A network DEA approach for series multi-stage processes

We present in this paper a general network DEA approach to deal with efficiency assessments in multi-stage processes. Our approach complies with the composition paradigm, where the efficiencies of the stages are estimated first and the overall efficiency of the system is obtained ex post. We use multi-objective programming as modeling framework. This provides us the means to assess unique and unbiased efficiency scores and, if required, to drive the efficiency assessments effectively in line with specific priorities given to the stages. A direct comparison with the multiplicative decomposition approach on data drawn from the literature brings into light the advantages of our method and some critical points that one should be concerned about when using the multiplicative efficiency decomposition.     

Theory of integer-valued data envelopment analysis under alternative returns to scale axioms

Kuosmanen and Kazemi Matin [Theory of integer valued data envelopment analysis. European Journal of Operational Research 2009;192:658–67] developed an axiomatic foundation for a data envelopment analysis (DEA) model that assumes subsets of input and output variables to be integer valued. In this paper we extend and generalize the axiomatic foundation for the integer DEA under variable, non-decreasing and non-increasing returns to scale. These model variants are achieved by introducing new axioms of natural convexity and natural augmentability. We also develop mixed integer linear programming (MILP) formulations for computing efficiency scores in these environments. An empirical example illustrates the approach.     

Common benchmarking and ranking of units with DEA

This paper develops a common framework for benchmarking and ranking units with DEA. In many DEA applications, decision making units (DMUs) experience similar circumstances, so benchmarking analyses in those situations should identify common best practices in their management plans. We propose a DEA-based approach for the benchmarking to be used when there is no need (nor wish) to allow for individual circumstances of the DMUs. This approach identifies a common best practice frontier as the facet of the DEA efficient frontier spanned by the technically efficient DMUs in a common reference group. The common reference group is selected as that which provides the closest targets. A model is developed which allows us to deal not only with the setting of targets but also with the measurement of efficiency, because we can define efficiency scores of the DMUs by using the common set of weights (CSW) it provides. Since these weights are common to all the DMUs, the resulting efficiency scores can be used to derive a ranking of units. We discuss the existence of alternative optimal solutions for the CSW and find the range of possible rankings for each DMU which would result from considering all these alternate optima. These ranking ranges allow us to gain insight into the robustness of the rankings.     

How car dealers adjust prices to reach the product efficiency frontier in the Spanish automobile market

This paper investigates the relationship between the dynamics of price discounts at the dealership level and product efficiency in the Spanish auto market. Using data envelopment analysis (DEA), product efficiency scores are estimated for 2092 different vehicles commercialized during 2010, using an innovative database that accounts for more than 75 technical attributes of each model. By alternating official and discounted prices on the DEA specification, we are able to propose a measure of competitive improvement in the retailing stage. We also introduce a decomposition of this measure into two indices that account for the “commercial effort” made by the dealer and the “intensification of competition” that results from the discounting efforts of the other dealers. Finally, we explore the importance of a number of drivers of dealer discounts. As expected, the results confirm the existence of an inverse relationship between product efficiency and dealer discount. Also as expected, discounts are significantly larger for generalist brands, aged models and gasoline engines.     

Incorporating quality into data envelopment analysis of nursing home performance: A case study

When using data envelopment analysis (DEA) as a benchmarking technique for nursing homes, it is essential to include measures of the quality of care. We survey applications where quality has been incorporated into DEA models and consider the concerns that arise when the results show that quality measures have been effectively ignored. Three modeling techniques are identified that address these concerns. Each of these techniques requires some input from management as to the proper emphasis to be placed on the quality aspect of performance. We report the results of a case study in which we apply these techniques to a DEA model of nursing home performance. We examine in depth not only the resulting efficiency scores, but also the benchmark sets and the weights given to the input and output measures. We find that two of the techniques are effective in insuring that DEA results discriminate between high and low quality performance.     

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.     

