A cost Malmquist productivity index

This paper develops a productivity index applicable when producers are cost minimisers and input prices are known. The index is inspired by the Malmquist index as extended to productivity measurement. The index developed here is defined in terms of input cost rather than input quantity distance functions. Hence, productivity change is decomposed into overall efficiency and cost technical change. Furthermore, overall efficiency change is decomposed into technical and allocative efficiency change and cost technical change into a part capturing shifts of input quantities and shifts of relative input prices. These decompositions provide a clearer picture of the root sources of productivity change. They are illustrated here in a sample of hospitals; results are computed using non-parametric mathematical programming.     

Operational and economic efficiency analysis of public hospitals in Greece

The continuous growth of hospital costs has driven governments in many countries to seek ways to improve their efficiency. In Greece, this has consistently been a major issue for almost two decades, as efficiency assessment and monitoring systems are lacking. In response to this need, the evaluation of the National Health System hospitals’ efficiency level is a precondition for planning, implementing and monitoring any promising reform. In this paper, a non-parametric modeling approach is employed to assess and analyze the efficiency of 87 Greek public hospitals over the period 2005–2009, using data envelopment analysis. The operational and economic aspects of the hospitals’ operation are considered on the basis of their service/case mix and cost structure. We also investigate the efficiency trends over time with the Malmquist index and a second stage regression analysis is performed to explain the operational and economic efficiency results in terms of the hospitals’ operating characteristics and the environment in which they operate.     

Estimating output allocative efficiency and productivity change: Application to Japanese banks

A new measure of output allocative efficiency is developed by comparing the input technical efficiency of a firm for the direct input requirement set and the indirect input requirement set proposed by Shephard [Indirect Production Functions, Verlag Anton Hain, Meisenheim Am Glan]. The ratio of the direct and indirect input quasi-distance functions serves as the measure of output allocative efficiency. As such, it measures the ratio of potential to actual inputs if the firm had chosen the revenue maximizing output mix. Using panel data on Japanese banks operating during 1992–1996 productivity growth is measured and decomposed into changes in output allocative efficiency, changes in input technical efficiency, and technical change. During the period, Japanese banks experienced productivity declines averaging 2% per year and could have used only 78–93% of actual inputs if they had chosen the revenue maximizing output mix.     

Evaluating public school district performance via DEA gain functions

Existing measures of input allocative efficiency may be biased when estimated via data envelopment analysis (DEA) because of the possibility of slack in the constraints defining the reference technology. In this paper we derive a new measure of input allocative efficiency and compare it to existing measures. We measure efficiency by comparing the actual outputs of a decision-making unit relative to Koopmans’ efficient subset of the direct and indirect output possibility sets. We estimate the existing measures and our new measure of input allocative efficiency for a sample of public school districts operating in Texas.     

Resolving a strange case of efficiency

In a recent paper in the Journal of the Operational Research Society, Tone proposes an alternative to the Farrell cost efficiency index to avoid the ‘strange case’ problem in which firms with identical inputs and outputs but with input prices differing by some factor (eg, one has input prices twice another) will have the same Farrell cost efficiency. We provide an alternative cost efficiency indicator that avoids this problem, allows for decomposition into technical and allocative efficiency, and is easily estimated using DEA type models.     

Estimating output gains by means of Luenberger efficiency measures

In this paper we propose a new measure of input allocative efficiency that we estimate using directional distance functions. Our new measure compares the gain in output if a firm reduces technical inefficiency for the direct production possibility set and the gain in output if the firm reduces technical inefficiency for the indirect production possibility set. Because the directional distance function uses a translated origin, the gain in output from an optimal reallocation of inputs can be estimated for non-radial expansions in output. We estimate efficiency for Japanese banks during 1992–1999. The gains in outputs from reducing allocative inefficiency by reallocating inputs are greater than the gains in outputs that can be attained by reducing technical inefficiency.     

Service quality and operating efficiency synergies for management control in the provision of financial services: Evidence from Greek bank branches

In this paper we concentrate on the assessment of the productive efficiency of bank branches. Bank branch operations are characterised by the effort made by management to pursue the banks' corporate objectives. The tangible part of this effort can be assessed by the operating efficiency of the branch while the intangible part is encapsulated by the quality of the provided services. The assessment of branch efficiency is pursued using data envelopment analysis methods enhanced by the value judgements of individual branch managers. This development gives insights on issues related to the appropriateness of branch input mix. The effort effectiveness is estimated by embodying three quality dimensions on the operating efficiency of bank branches. Empirical results are discussed from a sample of sixty eight commercial bank branches in Greece.     

