Relationships between Data Envelopment Analysis and Multicriteria Decision Analysis

We contrast the different approaches of Data Envelopment Analysis (DEA) and Multiple Criteria Decision Making (MCDM) to superficially similar problems. The concepts of efficiency and Pareto optimality in DEA and MCDM are compared, and a link is demonstrated between the ratio efficiency definition in DEA and a distance measure in input–output space based on linear value functions. The problem of weight sensitivity is discussed in terms of value measurement theory, highlighting the assumptions needed during model formulation in order to justify the use of value judgements to constrain weight flexibility in DEA. Finally, we propose a stochastic approach, in which a probability distribution on efficiencies can be derived for each decision making unit, as a basis for comparison.     

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.     

Measuring ecological efficiency with data envelopment analysis (DEA)

The measurement of ecological efficiency provides some important information for the companies’ environmental management. Ecological efficiency is usually measured by comparing environmental performance indicators. Data envelopment analysis (DEA) shows a high potential to support such comparisons, as no explicit weights are needed to aggregate the indicators. In general, DEA assumes that inputs and outputs are ‘goods’, but from an ecological perspective also ‘bads’ have to be considered. In the literature, ‘bads’ are treated in different and sometimes arbitrarily chosen ways. This article aims at the systematic derivation of ecologically extended DEA models. Starting from the assumptions of DEA in production theory and activity analysis, a generalisation of basic DEA models is derived by incorporating a multi-dimensional value function f. Extended preference structures can be considered by different specifications of f, e.g. specifications for ecologically motivated applications of DEA.     

Allfinanz,bancassurance and the future of banking

The purpose with this paper is first to analyse the strategies of Allfinanz (Bancassurance) in Germany and then to investigate if the German banks have become more efficient during the period since Allfinanz was introduced. Two methods are used to analyse efficiency: ‘financial ratio analysis’ (FRA) and ‘data envelopment analysis’ (DEA). FRA is useful in studying the change in productivity. DEA generates, efficiency scores and alternative and more efficient combinations of banks.     

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.     

The effects of exogenous variables in efficiency measurement—A monte carlo study

A Monte Carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis (DEA) method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control. In making efficiency measurements and comparisons, one must separate the effects of the environment (the exogenous factors) and the effects of the productive efficiency. There are two basic approaches to account for the effects of exogenous variables: (1) an one-step procedure which includes the exogenous variables directly in estimating the efficiency measures, and (2) a two-step procedure which first estimates the relative ‘gross’ efficiencies using inputs and outputs, then analyzes the effects of the exogenous variables on the ‘gross’ efficiency. The results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one-step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for. However, the effects of exogenous variables are significant for the two-step approach, especially for the DEA methods.     

Adapting and refining in multi-criteria decision-making

This paper describes the implementation of a Structured Methodology for Direct-Interactive Structured-Criteria (DISC) Multi-Criteria Decision-Making (MCDM), an eight-stage nomological adjusting cycle of activities that shape the information used to make a decision, requiring it be accessible, differentiable, abstractable, understandable, verifiable, measurable, refinable and usable. It shows, in a major IT strategic investment case, that Structured DISC MCDM provides a robust model that can be used for deep and serious consideration of multi-criteria decisions by a group of decision-makers over a long period. The paper describes the case as it moves through stages of the adjusting cycle and shows that, after completing the cycle, it reverses and becomes an adapting process, starting with refining the information. Refining is shown to be more extensive than previously understood, and to cover ‘alternatives & scores’, ‘criteria & weights’ and ‘set of alternatives’. Next the form of measurement is adapted. As the number of alternatives are reduced it can become more appropriate to directly compare the two or three most preferred alternatives relative to one another rather than objectively. Finally the criteria tree can be adapted using a ‘magnifying glass’ approach. This confines the evaluation to that part of the criteria tree in which the difference between a few preferred alternatives is mainly emphasised.     

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.     

