A Quasi-Malmquist Productivity Index

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of one-sided efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.     

Efficiency in government health spending: a super slacks-based model

This article evaluates the performance of health expenditure and demonstrates how productivity has changed over time for 46 selected countries in Europe and Central Asia by applying three nonparametric data envelopment analysis models that assume variable returns-to-scale, slacks-based measures (SBM), and Super SBM, respectively. Our results show that countries could have increased output by 1.2 % based on existing levels of inputs. The finding of decreased productivity growth is related to technical change, and super efficiency is found to provide a good framework for ranking efficient units. Based on the Super SBM model, we obtain proper scores and find the most efficient country.     

Multiple Objective Approach as an Alternative to Radial Projection in DEA

Radial projection is a standard technique applied in data envelopment analysis (DEA) to calculate efficiency scores for input and/or output variables. In this paper, we have studied the appropriateness of radial projection for target setting. We have created a situation where the decision making units (DMUs) are free to choose their own target values on the efficient frontier and then compared the results to those of radial projection. In practice, target values are primarily used for future goal attainment; hence, not only preferences but also, and on the whole, change in time frame, affect the choice of target values. Based on that, we conducted an empirical experiment with an aim to study how the DMUs choose their most preferred target values on the efficient frontier. The subjects, who all were students of the Helsinki School of Economics, were given the freedom to explore their personalized efficient frontiers by using a multiple objective linear programming (MOLP) approach. To study various and relevant scenarios, the personalized efficient frontiers for all students were constructed in such a way that the current position of each student in relation to the frontier made him/her inefficient, efficient, or super-efficient. The results show that the use of radial projection for target setting is too restrictive.     

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.     

Radial and nonradial measures of technical efficiency: An empirical illustration for Belgian local governments using an FDH reference technology

This paper serves two purposes. First, we argue that radial efficiency measures are inappropriate for the Free Disposal Hull (FDH) technology, and we provide a comparative analysis of alternative nonradial measures. In particular, using information on Belgian local government expenditures and output indicators we implement various radial and nonradial measures on the FDH reference technology, and we investigate to which extent these efficiency measures imply different distributions and rankings. Second, we analyze the patterns of measured technical efficiency implied by the various indices. Specifically, we investigate whether different measures make any substantial difference for the explanation of the calculated inefficiencies. The empirical results suggest that more important differences in rankings exist between radial and nonradial measures than between different nonradial alternatives; moreover, the radial and the nonradial efficiency measures do yield a somewhat different pattern of explanation.This is a revision of a paper presented at the 38th Conference of the Applied Econometrics Association in Athens (April 12–13, 1993). Comments of R. Goudriaan, Henry Tulkens, and two anonymous referees are gratefully acknowledged.     

The operating efficiency of financial holding and nonfinancial holding banks—Epsilou‐based measure metafrontier data envelopment analysis model

Previous bank efficiency studies assumed that the same efficient frontier system exists in different types of banks, but the conventional radial data envelopment analysis (DEA) model slacks are not counted in efficiency scores, and nonradial DEA models do not consider radial features. This paper develops an Epsilou‐based measure meta‐DEA approach for measuring the efficiencies and technology gaps of different bank types. The results are as the follows: The average efficiency and technology gaps of nonfinancial holding banks are better than those of financial holding banks. The nonfinancial holding banks are more efficient than financial holding banks in investment and other income.     

Measuring efficiency under fixed proportion technologies

Data Envelopment Analysis (DEA) applications frequently involve nonsubstitutable inputs and nonsubstitutable outputs (that is, fixed proportion technologies). However, DEA theory requires substitutability. In this paper, we illustrate the consequences of nonsubstitutability on DEA efficiency estimates, and we develop new efficiency indicators that are similar to those of conventional DEA models except that they require nonsubstitutability. Then, using simulated and real-world datasets that encompass fixed proportion technologies, we compare DEA efficiency estimates with those of the new indicators. The examples demonstrate that DEA efficiency estimates are biased when inputs and outputs are nonsubstitutable. The degree of bias varies considerably among Decision Making Units, resulting in substantial differences in efficiency rankings between DEA and the new measures. And, over 90% of the units that DEA identifies as efficient are, in truth, not efficient. We conclude that when inputs and outputs are not substituted for either technological or other reasons, conventional DEA models should be replaced with models that account for nonsubstitutability.     

Efficiency vectors, efficiency and performance measures: new methods for ranking efficient organizational units

We present and discuss measures for analyzing productivity in deterministic frontier models. A new efficiency measure is introduced allowing for discrimination among efficient organizational units. In addition, a new performance measure for analyzing productivity of organizational units is presented. This measure fulfills various properties of efficiency measures but relaxes the indicator property. Both new approaches are based on the development of efficiency vectors which is a new vector measure for measuring efficiency. The vector components are efficiency measures related to subsets of a production possibility set. The new approaches are applied in the context of data envelopment analysis.

