Efficiency bounds in Data Envelopment Analysis

This paper considers a proposal, by Chang and Guh, that the non-archimedean infinitesimal in the CCR data envelopment analysis model be replaced with a data-dependent finite magnitude. Whilst the intention of the proposal is clear: to reduce the CCR efficiency rating of certain problematic DMUs, it is found not to work in practice. An alternative implementation, which puts the CCR model into a mixed-binary linear programming framework, is developed. Chang and Guh's proposal is also related to the earlier modification to the CCR model, Constrained Facet Analysis. Both are seen as providing bounds on the relative efficiency of DMUs which are not properly enveloped in the CCR model.     

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

We consider a two-stage supply chain with one supplier and one manufacturer. The manufacturer faces a Poisson demand process where the arrival rate depends on the selling price, the announced delivery time, and the delivery reliability defined as the probability of satisfying the announced delivery time. Such a demand model generalizes the works in the literature by simultaneously considering the above three demand sensitivity factors. The main purpose of this paper is to study the equilibrium decisions in the supply chain with an all-unit quantity discount contract. We consider four scenarios regarding whether the leadtime standard, the delivery reliability standard, and the manufacturer’s capacity are endogenous, and whether the manufacturer’s production cost is its private information. We find that an all-unit quantity discount scheme can coordinate the supply chain for most cases. Managerial insights are observed regarding the impact of the three demand sensitivity factors. For example, the breakpoint in an optimal quantity discount contract always increases with the delivery reliability sensitivity under an exogenous delivery reliability, but may decrease under an endogenous delivery reliability; with asymmetric information, a higher variance of the manufacturer’s unit production costs leads to a lower unit wholesale price for the low-cost manufacturer.     

Avoiding infeasibility in DEA models with weight restrictions

The flexibility of weights assigned to inputs and outputs is a key aspect of DEA modeling. However, excessive weight variability and implausible weight values have led to the development of DEA models that incorporate weight restrictions, reflecting expert judgment. This in turn has created problems of infeasibility of the corresponding linear programs. We provide an existence theorem that establishes feasibility conditions for DEA multiplier programs with weight restrictions. We then propose a linear model that tests for feasibility and a nonlinear model that provides minimally acceptable adjustments to the original restrictions that render the program feasible. The analysis can be applied to restrictions on weight ratios, or to restrictions on virtual inputs or outputs.     

Integrating categorical variables in Data Envelopment Analysis models: A simple solution technique

This paper introduces a novel method to incorporate categorical non-discretionary variables in Data Envelopment Analysis (DEA) models. While solutions to this problem have been introduced before, they have rarely been employed in applied work. We surmise that existing solution concepts pose problems for applied researchers and develop a simple and straightforward alternative based on indicator variables. We thereby provide a flexible tool for models with categorical variables that–unlike the approaches mentioned above–can be solved with standard DEA software irrespective of scale assumptions even if no option for non-discretionary variables is available. Furthermore, there is no need to split the data and run multiple DEA, one for each data set generated. The model is extensible to categorical discretionary variables and in addition to non-hierarchical data.     

引入时间变量的数据包络分析模型

考虑到实际中的生产过程大多数都是多阶段的生产过程,而传统的数据包络分析模型只能对单阶段的生产过程进行评价.传统的数据包络分析模型在应用中的局限性很大.本文是在传统数据包络分析模型的基础上,通过引入离散的时间变量来建立对整个多阶段生产过程进行评价的数据包络分析模型.     

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.     

Controlled Envelopment by Face Extension in DEA

Data Envelopment Analysis (DEA) is an approach to assess the relative efficiency of organizations using multiple inputs to produce multiple outputs. This assessment is made from the standpoint most favourable to each organization. If an organization is not well enveloped, in the sense that it is not comparable to a sufficient number of other organizations (called referents), DEA may understate inefficiency. A lower bound on the efficiency measure may be obtained by requiring that the organization being evaluated be compared with at least k non-redundant referents. For any feasible choice of k, the procedure proposed here selects the most favourable set of referents, and guarantees a greatest lower bound on the efficiency measure, thus usefully complementing the information provided by conventional DEA.     

IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units)

IDEA (Imprecise Data Envelopment Analysis) extends DEA so it can simultaneously treat exact and imprecise data where the latter are known only to obey ordinal relations or to lie within prescribed bounds. AR-IDEA extends this further to include AR (Assurance Region) and the like approaches to constraints on the variables. In order to provide one unified approach, a further extension also includes cone-ratio envelopment approaches to simultaneous transformations of the data and constraints on the variables. The present paper removes a limitation of IDEA and AR-IDEA which requires access to actually attained maximum values in the data. This is accomplished by introducing a dummy variable that supplies needed normalizations on maximal values and this is done in a way that continues to provide linear programming equivalents to the original problems. This dummy variable can be regarded as a new DMU (Decision Making Unit), referred to as a CMD (Column Maximum DMU).     

Reducing Weight Flexibility in Data Envelopment Analysis

This paper explores the consequences of total weight flexibility in data envelopment analysis (DEA) assessments of the efficiency of decision-making units, and it suggests one possible way of limiting such flexibility. It is suggested that total weight flexibility can lead to some decision-making units being assessed, in effect, on only a small subset of their inputs and outputs, while the rest of their inputs and outputs are all but ignored. Constraining the weights in DEA assessments overcomes this problem. The paper suggests one way in which constraints can be placed for the case where the decision-making units to be assessed use only a single input. The method is illustrated using data on local-authority rates departments. Finally, the paper discusses the interpretation and usefulness of the information obtained from DEA assessments involving weights constraints.     

Restricting Weight Flexibility in Data Envelopment Analysis

In this paper we present a method, based on the use of proportions, for restricting weight flexibility in data envelopment analysis. This method is applicable when the decision-making units being evaluated have multiple inputs and outputs.     