Two-stage network DEA: when intermediate measures can be treated as outputs from the second stage

This paper investigates efficiency measurement in a two-stage data envelopment analysis (DEA) setting. Since 1978, DEA literature has witnessed the expansion of the original concept to encompass a wide range of theoretical and applied research areas. One such area is network DEA, and in particular two-stage DEA. In the conventional closed serial system, the only role played by the outputs from Stage 1 is to behave as inputs to Stage 2. The current paper examines a variation of that system. In particular, we consider settings where the set of final outputs comprises not only those that result from Stage 2, but can include, in addition, certain outputs from the previous (first) stage. The difficulty that this situation creates is that such outputs are attempting to play both an input and output role in the same stage. We develop a DEA-based methodology that is designed to handle what we term ‘time-staged outputs’. We then examine an application of this concept where the DMUs are schools of business.     

Production trade-offs and weight restrictions in data envelopment analysis

In this paper we suggest two equivalent ways in which the information about production trade-offs between the inputs and outputs can be incorporated into the models of data envelopment analysis (DEA). Firstly, this can be implemented by modifying envelopment DEA models. Secondly, the same information can be captured using weight restrictions in multiplier DEA models. Unlike other methods used for the assessment of weight restrictions, for example those based on value judgements or monetary considerations, the trade-off approach developed in this paper ensures that the radial target of any inefficient unit is technologically realistic and, therefore, the efficiency measure retains its traditional meaning of the extreme radial improvement factor. In other words, this paper suggests that ‘technology thinking’ could be used instead of ‘value thinking’ in the construction of weight restrictions, which offers real practical advantages. The method is equally applicable to the models under constant and variable returns-to-scale assumptions.     

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.     

The relationship between the efficiency of orthopedic wards and the socio-economic status of their patients

The purpose of this paper is to study the effect of the socio-economic status of patients on the efficiency of orthopedic wards in acute hospitals in Israel (20 hospitals), from the viewpoint of the regulator—Israel Ministry of Health. At the first stage, data envelopment analysis is used with two inputs, and three outputs, where one output is undesirable—“number of deaths”—which also reflects the quality of the health services. At the second stage, various nonparametric tests are utilized to test the relationship between the socio-economic status of patients and the efficiency. As by-product DEA provides benchmark analysis, which indicates the peers of each inefficient ward, and the I/O improvements are needed for achieving efficiency. Two versions of DEA were used: the output oriented version (variable returns to scale), and the non-oriented version (Additive). Further analysis provides comparison of the results with other simple efficiency measures. We also compare between the efficiency from the regulator viewpoint and the hospitals’ viewpoint.     

Radii of Classification Preservation in Data Envelopment Analysis: a Case Study of ‘Program Follow-Through’

Sensitivity and robustness of efficiency classifications for the additive model and its geometric equivalents in Data Envelopment Analysis (DEA) are addressed. The minimum distance (measured by a Tchebycheff norm) separating an organization from reclassification is computed via linear programming formulations and shown to constitute a generalized ‘residual’ for each organization. Without this sensitivity information, findings can be distorted when marginally efficient or inefficient units are distinguished solely on the basis of their classification. Analysis of these residuals from an earlier (inconclusive) DEA study further reveals how substantive differences in a sample's underlying groups can be detected. Properties of group efficiency and group proximity to the efficient frontier are investigated using these new indicators.     

A comparison of chance-constrained DEA and stochastic frontier analysis: bank efficiency in Taiwan

We employed both chance-constrained data envelopment analysis (CCDEA) and stochastic frontier analysis (SFA) to measure the technical efficiency of 39 banks in Taiwan. Estimated results show that there are significant differences in efficiency scores between chance-constrained DEA and stochastic frontier production function. The advanced setting of the chance-constrained mechanism of DEA does not change the instinctive differences between DEA and SFA approaches. We further find that the ownership variable is still a significant variable to explain the technical efficiency in Taiwan, irrespective of whether a DEA, CCDEA or SFA approach is used.     

