Short-run and long-run efficiency measures for multiplant firms

The usual Data Envelopment Analysis (DEA) model for measuring the relative efficiency assumes that all plants belong to distinct firms superior to them. For firms with more than one plant, Koopmans proposes a procedure for deriving the short-run production frontier for each firm. Modifying his idea, a DEA model is constructed in this paper for measuring the short-run efficiency of each plant within a firm. Based on the theory of production economics that the long-run production frontier is an envelop super-imposed upon all short-run production frontiers, another DEA model is constructed to measure the long-run efficiency of every plant. The long-run efficiency is always smaller than or equal to the short-run efficiency. Consequently, it is possible that an inefficient plant can only be improved in the long-run. With the models constructed in this paper, a decision-maker is able to distinguish between what can be achieved in the short-run and what in the long-run. To clarify the idea, an example of Taiwan forests is adopted for illustration. This revised version was published online in June 2006 with corrections to the Cover Date.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan

The efficiency of decision processes which can be divided into two stages has been measured for the whole process as well as for each stage independently by using the conventional data envelopment analysis (DEA) methodology in order to identify the causes of inefficiency. This paper modifies the conventional DEA model by taking into account the series relationship of the two sub-processes within the whole process. Under this framework, the efficiency of the whole process can be decomposed into the product of the efficiencies of the two sub-processes. In addition to this sound mathematical property, the case of Taiwanese non-life insurance companies shows that some unusual results which have appeared in the independent model do not exist in the relational model. In other words, the relational model developed in this paper is more reliable in measuring the efficiencies and consequently is capable of identifying the causes of inefficiency more accurately. Based on the structure of the model, the idea of efficiency decomposition can be extended to systems composed of multiple stages connected in series.     

Multi-period efficiency and Malmquist productivity index in two-stage production systems

Conventional two-stage data envelopment analysis (DEA) models measure the overall performance of a production system composed of two stages (processes) in a specified period of time, where variations in different periods are ignored. This paper takes the operations of individual periods into account to develop a multi-period two-stage DEA model, which is able to measure the overall and period efficiencies at the same time, with the former expressed as a weighted average of the latter. Since the efficiency of a two-stage system in a period is the product of the two process efficiencies, the overall efficiency of a decision making unit (DMU) in the specified period of time can be decomposed into the process efficiency of each period. Based on this decomposition, the sources of inefficiency in a DMU can be identified. The efficiencies measured from the model can also be used to calculate a common-weight global Malmquist productivity index (MPI) between two periods, in that the overall MPI is the product of the two process MPIs. The non-life insurance industry in Taiwan is used to verify the proposed model, and to explain why some companies performed unsatisfactorily in the specified period of time.     

Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.     

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.     

Measuring the performances of decision-making units using interval efficiencies

Efficiency is a relative measure because it can be measured within different ranges. The traditional data envelopment analysis (DEA) measures the efficiencies of decision-making units (DMUs) within the range of less than or equal to one. The corresponding efficiencies are referred to as the best relative efficiencies, which measure the best performances of DMUs and determine an efficiency frontier. If the efficiencies are measured within the range of greater than or equal to one, then the worst relative efficiencies can be used to measure the worst performances of DMUs and determine an inefficiency frontier. In this paper, the efficiencies of DMUs are measured within the range of an interval, whose upper bound is set to one and the lower bound is determined through introducing a virtual anti-ideal DMU, whose performance is definitely inferior to any DMUs. The efficiencies turn out to be all intervals and are thus referred to as interval efficiencies, which combine the best and the worst relative efficiencies in a reasonable manner to give an overall measurement and assessment of the performances of DMUs. The new DEA model with the upper and lower bounds on efficiencies is referred to as bounded DEA model, which can incorporate decision maker (DM) or assessor's preference information on input and output weights. A Hurwicz criterion approach is introduced and utilized to compare and rank the interval efficiencies of DMUs and a numerical example is examined using the proposed bounded DEA model to show its potential application and validity.     

Overall performance evaluation: new bounded DEA models against unreachability of efficiency

Data envelopment analysis (DEA) performance evaluation can be implemented from either optimistic or pessimistic perspectives. For an overall performance evaluation from both perspectives, bounded DEA models are introduced to evaluate decision making units (DMUs) in terms of interval efficiencies. This paper reveals unreachability of efficiency and distortion of frontiers associated with the existing bounded DEA models. New bounded DEA models against these problems are proposed by integrating the archetypal optimistic and pessimistic DEA models into a model with bounded efficiency. It provides a new way of deriving empirical estimates of efficiency frontiers in tune with that identified by the archetypal models. Without distortion of frontiers, all DMUs reach interval efficiencies in accordance with that determined by the archetypal models. A unified evaluation and classification result is derived and the efficiency relationships between DMUs are preserved. It is shown that the newly proposed models are more reliable for overall performance evaluation in practice, as illustrated empirically by two examples.     