A fair evaluation of certain stage in a two-stage structure: revisiting the typical two-stage DEA approaches

The efficiency of decision processes with a two-stage structure has been studied by some modified versions of Data Envelopment Analysis (DEA) methodology, such as the relational or centralized model, and the non-cooperative model. After revisiting the rationale of the centralized model provided by the literature, we find that some unfairness exist in its efficiency evaluation of certain stage. This unfairness leads to the usual underestimation of the overall efficiency by the centralized model. Furthermore, because the independent DEA model for one stage ignores its relation and coordination with the other stage and the two-stage system, externalities between these members may arise and lead to the seeming contradiction in efficiencies derived by independent DEA models for the stages and the black box system. Therefore, we argue that the efficiency of certain stage in the context of a two-stage structure should be reevaluated instead of simply using the independent DEA model. A sequence of leader-follower procedures, with data adjustment on intermediates, is proposed to eliminate the externalities and to ensure a fair evaluation. We find that, after this data adjustment, the reevaluation of the second stage for a given Decision Making Unit (DMU) yields the same result as obtained by the standard DEA model regarding the two-stage as a black box. Moreover, some explicit relations are established between the black box model, the centralized model, and the non-cooperative model. Two typical examples taken from the literature illustrate our main results. Our findings also imply that more emphasis should be placed on the game theoretic DEA approach to model the efficiency evaluation of two-stage processes.     

矩阵型网络DEA模型及其实证检验

针对传统DEA模型无法有效的评价矩阵型网络系统的效率,本文构建了矩阵型网络决策单元的生产可能集,建立了矩阵型网络DEA模型。在此基础上证明了决策单元在矩阵型网络DEA模型下为弱DEA有效的充分必要条件为其每个子系统均为弱DEA有效。最后,选用美国的十个电力公司作为决策单元对模型进行实证检验,得出结论:矩阵型网络DEA模型弥补了传统DEA模型无法反映内部有效性从而可能得到错误结果的缺陷,并能精确地计算出各个子过程的效率,辨识出具体需要改进的子过程。同时新模型为评价复杂系统的效率提供了新的思路。     

Supplier Rationalization: A Sourcing Decision Model

We draw on extant literature on strategic sourcing and supply base rationalization to anchor our argument that measuring supplier performance diversity is germane to executing an effective supply base rationalization strategy. We explicate how a novel approach to data envelopment analysis (DEA) efficiency assessment can be utilized to measure this performance diversity. More specifically, our methods are anchored in cross efficiency analysis in DEA that allows for evaluating the efficiency of a supplier with respect to the optimal weights (strengths) of its peers. This methodology is applied to an actual supplier dataset of a large multinational telecommunications company in categorizing their supply base into groups for effective supplier rationalization. We conclude that measuring and analyzing the performance diversity within the framework of DEA provides a mechanism for firms to better balance a rationalized and diversified supply base with unique skills.     

DEA game cross-efficiency approach to Olympic rankings

A number of studies have used data envelopment analysis (DEA) to evaluate the performance of the countries in Olympic games. While competition exists among the countries in Olympic games/rankings, all these DEA studies do not model competition among peer decision making units (DMUs) or countries. These DEA studies find a set of weights/multipliers that keep the efficiency scores of all DMUs at or below unity. Although cross efficiency goes a further step by providing an efficiency measure in terms of the best multiplier bundle for the unit and all the other DMUs, it is not always unique. This paper presents a new and modified DEA game cross-efficiency model where each DMU is viewed as a competitor via non-cooperative game. For each competing DMU, a multiplier bundle is determined that optimizes the efficiency score for that DMU, with the additional constraint that the resulting score should be at or above that DMU 's estimated best performance. The problem, of course, arises that we will not know this best performance score for the DMU under evaluation until the best performances of all other DMUs are known. To combat this “chicken and egg” phenomenon, an iterative approach leading to the Nash equilibrium is presented. The current paper provides a modified variable returns to scale (VRS) model that yields non-negative cross-efficiency scores. The approach is applied to the last six Summer Olympic Games. Our results may indicate that our game cross-efficiency model implicitly incorporates the relative importance of gold, silver and bronze medals without the need for specifying the exact assurance regions.     