Interval cross efficiency for fully ranking decision making units using DEA/AHP approach

Data envelopment analysis (DEA) is a popular technique for measuring the relative efficiency of a set of decision making units (DMUs). Fully ranking DMUs is a traditional and important topic in DEA. In various types of ranking methods, cross efficiency method receives much attention from researchers because it evaluates DMUs by using self and peer evaluation. However, cross efficiency score is usual nonuniqueness. This paper combines the DEA and analytic hierarchy process (AHP) to fully rank the DMUs that considers all possible cross efficiencies of a DMU with respect to all the other DMUs. We firstly measure the interval cross efficiency of each DMU. Based on the interval cross efficiency, relative efficiency pairwise comparison between each pair of DMUs is used to construct interval multiplicative preference relations (IMPRs). To obtain the consistency ranking order, a method to derive consistent IMPRs is developed. After that, the full ranking order of DMUs from completely consistent IMPRs is derived. It is worth noting that our DEA/AHP approach not only avoids overestimation of DMUs’ efficiency by only self-evaluation, but also eliminates the subjectivity of pairwise comparison between DMUs in AHP. Finally, a real example is offered to illustrate the feasibility and practicality of the proposed procedure.     

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.     

Data envelopment analysis with common weights: the compromise solution approach

A characteristic of data envelopment analysis (DEA) is to allow individual decision-making units (DMUs) to select the factor weights that are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. In order to rank all the DMUs on the same scale, this paper proposes a compromise solution approach for generating common weights under the DEA framework. The efficiency scores calculated from the standard DEA model are regarded as the ideal solution for the DMUs to achieve. A common set of weights which produces the vector of efficiency scores for the DMUs closest to the ideal solution is sought. Based on the generalized measure of distance, a family of efficiency scores called ‘compromise solutions’ can be derived. The compromise solutions have the properties of unique solution and Pareto optimality not enjoyed by the solutions derived from the existing methods of common weights. An example of forest management illustrates that the compromise solution approach is able to generate a common set of weights, which not only differentiates efficient DMUs but also detects abnormal efficiency scores on a common base.     

A game theoretical model of DEA efficiency

Motivated by the inherent competitive nature of the DEA efficiency assessment process, some effort has been made to relate DEA models to game theory. Game theory is considered not only a more natural source of representing competitive situations, but also beneficial in revealing additional insights into practical efficiency analysis. Past studies are limited to connecting efficiency games to some particular versions of DEA models. The generalised DEA model considered in this study unifies various important DEA models and presents a basic formulation for the DEA family. By introducing a generalised convex cone constrained efficiency game model in assembling the generalised DEA model, a rigorous connection between game theory and the DEA family is established. We prove the existence of optimal strategies in the generalised efficiency game. We show the equivalence between game efficiency and DEA efficiency. We also provide convex programming models for determination of the optimal strategies of the proposed games, and show that the game efficiency unit corresponds to the non-dominated solution in its corresponding multi-objective programming problem. Our study largely extends the latest developments in this area. The significance of such an extension is for research and applications of both game theory and DEA.     

A multiple criteria ranking method based on game cross-evaluation approach

The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87?C100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278?C1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative??s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.     

Alternative statistical regression studies of the effects of Joint and Service Specific advertising on military recruitment

Three different regression approaches use a large database developed by the Wharton Center for Applied Research (WCAR) to study the effects of Joint versus Service Specific advertising on military recruitment. (Here ‘Joint’ refers to advertising designed to serve recruitment for all four services simultaneously. Service Specific refers to advertising administered separately by each of the four services.) These regression approaches and the data and models are examined with special reference to US Army recruitment. The WCAR study led to a recommendation to replace Service Specific with Joint advertising. This recommendation was called into question by the RAND Corporation in its study that used a different regression approach. A third study that combines regressions with data envelopment analysis (DEA) is presented in this paper. This study utilizes recently developed methods based on DEA which, when incorporated in the regression, make it possible to distinguish between efficient and inefficient performances. The resulting regression yields results that show Joint advertising to be not only less efficient but also to attract potential recruits from the Army to other services. Implications for further research are set forth, which can also cast light on commercial practice by regarding Joint as a type of ‘category advertising’ and Service Specific as a type of ‘brand advertising’.