Exploring the use of DEA for formative evaluation in primary diabetes care: An application to compare English practices

Primary care is currently at the heart of the UK National Health Service policy. Primary care trusts have the crucial role of improving the efficiency and equity in primary care delivery. However, few studies have focused on performance assessment in primary care provision. In this paper, we examine the role of data envelopment analysis (DEA) in helping decision makers to understand and improve the performance of primary care practices. We discuss the results from a study of 14 practices in England in terms of their delivery of diabetes services. In order to take into account the multiple values that underlie public services provision, we have considered several different perspectives for evaluation. These were: technical, allocative and cost efficiency, clinical and patient-focused effectiveness, and equity. The approach adopted involved a deep engagement with the practices. The purpose was to understand the structures and processes supporting effective practice using DEA in a formative role rather than the more usual summative role with a large data set. This approach is in the tradition of the developmental engagement approach of operational research.     

Cost,revenue and profit efficiency measurement in DEA: A directional distance function approach

Estimation of efficiency of firms in a non-competitive market characterized by heterogeneous inputs and outputs along with their varying prices is questionable when factor-based technology sets are used in data envelopment analysis (DEA). In this scenario, a value-based technology becomes an appropriate reference technology against which efficiency can be assessed. In this contribution, the value-based models of Tone (2002) are extended in a directional DEA set up to develop new directional cost- and revenue-based measures of efficiency, which are then decomposed into their respective directional value-based technical and allocative efficiencies. These new directional value-based measures are more general, and include the existing value-based measures as special cases. These measures satisfy several desirable properties of an ideal efficiency measure. These new measures are advantageous over the existing ones in terms of (1) their ability to satisfy the most important property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3) flexibility in providing the decision makers with the option of specifying preferable direction vectors to incorporate their preferences. Finally, under the condition of no prior unit price information, a directional value-based measure of profit inefficiency is developed for firms whose underlying objectives are profit maximization. For an illustrative empirical application, our new measures are applied to a real-life data set of 50 US banks to draw inferences about the production correspondence of banking industry.     

A DEA approach to derive individual lower and upper bounds for the technical and allocative components of the overall profit efficiency

In this paper, we propose a slack-based data envelopment analysis approach to be used in economic efficiency analyses when the objective is profit maximization. The focus is on the measurement of the technical component of the overall efficiency with the purpose of guaranteeing the achievement of the Pareto efficiency. As a result, we will be able to estimate correctly the allocative component in the sense that this latter only reflects the improvements that can be accomplished by reallocations along the Pareto-efficient frontier. Some new measures of technical and allocative efficiency in terms of both profit ratios and differences of profits are defined. We do not make any assumption on the way the technical efficiency is to be measured, that is, we do not use, for example, either a hyperbolic measure or a directional distance function, which allows us to extend this approach and derive individual lower and upper bounds for these efficiency components. To do it, we use novel models of minimum distance to the frontier. This broadens the range of possibilities for the explanation of the overall efficiency in terms of technical and allocative inefficiencies.     

Efficient firm groups: Allocative efficiency in cooperative games

The concept of efficiency in groups postulates that a coalition of firms has to record a smaller distance toward the aggregate technology frontier compared with the sum of individual distances. Efficiency analysis (either allocative or technical) is defined with respect to cooperative firm game in order to provide operational distance functions, the so-called pseudo-distance functions. These pseudo-distances belong to the core interior of the allocative firm game, in other terms, any given firm coalition may always improve its allocative efficiency. We prove that such a result is impossible for technical efficiency, i.e., the technical efficiency cannot increase for all possible coalitions.     

A circular global profit Malmquist productivity index in data envelopment analysis

To remove the difficulty caused by different profit frontiers in different periods of time for calculating profit efficiency changes and its components, this paper proposes a circular global profit Malmquist productivity index. This index is applicable when the input costs and output prices are known and when producers seek to maximize the total profit of their decision making units (DMUs). To this end, first, two methods are introduced to obtain the common costs and prices with or without the decision maker’s preferences, and then, a common profit efficient frontier is obtained. The proposed index can be decomposed into several circular components, viz., profit efficiency change, profit technical change, technical efficiency change, allocative efficiency change, technical change, and cost/price change. The proposed index is then generalised to compare the productivity of two different units at two different points in time. The global profit Malmquist productivity index developed here is unique and is computed using nonparametric linear programming model known as data envelopment analysis (DEA), and there is no need to resort to the geometric mean in the calculation. To illustrate the proposed index and its components, numerical examples at three successive periods of time are given.     