Economic efficiency when prices are not fixed: disentangling quantity and price efficiency

This paper proposes an approach to compute cost efficiency in contexts where units can adjust input quantities and to some degree prices so that through their joint determination they can minimise the aggregate cost of the outputs they secure. The model developed is based on the data envelopment analysis (DEA) framework and can accommodate situations where the degree of influence over prices ranges from minimal to considerable. When units cannot influence prices at all the model proposed reduces to the standard cost efficiency DEA model for the case where prices are taken as exogenous. In addition to the cost efficiency model, we introduce an additive decomposition of potential cost savings into a quantity and a price component, based on Bennet indicators.     

基于偏好DEA模型的中国纺织业效率评价

基于具有输入输出指标偏好信息的数据包络分析模型评价中国纺织工业的效率,给出了描述规模报酬不变和规模报酬可变假设的DEA模型及其对偶规划的一种形式。模型克服传统DEA模型应用中常见的决策单元权重为零进而高估决策单元效率的不合理现象,有效地测算了中国31个地区纺织工业的经济运行效率,并分析了地区间效率水平差异的原因。利用各决策单元在经验生产前沿面上的投影点,估计了中国纺织工业的随机生产前沿函数,最后用效率弹性线性递减模型分析了销售收入、人均资产、台港澳和外商投资对各地区效率的微观影响关系。     

基于可变权重的DEA效率评价模型

传统DEA模型将投入、产出权重视为固定变量。为了更合理地对决策单元的效率进行评价,本文研究了如何将有关投入、产出变量的权重的更多信息融入效率评价模型,提出了可变权重的概念,给出了一种基于可变权重的DEA效率评价模型。本文模型是CCR模型的推广。在有关权重信息可得的前提下,本文模型较之CCR模型中效率评价上更为合理。但是,如何准确度量投入、产出权重并将其函数化,是本文方法应用的难点。一个算例分析演示了本文模型。     

Efficiency evaluations with context-dependent and measure-specific data envelopment approaches: An application in a World Bank supported project

We evaluate the efficiency of decision making units (DMUs) in a World Bank supported Social Risk Mitigation Project (SRMP) in Turkey through context-dependent and measure-specific data envelopment analysis (DEA) approaches. The results suggest that the efficiency evaluations with context-dependent and measure-specific DEA play various roles in an organization such as setting attainable targets to DMUs, setting long and short term targets to DMUs separately, grouping of DMUs, and improving internal competition between DMUs. Four main contributions of this study can be summarized as follows. Firstly, the study shows the applicability of context-dependent and measure-specific DEA methodologies in a World Bank supported large scale project to increase the effectiveness of the project. Secondly, it outlines some important managerial conclusions of context-dependent DEA clustering approach. Moreover, we propose an alternative approach for attractiveness scores computations in case of exogenous group formations. Finally, the study proposes and applies measure-specific version of context-dependent DEA approach.     

Production efficiency in Indian agriculture: An assessment of the post green revolution years

In this paper we use the nonparametric method of Data Envelopment Analysis (DEA) to obtain Pareto-Koopmans measures of technical efficiency of individual states over the years 1970–71 through 2000–01 in a multi-output, multi-input model of agricultural production. We disaggregate overall efficiency into two distinct components representing output and input efficiencies and identify the contribution of individual outputs and inputs to the measured level of overall efficiency. Because introduction of modern inputs has been a major component of the process of modernization of Indian agriculture, we examine to what extent different states succeeded in utilizing the modern inputs compared to the traditional inputs. Variations in the DEA efficiency scores across states and over years is explained in terms of differences in various institutional and demographic factors in a second stage regression analysis.     

