Centralized Resource Allocation Using Data Envelopment Analysis

While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.     

A new methodology to measure efficiencies of inputs (outputs) of decision making units in Data Envelopment Analysis with application to agriculture

This paper aims at developing a new methodology to measure and decompose global DMU efficiency into efficiency of inputs (or outputs). The basic idea rests on the fact that global DMU's efficiency score might be misleading when managers proceed to reallocate their inputs or redefine their outputs. Literature provides a basic measure for global DMU's efficiency score. A revised model was developed for measuring efficiencies of global DMUs and their inputs (or outputs) efficiency components, based on a hypothesis of virtual DMUs. The present paper suggests a method for measuring global DMU efficiency simultaneously with its efficiencies of inputs components, that we call Input decomposition DEA model (ID-DEA), and its efficiencies of outputs components, that we call output decomposition DEA model (OD-DEA). These twin models differ from Supper efficiency model (SE-DEA) and Common Set Weights model (CSW-DEA). The twin models (ID-DEA, OD-DEA) were applied to agricultural farms, and the results gave different efficiency scores of inputs (or outputs), and at the same time, global DMU's efficiency score was given by the Charnes, Cooper and Rhodes (Charnes et al., 1978) [1], CCR78 model. The rationale of our new hypothesis and model is the fact that managers don't have the same information level about all inputs and outputs that constraint them to manage resources by the (global) efficiency scores. Then each input/output has a different reality depending on the manager's decision in relationship to information available at the time of decision. This paper decomposes global DMU's efficiency into input (or output) components' efficiencies. Each component will have its score instead of a global DMU score. These findings would improve management decision making about reallocating inputs and redefining outputs. Concerning policy implications of the DEA twin models, they help policy makers to assess, ameliorate and reorient their strategies and execute programs towards enhancing the best practices and minimising losses.     

Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on joint chance constraints. An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.     

Hierarchies and Groups in DEA

Conventional applications of data envelopment analysis (DEA) presume the existence of a set of similar decision making units, wherein each unit is evaluated relative to other members of the set. Often, however, the DMUs fall naturally into groupings, giving rise first to the problem of how to view the groups themselves as DMUs, and second to the issue of how to deal with several different ratings for any given DMU when groupings can be formed in different ways. In the present paper we introduce the concept of hierarchical DEA, where efficiency can be viewed at various levels. We provide a means for adjusting the ratings of DMUs at one level to account for the ratings received by the groups (into which these DMUs fall) at a higher level. We also develop models for aggregating different ratings for a DMU arising from different possible groupings. An application of these models to a set of power plants is given.     

Cross redundancy and sensitivity in DEA models

Data envelopment analysis (DEA) measures the efficiency of each decision making unit (DMU) by maximizing the ratio of virtual output to virtual input with the constraint that the ratio does not exceed one for each DMU. In the case that one output variable has a linear dependence (conic dependence, to be precise) with the other output variables, it can be hypothesized that the addition or deletion of such an output variable would not change the efficiency estimates. This is also the case for input variables. However, in the case that a certain set of input and output variables is linearly dependent, the effect of such a dependency on DEA is not clear. In this paper, we call such a dependency a cross redundancy and examine the effect of a cross redundancy on DEA. We prove that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the CCR or BCC models. Furthermore, we present a sensitivity analysis to examine the effect of an imperfect cross redundancy on DEA by using accounting data obtained from United States exchange-listed companies.     

Long-term efficiency of public service provision in a context of budget restrictions. An application to the education sector

This paper proposes an extension of the non-parametric long-term evaluation of efficiency, the conditional panel data DEA model, which takes into account the panel structure of the data and, at the same time, incorporates the role of contextual factors in the estimations. Its application to the education sector for the period analyzed (2009–2014) shows the utility of this method, since it obtains more representative efficiency scores for the complete time-period, is more robust to external shocks, and allows improvements to the decision-making process in the allocation of the budget available for the public education sector. The results are clear and present an evolution towards the convergence of the efficiency scores, precisely in a time period when hard budget constraints severely reduced the resources available for public schools.     

The appreciative democratic voice of DEA: A case of faculty academic performance evaluation

Data envelopment analysis (DEA) is in fact more than just being an instrument for measuring the relative efficiencies of a group of decision making units (DMU). DEA models are also means of expressing appreciative democratic voices of DMUs. This paper proposes a methodology for allocating premium points to a group of professors using three models sequentially: (1) a DEA model for appreciative academic self-evaluation, (2) a DEA model for appreciative academic cross-evaluation, and (3) a Non-DEA model for academic rating of professors for the purpose of premium allocations. The premium results, called DEA results, are then compared with the premium points “nurtured” by the Dean, called N bonus points. After comparing DEA results and N bonus points, the Dean reassessed his initial bonus points and provided new ones – called DEA-N decisions. The experience indicates that judgmental decisions (Dean's evaluations) can be enhanced by making use of formal models (DEA and Non-DEA models). Moreover, the appreciative and democratic voices of professors are virtually embedded in the DEA models.     