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.     

On the Use of Ordinal Data in Data Envelopment Analysis

In many problems involving efficiency analysis using DEA, certain factors may be measurable only on an ordinal scale. Specifically, it may be possible only to rank order the DMUs according to a factor, rather than being able to assign a specific numerical value of that factor to each DMU. To illustrate this, we examine a problem involving the evaluation of new technology installations. The presence of qualitative factors in such an environment motivates the need to investigate how such factors can be incorporated into existing efficiency measurement models. In particular, a procedure is presented for incorporating an ordinal factor into the DEA structure, with the resulting formulation being a particular form of cone ratio model. The model is then applied to the technology installation efficiency problem.     

模糊数据包络分析方法有效性分析

传统数据包络分析(DEA)模型只能用来评价具有精确投入和产出数据的决策单元.然而在实践中决策单元的投入产出数据可能存在一定模糊性.为了评价具有模糊投入产出数据的决策问题,研究工作者提出了模糊数据包络分析模型,并给出了相应的有效性定义.对于不同研究者提出的有效性定义方式有众多地方需要改进.通过这些改进提出了相关模型及新的有效性定义方式,并给出了相关实例.     

一类基于属性变量的DEA模型

系统评价不仅应重视系统的经济特征,还必须重视系统的非经济特征.在评价系统的非经济特征时必须考虑属性变量,即不能以货币衡量的反映系统非经济特征的定量变量.在过去关于DEA的研究中并未涉及到这种变量.本文对属性变量进行了明确的定义,并提出一种基于属性变量的DEA效率评价模型,最后通过实例演示了模型的合理性.     

Fuzzy BCC Model for Data Envelopment Analysis

Fuzzy Data Envelopment Analysis (FDEA) is a tool for comparing the performance of a set of activities or organizations under uncertainty environment. Imprecise data in FDEA models is represented by fuzzy sets and FDEA models take the form of fuzzy linear programming models. Previous research focused on solving the FDEA model of the CCR (named after Charnes, Cooper, and Rhodes) type (FCCR). In this paper, the FDEA model of the BCC (named after Banker, Charnes, and Cooper) type (FBCC) is studied. Possibility and Credibility approaches are provided and compared with an -level based approach for solving the FDEA models. Using the possibility approach, the relationship between the primal and dual models of FBCC models is revealed and fuzzy efficiency can be constructed. Using the credibility approach, an efficiency value for each DMU (Decision Making Unit) is obtained as a representative of its possible range. A numerical example is given to illustrate the proposed approaches and results are compared with those obtained with the -level based approach.     

Data Envelopment Analysis of multiple response experiments

Taguchi method is the usual strategy in robust design and involves conducting experiments using orthogonal arrays and estimating the combination of factor levels that optimizes a given performance measure, typically a signal-to-noise ratio. The problem is more complex in the case of multiple responses since the combinations of factor levels that optimize the different responses usually differ. In this paper, an Artificial Neural Network, trained with the experiments results, is used to estimate the responses for all factor level combinations. After that, Data Envelopment Analysis (DEA) is used first to select the efficient (i.e. non-dominated) factor level combinations and then for choosing among them the one which leads to a most robust quality loss penalization. Mean Square Deviations of the quality characteristics are used as DEA inputs. Among the advantages of the proposed approach over traditional Taguchi method are the non-parametric, non-linear way of estimating quality loss measures for unobserved factor combinations and the non-parametric character of the performance evaluation of all the factor combinations. The proposed approach is applied to a number of case studies from the literature and compared with existing approaches.     

Relationships between Data Envelopment Analysis and Multicriteria Decision Analysis

We contrast the different approaches of Data Envelopment Analysis (DEA) and Multiple Criteria Decision Making (MCDM) to superficially similar problems. The concepts of efficiency and Pareto optimality in DEA and MCDM are compared, and a link is demonstrated between the ratio efficiency definition in DEA and a distance measure in input–output space based on linear value functions. The problem of weight sensitivity is discussed in terms of value measurement theory, highlighting the assumptions needed during model formulation in order to justify the use of value judgements to constrain weight flexibility in DEA. Finally, we propose a stochastic approach, in which a probability distribution on efficiencies can be derived for each decision making unit, as a basis for comparison.     

The Potential for Endogeneity Bias in Data Envelopment Analysis

Data envelopment analysis has become an important technique for modelling the relationship between inputs and outputs in the production process, particularly in the public sector. However, whenever measures of the output of public sector activity receive public attention, there is a strong possibility that there will be a feedback from the achieved output to the resources devoted to the activity. In other words, the level of resources is endogenous. The implications of such endogeneity for standard econometric estimation techniques are well known, and methods exist to deal with the problem. Most commentators have assumed that endogeneity poses no analogous problems for DEA because the technique merely places an envelope around feasible production possibilities. Using Monte Carlo simulation techniques, however, this paper shows that the efficiency estimates generated by DEA in the presence of endogeneity can be subject to bias, in the sense that inefficient units using low levels of the endogenous resource may be set tougher efficiency targets than equally inefficient units using more of the resource, particularly when sample sizes are small. The paper concludes that, in such circumstances, great caution should be exercised when comparing efficiency measures for units using different levels of the endogenous input.     

Preference, Production and Performance in Data Envelopment Analysis

This paper attempts to provide a systematic approach to the DEA model building. To this end, we try to identify some essential aspects of DEA modelling. Three key building blocks in a DEA model are identified: they are preference order, production possibility set and performance measure. It is shown that the preferences and performance measurements used in the standard DEA models are only particular examples in this framework. It is also illustrated in this work that this methodology is useful in building new DEA models to handle nonstandard applications such as those involve non-Pareto preferences or undesirable inputs-outputs.