Measurement and sources of overall and input inefficiencies: Evidences and implications in hospital services

Traditional data envelopment analysis (DEA) focuses exclusively on measuring the overall efficiency of a decision making unit (DMU). Yet, variables that have explanatory power for the overall operational inefficiency of a DMU may not necessarily be the same as those that affect its individual input inefficiencies. On many occasions, variables that explain the overall inefficiency of a DMU can be inconsistent or incongruent with those that cause its individual input inefficiencies. Therefore, we conjecture that an overall inefficiency score alone may have limited value for decision making since such a process requires fine-tuning and adjustments of specific input factors of the DMU in order to maximize its overall efficiency. In this paper, the utilization and financial data of a set of hospitals in California is used to empirically test the above conjecture.Our study has several important contributions and practical implications. First, we fine-tune previous efficiency measures on hospitals by refining input and output measures. Second, with variables on organization, management, demographics, and market competition, we identify specific factors associated with a hospital's overall operational inefficiency. More importantly, by decomposing the overall DEA operational inefficiency score into different individual input inefficiencies (including slacks), we further identify specific variables that cause individual input inefficiency. Third, significant differences are observed among factors of the overall inefficiency and individual input inefficiencies. These findings have important implications for identifying congruent factors for performance standard setting and evaluation; it also provides invaluable information for guiding effective resource allocation and better decision making for improving hospital operational efficiency.     

Developing a decomposable measure of profit efficiency using DEA

In for-profit organizations efficiency measurement with reference to the potential for profit augmentation is particularly important as is its decomposition into technical, and allocative components. Different profit efficiency approaches can be found in the literature to measure and decompose overall profit efficiency. In this paper, we highlight some problems within existing approaches and propose a new measure of profit efficiency based on a geometric mean of input/output adjustments needed for maximizing profits. Overall profit efficiency is calculated through this efficiency measure and is decomposed into its technical and allocative components. Technical efficiency is calculated based on a non-oriented geometric distance function (GDF) that is able to incorporate all the sources of inefficiency, while allocative efficiency is retrieved residually. We also define a measure of profitability efficiency which complements profit efficiency in that it makes it possible to retrieve the scale efficiency of a unit as a component of its profitability efficiency. In addition, the measure of profitability efficiency allows for a dual profitability interpretation of the GDF measure of technical efficiency. The concepts introduced in the paper are illustrated using a numerical example.     

Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis

This paper replaces ordinary DEA formulations with stochastic counterparts in the form of a series of chance constrained programming models. Emphasis is on technical efficiencies and inefficiencies which do not require costs or prices, but which are nevertheless basic in that the achievement of technical efficiency is necessary for the attainment of ‘allocative’, ‘cost’ and other types of efficiencies.     

Information Management,Organization and Managerial Effectiveness

In this paper we argue that information management is not only about managing the information resources of an organization as an economic activity; it is also about the use that individuals make of their information inputs and outputs. The discussion centres on individual managers, particularly on how successful they are in converting information into effective action. The management of complexity is seen as the cornerstone of managerial activities; managers are always faced with the problem of matching their limited information-processing capacity to the much larger information space implied by their responsibilities and commitments. It is argued that managers can employ at least three possible strategies to achieve an adequate matching: they can make adjustments to the organization structure; they can design their organizational conversations; and they can aim at a good manager-to-task fit.     

Assessing the performance of biogas plants with multi-criteria and data envelopment analysis

This paper performs an assessment of 41 agricultural biogas plants located in Austria to determine their relative performance in terms of economic, environmental, and social criteria and corresponding indicators. The comparison of these renewable energy conversion plants is based on two complementary analyses. Data envelopment analysis (DEA) was conducted to provide measures of radial efficiency relative to the observed frontier of production possibilities. Multi-criteria decision analysis (MCDA), using the IRIS/ELECTRE TRI methodology, was conducted to obtain a different perspective on the results, and as a tool that would enable to incorporate managerial preferences easily. To be able to use IRIS while keeping the spirit behind DEA, the evaluation criteria were defined as different output/input efficiency ratios, and no information about criteria weights was introduced at the outset. The results suggest that MCDA, and the use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to DEA.     

Single-Period Markowitz Portfolio Selection,Performance Gauging,and Duality: A Variation on the Luenberger Shortage Function

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimization.     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments

This paper enhances cost efficiency measurement methods to account for different scenarios relating to input price information. These consist of situations where prices are known exactly at each decision making unit (DMU) and situations with incomplete price information. The main contribution of this paper consists of the development of a method for the estimation of upper and lower bounds for the cost efficiency (CE) measure in situations of price uncertainty, where only the maximal and minimal bounds of input prices can be estimated for each DMU. The bounds of the CE measure are obtained from assessments in the light of the most favourable price scenario (optimistic perspective) and the least favourable price scenario (pessimistic perspective). The assessments under price uncertainty are based on extensions to the Data Envelopment Analysis (DEA) model that incorporate weight restrictions of the form of input cone assurance regions. The applicability of the models developed is illustrated in the context of the analysis of bank branch performance. The results obtained in the case study showed that the DEA models can provide robust estimates of cost efficiency even in situations of price uncertainty.