Impacts of random noise and specification on estimates of capacity derived from data envelopment analysis

Data envelopment analysis (DEA) is widely used to estimate the efficiency of firms and has also been proposed as a tool to measure technical capacity and capacity utilization (CU). Random variation in output data can lead to downward bias in DEA estimates of efficiency and, consequently, upward bias in estimates of technical capacity. This can be particularly problematic for industries such as agriculture, aquaculture and fisheries where the production process is inherently stochastic due to environmental influences. This research uses Monte Carlo simulations to investigate possible biases in DEA estimates of technically efficient output and capacity output attributable to noisy data and investigates the impact of using a model specification that allows for variable returns to scale (VRS). We demonstrate a simple method of reducing noise induced bias when panel data is available. We find that DEA capacity estimates are highly sensitive to noise and model specification. Analogous conclusions can be drawn regarding DEA estimates of average efficiency.     

Qualitative and quantitative data envelopment analysis with interval data

In this paper, we investigate DEA with interval input-output data. First we show various extensions of efficiency and that 25 of them are essential. Second we formulate the efficiency test problems as mixed integer programming problems. We prove that 14 among 25 problems can be reduced to linear programming problems and that the other 11 efficiencies can be tested by solving a finite sequence of linear programming problems. Third, in order to obtain efficiency scores, we extend SBM model to interval input-output data. Fourth, to moderate a possible positive overassessment by DEA, we introduce the inverted DEA model with interval input-output data. Using efficiency and inefficiency scores, we propose a classification of DMUs. Finally, we apply the proposed approach to Japanese Bank Data and demonstrate its advantages.     

Dual models of interval DEA and its extension to interval data

The purpose of this paper is to develop a new DEA with an interval efficiency. An original DEA model is to evaluate each DMU optimistically. There is another model called “Inverted DEA” to evaluate each DMU pessimistically. But, there are no relations essentially between DEA and inverted DEA. Thus, we formulate a DEA model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints. Thus, two end points can construct an interval efficiency. With the same idea, we deal with the interval inefficiency model which is inverse to interval efficiency. Finally, we extend the proposed DEA model to interval data and fuzzy data.     

Dynamic data envelopment analysis: A relational analysis

This paper proposes a dynamic data envelopment analysis (DEA) model to measure the system and period efficiencies at the same time for multi-period systems, where quasi-fixed inputs or intermediate products are the source of inter-temporal dependence between consecutive periods. A mathematical relationship is derived in which the complement of the system efficiency is a linear combination of those of the period efficiencies. The proposed model is also more discriminative than the existing ones in identifying the systems with better performance. Taiwanese forests, where the forest stock plays the role of quasi-fixed input, are used to illustrate this approach. The results show that the method for calculating the system efficiency in the literature produces over-estimated scores when the dynamic nature is ignored. This makes it necessary to conduct a dynamic analysis whenever data is available.     

Measuring the efficiency of forest districts with multiple working circles

Data envelopment analysis (DEA) is a methodology extensively applied to measuring the relative efficiency of decision making units with multiple inputs and multiple outputs. Herein, a DEA model is developed to measure the efficiency of forest districts which are divided into a number of subdistricts called working circles (WCs). The idea is to construct district production frontiers from the WCs of individual districts. Superimposing the district production frontiers of different districts one derives the forest production frontier. The closeness of a district production frontier to the forest production frontier indicates this district's efficiency. As an illustration, the developed model measures the eight districts, with a total of thirty-four WCs, of the national forests of the Republic of China on Taiwan. The results provide the top management with an idea of how far each district can be expected to improve its performance when compared with other districts.     

Super-efficiency and DEA sensitivity analysis

This paper discusses and reviews the use of super-efficiency approach in data envelopment analysis (DEA) sensitivity analyses. It is shown that super-efficiency score can be decomposed into two data perturbation components of a particular test frontier decision making unit (DMU) and the remaining DMUs. As a result, DEA sensitivity analysis can be done in (1) a general situation where data for a test DMU and data for the remaining DMUs are allowed to vary simultaneously and unequally and (2) the worst-case scenario where the efficiency of the test DMU is deteriorating while the efficiencies of the other DMUs are improving. The sensitivity analysis approach developed in this paper can be applied to DMUs on the entire frontier and to all basic DEA models. Necessary and sufficient conditions for preserving a DMU’s efficiency classification are developed when various data changes are applied to all DMUs. Possible infeasibility of super-efficiency DEA models is only associated with extreme-efficient DMUs and indicates efficiency stability to data perturbations in all DMUs.     