存在保证域的模糊非径向偏好DEA模型——基于中科院24个研究所的实证分析

数据包络分析（DEA）是一种非参数化的方法,用于评价具有类似输入和输出的决策单元的效率。传统的非径向DEA模型假设输入和输出数据均为准确值,且对权重变量不加以限制,本文构建了存在保证域的模糊非径向偏好DEA模型,并给出了一种基于模糊数截集的模型求解方法,有效地解决了输入和输出全部或部分为模糊数的决策单元评价问题。最后给出了一个中科院研究所效率评价的实例说明了方法的有效性。     

Efficiency decomposition in network data envelopment analysis with slacks-based measures

Conventional data envelopment analysis (DEA) treats the production system as a black box when measuring efficiency, ignoring its internal structure. By taking the operations of the component processes of the system into consideration, several network DEA models have been developed. Of these, the slacks-based measure (SBM) approach has attracted much attention for its ability to provide suitable efficiency measures, especially for weakly efficient production units. This paper proposes a general SBM model for network systems, and is able to decompose the system efficiency into a weighted average of the process efficiencies. This relationship holds for all types of network structure. An example shows that the network model has stronger discriminating power than the conventional black-box model, and the system efficiency is indeed a weighted average of the process efficiencies. The decomposition of the system efficiency helps identify key factors to improve the performance of a production unit.     

Developing a supplier selection system through integrating fuzzy AHP and fuzzy DEA: a case study on an auto lighting system company in Taiwan

Supplier selection plays a very important role in supply chain management. This study intends to develop a novel performance evaluation method, which integrates both fuzzy analytical hierarchy process (AHP) method and fuzzy data envelopment analysis (DEA) for assisting organisations to make the supplier selection decision. Fuzzy AHP method is first applied to find the indicators’ weights through expert questionnaire survey. Then, these weights are integrated with fuzzy DEA. We use α -cut set and extension principle of fuzzy set theory to simplify the fuzzy DEA as a pair of traditional DEA model. Finally, fuzzy ranking using maximising and minimising set method is able to rank the evaluation samples. A case study on an internationally well-known auto lighting OEM company shows that the proposed method is very suitable for practical applications.     

两阶段DEA前沿面投影问题研究——兼对我国上市银行运营绩效进行评价

DEA方法,即数据包络分析方法,是一种用于评价决策单元(Decision Making Units,DMUs)相对有效性的实证方法。近年来DEA方法已经广泛的应用于各行各业的绩效评价中,并发展出两阶段DEA方法。两阶段DEA方法相对于传统DEA方法的优势在于,它不但可以提供被评价对象的总体效率值,还可以分别生成每一阶段的效率值。但正是由于中间要素的存在,按照传统的DEA方法来调整两阶段DEA投入、产出要素的优化过程已不能成功投影在有效前沿面上。本文基于两阶段DEA方法,通过加入"虚拟中间要素"在两阶段DEA中嵌入一个"虚拟阶段",这样不但完善了两阶段DEA的逻辑结构,而且成功的将被评价单元投影到有效前沿面。最后本文应用以上方法对我国上市银行的运营绩效进行了实证分析。实证结果令我们意外的是,国有商业银行运营绩效优于股份制银行。     

A qualitative perspective to deriving weights from pairwise comparison matrices

Deriving weights from pairwise comparison matrices (PCM) is a highly researched topic. The analytic hierarchy process (AHP) traditionally uses the eigenvector method for the purpose. Numerous other methods have also been suggested. A distinctive feature of all these methods is that they associate a quantitative meaning to the judgemental information given by the decision-maker. In contrast, the verbal scale used in AHP to capture judgements does not associate such a quantitative meaning. Though this issue of treating judgements qualitatively is recognized in the extant literature on multi-criteria decision making, unfortunately, there is no research effort so far in the AHP literature. Deriving motivation from the application of data envelopment analysis (DEA) for deriving weights, it is proposed in this paper that DEA models developed to deal with a mix of qualitative and quantitative factors can be used to derive weights from PCMs by treating judgements as qualitative factors. The qualitative DEA model is discussed and illustrated in this paper.