Sensitivity Analysis of an Efficient DMU in DEA Model with Variable Returns to Scale (VRS)

In this paper we consider the Variable Returns to Scale (VRS) Data Envelopment Analysis (DEA) model. In a DEA model each Decision Making Unit (DMU) is classified either as efficient or inefficient. Changes in inputs or outputs of any DMU can alter its classification, i.e. an efficient DMU can become inefficient and vice versa. The goal of this paper is to assess changes in inputs and outputs of an extreme efficient DMU that will not alter its efficiency status, thus obtaining the region of efficiency for that DMU. Namely, a DMU will remain efficient if and only if after applying changes this DMU stays in that region. The representation of this region is done using an iterative procedure. In the first step an extended DEA model, whereby a DMU under evaluation is excluded from the reference set, is used. In the iterative part of the procedure, by using the obtained optimal simplex tableau we apply parametric programming, thus moving from one facet to the adjacent one. At the end of the procedure we obtain the complete region of efficiency for a DMU under consideration.     

Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammons mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way.JEL Classification: C14, C61, D24, M2     

Research performance evaluation of Chinese university: A non-homogeneous network DEA approach

Performance evaluation for universities or research institutions has become a hot topic in recent years. However, the previous works rarely investigate the multiple departments’ performance of a university, and especially, none of them consider the non-homogeneity among the universities’ departments. In this paper, we develop data envelopment analysis (DEA) models to evaluate the performance of general non-homogeneous decision making units (DMUs) with two-stage network structures and then apply them to a university in China. Specifically, the first stage is faculty research process, and the second stage is student research process. We first spit each DMU (i.e. department) into a combination of several mutually exclusive maximal input subgroups and output subgroups in terms of their homogeneity in both stages. Then an additive DEA model is proposed to evaluate the performance of the overall efficiency of the non-homogeneous DMUs with two-stage network structure. By analyzing the empirical results, some implications are provided to support the university to promote the research performance of each department as well as the whole university.     

Lower Bound Restrictions on Intensities in Data Envelopment Analysis

We propose an extension to the basic DEA models that guarantees that if an intensity is positive then it must be at least as large as a pre-defined lower bound. This requirement adds an integer programming constraint known within Operations Research as a Fixed-Charge (FC) type of constraint. Accordingly, we term the new model DEA_FC. The proposed model lies between the DEA models that allow units to be scaled arbitrarily low, and the Free Disposal Hull model that allows no scaling. We analyze 18 datasets from the literature to demonstrate that sufficiently low intensities—those for which the scaled Decision-Making Unit (DMU) has inputs and outputs that lie below the minimum values observed—are pervasive, and that the new model ensures fairer comparisons without sacrificing the required discriminating power. We explain why the low-intensity phenomenon exists. In sharp contrast to standard DEA models we demonstrate via examples that an inefficient DMU may play a pivotal role in determining the technology. We also propose a goal programming model that determines how deviations from the lower bounds affect efficiency, which we term the trade-off between the deviation gap and the efficiency gap.     

A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies

Data Envelopment Analysis (DEA) is a linear programming methodology for measuring the efficiency of Decision Making Units (DMUs) to improve organizational performance in the private and public sectors. However, if a new DMU needs to be known its efficiency score, the DEA analysis would have to be re-conducted, especially nowadays, datasets from many fields have been growing rapidly in the real world, which will need a huge amount of computation. Following the previous studies, this paper aims to establish a linkage between the DEA method and machine learning (ML) algorithms, and proposes an alternative way that combines DEA with ML (ML-DEA) algorithms to measure and predict the DEA efficiency of DMUs. Four ML-DEA algorithms are discussed, namely DEA-CCR model combined with back-propagation neural network (BPNN-DEA), with genetic algorithm (GA) integrated with back-propagation neural network (GANN-DEA), with support vector machines (SVM-DEA), and with improved support vector machines (ISVM-DEA), respectively. To illustrate the applicability of above models, the performance of Chinese manufacturing listed companies in 2016 is measured, predicted and compared with the DEA efficiency scores obtained by the DEA-CCR model. The empirical results show that the average accuracy of the predicted efficiency of DMUs is about 94%, and the comprehensive performance order of four ML-DEA algorithms ranked from good to poor is GANN-DEA, BPNN-DEA, ISVM-DEA, and SVM-DEA.     

On Returns to Scale under Weight Restrictions in Data Envelopment Analysis

Weextend the concept of returns to scale in Data Envelopment Analysis(DEA) to the weight restriction environments. By the additionof weight restrictions, the status of returns to scale, i.e., increasing, constant and decreasing may suffer a change. Wefirst define ``returns to scale' under weight restrictions andpropose a method for identifying the status of returns to scale.Then, it is demonstrated that the region of the most productivescale size (MPSS) will usually be narrowed by this addition.For an inefficient decision making unit (DMU), a simple rulefor determining the status of returns to scale of its projectedDMU will be presented. An empirical study compares the resultsof the proposed method with those of the BCC model and demonstratesthe change in the MPSS for both models.     