A new criterion for technical efficiency measures: non‐monotonicity across dimensions axioms

Based on non‐parametric deterministic production technologies radial and non‐radial measures of technical efficiency are evaluated using properties guaranteeing insensitivity to the dimensionality of technology. These new axioms are important in empirical research and may especially prevent manipulation of results when implementing these benchmark methodologies in private or public organizations. An empirical example illustrates to which extent a series of radial and non‐radial technical efficiency measures satisfies the proposed axioms. Copyright © 1999 John Wiley & Sons, Ltd.     

The benefits of non-radial vs. radial super-efficiency DEA: an application to burden-sharing amongst NATO member nations

Using radial super-efficiency data envelopment analysis (DEA) has improved the discriminating performance across efficient decision-making units (DMUs). This paper extends the super-efficiency approach to a non-radial super-efficiency DEA (NRSE-DEA) index. NRSE-DEA is shown to be invariant to units of input (output) measurement. NRSE-DEA is illustrated here via an application to NATO burden-sharing assessment in which the DMUs are the member nations of NATO. The NRSE-DEA provides additional insights into the ranking of efficient countries, suggesting which are absorbing a particularly large share of NATO responsibilities. The NRSE-DEA generates a smaller set of efficient DMUs. This, in turn, provides more discriminatory power, a more accurate measure of super-efficiency, a more meaningful ranking of the efficient burden sharing countries, and a more reliable assessment of contributions by NATO members, amongst other policy issues.     

Measuring potential gains from reallocation of resources

In this work we consider the case when efficient operation of individual economic units does not necessarily imply efficiency for a group of these units. Merging theoretical findings of Li and Ng (Int Adv Econ Res, 1995, 1, 377.) and Färe and Zelenyuk (Eur J Oper Res, 2003, 146, 615), we develop new group-wise efficiency indexes that measure the extent to which the performance of a group of economic units can be enhanced, even if all these units are individually efficient. The existence of such potential improvement is attributed to non-optimal allocation of inputs across the individual economic units from the point of view of a group of these units.     

The scale of hospital production in different settings: one size does not fit all

This paper analyses the productive efficiency of 141 public hospitals from 1998 to 2004 in two Canadian provinces; one a small province with a few small cities and a generally more rural population and the other a large province that is more urban in nature, with a population who mainly live in large cities. The relative efficiencies of the hospitals, the changes in productivity during this time period, and the relationship between efficiency and the size or scale of the hospitals are investigated using data envelopment analysis. The models for the production of health care use case mix adjusted hospital discharges as the output, and nursing hours as inputs. We find clear differences between the two provinces. Making use of ‘own’ and ‘meta’ technical efficiency frontiers, we demonstrate that efficient units in the larger and more urban province are larger than non-efficient units in that province. However, efficient hospitals in the smaller and more rural province are smaller than non-efficient hospitals in that province. Overall, efficient hospitals in the larger more urban province are larger than efficient hospitals in the smaller more rural province. This has interesting policy implications—different hospitals may have different optimal sizes, or different efficient modes of operation, depending on location, the population they serve, and the policies their respective provincial governments wish to implement. In addition, there are lessons to be learned by comparing the hospitals across the two provinces, since the inefficient hospitals in the small rural province predominantly use hospitals from the large urban province as benchmarks, such that substantially larger improvement potential can be identified by inter-provincial rather than intra-provincial benchmarking analysis.     

Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates

Many studies devoted to efficiency performance evaluation in the education sector are based on measures of central tendency at school level as, for example, the average values of students belonging to the same school. Although this is a common and accepted way of summarizing data from the original observations (students), it is not less true that this approach neglects the existing dispersion of data, which may become a serious problem if variability across schools is high. Additionally, imprecision may arise when experts on each evaluated subject select the battery of questions, with different levels of difficulty, which will be the base for the final questionnaires completed by students. This paper uses data from US students and schools participating in PISA (Programme for International Student Assessment) 2015 to illustrate that schools' efficiency measures based on aggregate data and imprecision may reflect an inaccurate picture of their performance if they are compared to measures estimated accounting for broader information provided by all students of the same school. In order to operationalize our approach, we resort to Fuzzy Data Envelopment Analysis. This methodology allows us to deal with the notion of fuzziness in some variables such as the socio-economic status of students or test scores. Our results indicate that the estimated measures of performance obtained with the fuzzy DEA approach are highly correlated with those calculated with traditional DEA models. However, we find some relevant divergences in the identification of efficient units when we account for data dispersion and vagueness.     

The Dynamics of Efficiency Improving Input Allocation

A dynamic theory of efficiency improving input reallocations is presented which relaxes the assumption that decision-making units have the ability to reorganize their activities instantaneously to achieve efficient input allocations. Explicit account is taken of the decision-making unit’s gradual transition to an efficient input allocation. A balanced panel data set covering 906 U.S. agricultural banks is constructed for the period 1996–2000 and we find that these banks are allocatively efficient but technically inefficient. The explicit solution for the optimal input use finds evidence of gradual transitions for two of the three inputs, with the labor input transition being the slowest. The efficiency improving path finds the firm transitions toward an efficient allocation by simultaneously improving on technical efficiency instantaneously and on allocative efficiency intertemporally, which suggests a non-linear path toward the most efficient allocation.     