About negative efficiencies in Cross Evaluation BCC input oriented models

It will be shown in this paper that the input oriented DEA BCC model can generate negative efficiencies that are usually hidden in the model. The impact of these negative efficiencies becomes obvious when using input oriented Cross Evaluation models. With the help of an example with one input and one output, the conditions for the possible occurrence of negative efficiencies will be shown. Furthermore, we will show that a small intuitive change in the BCC multipliers model, previously presented in other papers, corrects this situation. We show why this change is used and compared it with an alternative formulation, which avoid negative efficiencies, namely the Non-Decreasing Returns to Scale (NDRS) model. We also show that the formulation studied in this paper is less restrictive than the NDRS model. The study of this variation in the DEA BCC model will be complemented with the formulation of the dual envelope model. This model changes the original frontier. Using the concept of non-observed DMUs, those variations can be graphically analyzed. We have also carried out some algebraic studies concerning benchmarks, multipliers and returns to scale.     

我国跨境电商上市企业经营效率研究——基于三阶段DEA-Malmquist指数方法

以33家跨境电商上市企业为研究对象,基于三阶段DEA和Malmquist指数模型从静态和动态两个角度出发,对2013-2018年我国跨境电商上市企业的综合效率、全要素生产效率指数及两者的分解效率进行测度并对比分析,同时分析了宏观经济环境、政府干预和企业自身经营情况等因素对经营效率的影响.结果表明:样本企业经营效率存在个体差异,且外部环境对其经营效率具有显著影响;纯技术效率和规模效率参差不齐是导致综合技术效率分化严重的主要原因.基于此,跨境电商上市企业应积极配合政策变化,加强营销能力,及时调整经营规模,以防范宏观经济风险,提高企业经营效率.     

Network DEA: A slacks-based measure approach

Traditional DEA models deal with measurements of relative efficiency of DMUs regarding multiple-inputs vs. multiple-outputs. One of the drawbacks of these models is the neglect of intermediate products or linking activities. After pointing out needs for inclusion of them to DEA models, we propose a slacks-based network DEA model, called Network SBM, that can deal with intermediate products formally. Using this model we can evaluate divisional efficiencies along with the overall efficiency of decision making units (DMUs).     

Slack-adjusted DEA for time series analysis: Performance measurement of Japanese electric power generation industry in 1984–1993

Using a new slack-adjusted data envelopment analysis (SA-DEA) model which explicitly incorporates an influence of slacks into its efficiency measurement, this study discusses a use of various efficiencies and index measures for DEA dynamic analysis. An analytical formulation to determine the type of return to scale (RTS) is proposed for the new DEA model. This paper mathematically discusses when multiple solutions occur on RTS and how to deal with such a difficulty. As an important case study, this paper applies the proposed DEA approach to examine the performance of Japanese electric power generation companies from 1984 to 1993. Two policy implications are suggested for guiding the Japanese electric power industry.     

Interval DEA模型中决策单元的投影问题

在传统的DEA模型中,最优相对效率模型是在不大于1的范围内研究决策单元的效率的,最差相对效率模型是在不小于1的范围内研究决策单元的效率,这两种模型在研究投影问题时,是在不同的范围内进行的,有一定的片面性.将在interval DEA模型中,研究决策单元的投影问题,该模型是在相同的约束域内研究最优和最差相对效率模型,得出的结论将更加全面,通过两个定理给出了非DEA有效的决策单元在DEA有效面上的投影表达式和非DEA无效的决策单元在DEA无效面上的投影表达式.同时,通过一个实例对决策单元在interval DEA模型中的投影结果与在传统的DEA模型的投影结果进行了比较,发现投影结果比传统模型得到的投影结果对实际的生产有更强的指导意义.     

基于公共权重的区间DEA效率评价及其排序方法研究

针对传统区间数据包络分析方法,在确定每一个决策单元区间效率的上界和下界时,存在的评价尺度不一致且计算复杂等问题,本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型,并给出了一种考虑决策者偏好信息的可能度排序方法,用以解决区间效率的全排序问题。最后,以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。