Adjusting for the environment in DEA: A comparison of alternative models based on empirical data

Due to the existence of free software and pedagogical guides, the use of Data Envelopment Analysis (DEA) has been further democratized in recent years. Nowadays, it is quite usual for practitioners and decision makers with no or little knowledge in operational research to run their own efficiency analysis. Within DEA, several alternative models allow for an environmental adjustment. Four alternative models, each user-friendly and easily accessible to practitioners and decision makers, are performed using empirical data of 90 primary schools in the State of Geneva, Switzerland. Results show that the majority of alternative models deliver divergent results. From a political and a managerial standpoint, these diverging results could lead to potentially ineffective decisions. As no consensus emerges on the best model to use, practitioners and decision makers may be tempted to select the model that is right for them, in other words, the model that best reflects their own preferences. Further studies should investigate how an appropriate multi-criteria decision analysis method could help decision makers to select the right model.     

Some extensions of techniques to handle non-discretionary factors in data envelopment analysis

Data Envelopment Analysis (DEA) assumes, in most cases, that all inputs and outputs are controlled by the Decision Making Unit (DMU). Inputs and/or outputs that do not conform to this assumption are denoted in DEA asnon-discretionary (ND) factors. Banker and Morey [1986] formulated several variants of DEA models which incorporated ND with ordinary factors. This article extends the Banker and Morey approach for treating nondiscretionary factors in two ways. First, the model is extended to allow for thesimultaneous presence of ND factors in both the input and the output sets. Second, a generalization is offered which, for the first time, enables a quantitative evaluation ofpartially controlled factors. A numerical example is given to illustrate the different models.The editor for this paper was Wade D. Cook.     

Target and technical efficiency in DEA: controlling for environmental characteristics

In this paper we propose a target efficiency DEA model that allows for the inclusion of environmental variables in a one stage model while maintaining a high degree of discrimination power. The model estimates the impact of managerial and environmental factors on efficiency simultaneously. A decomposition of the overall technical efficiency into two components, target efficiency and environmental efficiency, is derived. Estimation of target efficiency scores requires the solution of a single large non-linear optimization problem and provides both a joint estimation of target efficiency scores from all DMUs and an estimation of a common scalar expressing the environmental impact on efficiency for each environmental factor. We argue that if the indices on environmental conditions are constructed as the percentage of output with certain attributes present, then it is reasonable to let all reference DMUs characterized by a composed fraction lower than the fraction of output possessing the attribute of the evaluated DMU enter as potential dominators. It is shown that this requirement transforms the cone-ratio constraints on intensity variables in the BM-model (Banker and Morey 1986) into endogenous handicap functions on outputs. Furthermore, a priori information or general agreements on allowable handicap values can be incorporated into the model along the same lines as specifications of assurance regions in standard DEA.

各行业企业物流发展不平衡性评价分析

重新整合数据包络分析法(DEA),在传统CCR模型基础上,补充决策单元(DMU)排序方法.使其不但能够指出各决策单元是否有效及无效的原因和程度.同时得到各决策单元的优先排序。并利用该方法对2003-2004年我国十个行业的企业物流发展状况进行评价分析.指出各行业企业物流发展的特点及其存在问题.并对这十个行业的企业物流发展水平进行了排名。     

A PCA–DEA approach to measure the quality of life in Estonian counties

This paper investigates the application of a PCA–DEA model to assess the quality of life (QOL) scores in Estonian counties and analyses the model's results. The dataset is a balanced panel of 15 Estonian counties covering the period from 2000 to 2011. We consider a PCA–DEA model as an alternative method to estimate and predict QOL scores and rankings of Estonian counties. The method consists of a two-stage analysis that begins with a principal component analysis. In the second stage, the standard DEA is used. The results from the conventional DEA model and the PCA–DEA model are compared and discussed. A comparison of the methodologies demonstrates that a PCA–DEA model provides a powerful tool for performance ranking. The rankings of Estonian counties using QOL scores for different model specifications are presented. Finally, the QOL ranking of Estonian counties is revised using PCA–DEA.     

Performance evaluation using data envelopment analysis in the presence of time lags

Data Envelopment Analysis (DEA) is a methodology that computes efficiency values for decision making units (DMU) in a given period by comparing the outputs with the inputs. In many applications, inputs and outputs of DMUs are monitored over time. There might be a time lag between the consumption of inputs and the production of outputs. We develop an approach that aims to capture the time lag between the outputs and the inputs in assigning the efficiency values to DMUs. We propose using weight restrictions in conjunction with the model. Our computational results on randomly generated problems demonstrate that the developed approach works well under a large variety of experimental conditions. We also apply our approach on a real data set to evaluate research institutions.