浅析港口装卸过程中的作业效率

主要讨论在港口装卸过程中的作业效率问题。虽然现今港口装卸工艺不断提高,但是人员的有效利用更能提高企业的效率。文中分别从港口的一线工人现状,存在的问题以及对其所采取的对策三个方面逐步展开来对港口装卸过程中作业效率进行分析。第一部分,主要阐述了在现代化的今天,港口装卸的一线工人体现出来的五大现状以及对其工资,所实行的分配制度等进行了一个简单的介绍。第二部分,主要论述了港口装卸过程中的作业工人还存在的一些问题,具体从三个方面来探讨,即人员来源,技术水平以及作业工安全。第三部分,根据前两部分的内容,提出了提高港口装卸过程中的作业工效率的六大措施,从生理到心理都提出了不同的建议。希望能够对港口企业在管理港口一线工人的工作中起到一定的借鉴作用。     

Efficiency aggregation with enhanced Russell measures in data envelopment analysis

In aggregation for data envelopment analysis (DEA), a jointly determined aggregate measure of output and input efficiency is desired that is consistent with the individual decision making unit measures. An impasse has been reached in the current state of the literature, however, where only separate measures of input and output efficiency have resulted from attempts to aggregate technical efficiency with the radial measure models commonly employed in DEA. The latter measures are “incomplete” in that they omit the non-zero input and output slacks, and thus fail to account for all inefficiencies that the model can identify. The Russell measure eliminates the latter deficiency but is difficult to solve in standard formulations. A new approach has become available, however, which utilizes a ratio measure in place of the standard formulations. Referred to as an enhanced Russell graph measure (ERM), the resulting model is in the form of a fractional program. Hence, it can be transformed into an ordinary linear programming structure that can generate an optimal solution for the corresponding ERM model. As shown in this paper, an aggregate ERM can then be formed with all the properties considered to be desirable in an aggregate measure—including jointly determined input and output efficiency measures that represent separate estimates of input and output efficiency. Much of this paper is concerned with technical efficiency in both individual and system-wide efficiency measures. Weighting systems are introduced that extend to efficiency-based measures of cost, revenue, and profit, as well as derivatives such as rates of return over cost. The penultimate section shows how the solution to one model also generates optimal solutions to models with other objectives that include rates of return over cost and total profit. This is accomplished in the form of efficiency-adjusted versions of these commonly used measures of performance.     

Learning from input–output mixes in DEA: a proportional measure for slack‐based efficient projections

Several Data Envelopment Analysis (DEA) models use a radial distance measure that is based on the Debreu–Farrell notion of (in)efficiency. While this measure has an attractive interpretation, its use may be problematic if slacks or zeros are present in the data. The additive DEA model can perfectly deal with these problems, but the meaning of its associated scores is less intuitive than the one attached to the radial measures. We introduce an alternative efficiency measure, based on the results of the additive model, that can be decomposed in a Debreu–Farrell component and a factor that captures differences in input–output mixes with respect to those of the best practice reference observation. On an aggregate level, this second component can be considered as an indicator of the dispersion between radial efficiency measurement and results based on the Pareto–Koopmans efficiency notion. On the individual level, the measure allows us to regard relative inefficiency as resulting from (i) a divergence of implicit cost price vectors, and (ii) a cost level that is too high, even after adjustment for the implicit cost prices. Copyright © 1999 John Wiley & Sons, Ltd.     

浅析基建工程合同结算的影响因素及对策

本文从基建工程项目结算审核过程中遇到的问题及加强建设管理和施工单位两方面着手,分析了矛盾产生的根本原因,并提出有效措施来减少工程结算中的问题,提高工程结算和审核效率。     

The Efficiency of Input Use During the Early Transition in Hungary

This paper uses Hungarian firm level panel data for the agricultural and light manufacturing sectors during the early years of the transition to investigate differences and changes in the efficiency of input use. Programming techniques measure scale and technical efficiency. The simple radial measure, as well as two other measures that account for programming slacks, are used. The results show little wastage of materials and labour, but inefficient use of energy and capital, which suggests that the development of input markets was uneven. The price liberalisation of 1989 widened efficiency differences, especially in agriculture, but this sector recovered quickest, actually using capital more efficiently by 1991. However, energy efficiency levels were low in the period of soft budget constraints and fell still further after the reforms, suggesting that a free market for energy was not established, particularly in agriculture.     

The impact of HR practices on the performance of business units

This article examines the impact of HR practices and organisational commitment on the operating performance and profitability of business units. Using a predictive design with a sample of 50 autonomous business units within the same corporation, the article reveals that both organisational commitment and HR practices are significantly related to operational measures of performance, as well as operating expenses and pre‐tax profits.