model is less than or equal to that given by DEA-R model. In case of single input or single output the efficiency scores in CCR and DEA-R models are identical. The paper deals with DEA-R models without explicit inputs, i.e. models where only pure outputs or index data are taken into account. A basic DEA-R model without explicit inputs is formulated and a relation between output-oriented DEA models without explicit inputs and output-oriented DEA-R models is analyzed. Central resource allocation and slack-based measure models within DEA-R framework are examined. Finally they are used for projections of decision making units on the efficient frontier. The results of the proposed models are applied for efficiency evaluation of 15 units (Chinese research institutes) and they are discussed.     

DEA production games with fuzzy output prices

In DEA production models the technology is assumed to be implicit in the input-output data given by a set of recorded observations. DEA production games assess the benefits to different firms of pooling their resources and sharing their technology. The crisp version of this type of problems has been studied in the literature and methods to obtain stable solutions have been proposed. However, no solution approach exists when there is uncertainty in the unit output prices, a situation that can clearly occur in practice. This paper extends DEA production games to the case of fuzzy unit output prices. In that scenario the total revenue is uncertain and therefore the corresponding allocation among the players is also necessarily uncertain. A core-like solution concept is introduced for these fuzzy games, the Preference Least Core. The computational burden of obtaining allocations of the fuzzy total profit reached through cooperation that belong to the preference least core is high. However, the results presented in the paper permit us to compute the fuzzy total revenue obtained by the grand coalition and a fuzzy allocation in the preference least core by solving a single linear programming model. The application of the proposed approach is illustrated with the analysis of two cooperative production situations originated by data sets from the literature.     

Determining a sequence of targets in DEA

Data Envelopment Analysis (DEA) can be used for assessing the relative efficiency of a number of operating units, finding, for each inefficient unit, a target operating point lying on the efficient frontier. Most DEA models project an inefficient unit onto a most distant target, which makes its attainment more difficult. In this paper, we advocate determining a sequence of targets, each one within an appropriate, short distance of the preceding. The proposed Constant Returns to Scale approach has two interesting features: (a) the sequence of targets ends in the efficient frontier and (b) the final, efficient target is generally closer to the original unit than the one-step projection is.     

A two-phase approach for setting targets in DEA with negative data

Conventional DEA models have been introduced to deal with non-negative data. In the real world, in some occasions, we have outputs and/or inputs, which can take negative data. In DEA literature some approaches have been presented for evaluating performance of units, which operate with negative data. In this paper, firstly, we give a brief review of these works, then we present a new additive based approach in this framework. The proposed model is designed to provide a target with non-negative value associated with negative components for each observed unit, failed by other methods. An empirical application in banking is then used to show the applicability of the proposed method and make a comparison with the other approaches in the literature.     

外源投入型两阶段制造系统网络DEA效率分析研究

制造过程评价是改善制造系统效率的重要一环,传统的评价方法将每个制造系统决策单元视为黑箱来研究整体效率,忽略了中间产品转化信息及投入要素在各子过程中的配置信息。针对两阶段(第二阶段有外源性新投入)制造系统的效率评估问题,分别在固定规模报酬和可变规模报酬假设下,充分利用制造系统中间产品的转化及外源投入要素的配置信息,建立了制造系统网络DEA效率测度及分解模型,建模方法遵循客观评价原则,无需事先主观确定子效率和系统效率之间的组合关系。并将其应用于钢铁制造系统效率测度与分解,研究结果表明该方法能够挖掘决策单元内部子单元的效率情况,帮助决策者发现复杂制造过程非有效的根源,为复杂制造过程的整体效率测度及分解提供了有效的分析方法。     

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

Super-efficiency in DEA by effectiveness of each unit in society

One of the most important topics in management science is determining the efficiency of Decision Making Units (DMUs). The Data Envelopment Analysis (DEA) technique is employed for this purpose. In many DEA models, the best performance of a DMU is indicated by an efficiency score of one. There is often more than one DMU with this efficiency score. To rank and compare efficient units, many methods have been introduced under the name of super-efficiency methods. Among these methods, one can mention Andersen and Petersen’s (1993) [1] super-efficiency model, and the slack-based measure introduced by Tone (2002) [4]. Each of the methods proposed for ranking efficient DMUs has its own advantages and shortcomings. In this paper, we present a super-efficiency method by which units that are more effective and useful in society have better ranks. In fact, in order to determine super-efficiency by this method, the effectiveness of each unit in society is considered rather than the cross-comparison of the units. To do so, we divide the inputs and outputs into two groups, desirable and undesirable, at the discretion of the manager, and assign weights to each input and output. Then we determine the rank of each DMU according to the weights and the desirability of inputs and outputs.     

Integrated bank performance assessment and management planning using hybrid minimax reference point – DEA approach

The purpose of assessing past performances and setting future targets for an organisation such as a bank branch is to find where the branch stands in comparison to its peers within the bank branch network and how to improve the efficiency of its operations relatively when compared to the best practice branches. However, future performance targets may be set arbitrarily by the head-office and thus could be unrealistic and not achievable by a branch. A hybrid minimax reference point-data envelopment analysis (HMRP-DEA) approach is investigated to incorporate the value judgements of both branch managers and head-office directors and to search for the most preferred solution (MPS) along the efficient frontier for each bank branch. The HMRP-DEA approach is composed of three minimax models, including the super-ideal point model, the ideal point model and the shortest distance model, which share the same decision and objective spaces, are different from each other only in their reference points and weighting schema, and are proven to be equivalent to the output-oriented DEA dual models. These models are examined both analytically and graphically in this paper using a case study, which provides the unprecedented insight into integrated efficiency and trade-off analyses. The HMRP-DEA approach uses DEA as an ex-post-facto evaluation tool for past performance assessment and the minimax reference point approach as an ex-ante planning tool for future performance forecasting and target setting. Thus, the HMRP-DEA approach provides an alternative means for realistic target setting and better resource allocation. It is examined by a detailed investigation into the performance analysis for the fourteen branches of an international bank in the Greater Manchester area.     

Review of ranking methods in the data envelopment analysis context

Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.