Rodney H. Green

Cross-Evaluation in DEA - Improving Discrimiation Among DMUs

AbstractThere is a need to distinguish among efficient DMUs in Data Envelopment Analysis (DEA). We introduce cross-evaluation in DEA as a logical extension of the reference set count, an idea which is already well established in the literature as a way of discriminating among efficient DMUs. We argue that cross-evaluation is more general, and more powerful than the reference-set count. Next we describe four variants of cross-evaluation, each with its own particular meaning; then we describe their implementations as secondary goals to the usual DEA efficiency-maximising primary goal. We compare the performance of the four variants on a dozen data sets that have appeared in the DEA literature, paying particular attention to the effect of the different input-output structures among the data sets. We then illustrate, with one constructed example and one semi-realistic simulation, that cross-evaluation can give better results (in terms of robustly recovering unobserved ‘real’ efficiencies) than simple DEA effi...

Testing the Reliability of Weight Elicitation Methods: Direct Rating Versus Point Allocation

Two commonly used methods of assigning numerical judgments (i.e., importance weights) to attributes in order to signify their relative importance are point allocation (PA) and direct rating (DR). These methods may seem to be minor variants of each other, yet they produce very different profiles of attribute weights when rank ordered from most to least important. The weights elicited by DR were more reliable than those elicited by PA in a test–retest situation. An important practical implication of this is for multicriteria decision making. Using peoples test–retest data as attribute weights on simulated alternative values revealed that the same alternative would be chosen on 88% of occasions with DR, but only 74% of occasions with PA. Moreover, subjects reacted more favorably to DR than to PA.

Hierarchies and Groups in DEA

Conventional applications of data envelopment analysis (DEA) presume the existence of a set of similar decision making units, wherein each unit is evaluated relative to other members of the set. Often, however, the DMUs fall naturally into groupings, giving rise first to the problem of how to view the groups themselves as DMUs, and second to the issue of how to deal with several different ratings for any given DMU when groupings can be formed in different ways. In the present paper we introduce the concept of hierarchical DEA, where efficiency can be viewed at various levels. We provide a means for adjusting the ratings of DMUs at one level to account for the ratings received by the groups (into which these DMUs fall) at a higher level. We also develop models for aggregating different ratings for a DMU arising from different possible groupings. An application of these models to a set of power plants is given.

Dual-role factors in data envelopment analysis

This paper presents a methodology for dealing with performance evaluation settings where factors can simultaneously play both input and output roles. Model structures are developed for classifying Decision-Making Units (DMUs) into three groups according to whether such a factor is behaving like an output, an input, or is in equilibrium, neither wanting to lose or gain any of the factors. We connect these ideas to those involving increasing, decreasing and constant returns to scale. Examples of factors that play this dual-role are: trainees in organizations, such as nurses, medical students, and doctoral students; awards to scholars or university departments; certain revenue—generating transactions in banks, and so on. We apply the model to the analysis of a set of university departments. In some settings, a dual-role factor may be one that can be reallocated, such as would be the case when DMUs are managed by a central authority. We develop the appropriate model structures to permit such a reallocation. We present two such structures, with the first involving reallocation from an existing allocation, and the second, a zero-base allocation.

Project prioritization: a resource-constrained data envelopment analysis approach

Abstract The problem considered in this paper is that of selecting, from a larger set of proposals, a subset of projects to be undertaken. Each project is expected to make use of input resources under a number of headings to produce outputs under a number of headings. It is desired to establish a subset of projects that can be justified as making the best use of available resources. There is no a priori agreement amongst all concerned about how inputs and outputs should be weighted and combined to facilitate the evaluation and selection of the projects. In essence, our approach treats each subset of the projects that could feasibly be selected within the resource constraints as a single, composite project. These composite projects are then evaluated, by data envelopment analysis, against a ‘production technology’ defined by the available projects. In fact, evaluation and selection are combined in a single model by placing the data envelopment analysis model within a mixed-binary linear programming framework. This model is illustrated using Oral, Kettani and Lang’s [1, Management Science 1991; 37(7): 871–883] data on 37 R&D projects. Extensions to the basic model are discussed in the context of prioritizing highway safety retrofit projects.

A heuristic for facilities layout planning

A new matrix representation of a planar graph and its dual is presented. This is then used to implement a heuristic for facilities layout planning.

The judge, the model of the judge, and the model of the judged as judge: Analyses of the UK 1992 research assessment exercise data for business and management studies

This paper examines the judgments (part of a multi-million pound government-sponsored resource allocation exercise) made by a panel of experts about the research rating of UK business schools during 1988-1992. We use policy capture to determine, and critically evaluate, how business schools were judged. We suggest methods to improve the process of judgment-principally, using DEA as an idealized model whereby the judged institutions judge themselves, consistent with policy constraints.

EFFICIENCY BOUNDS IN DATA ENVELOPMENT ANALYSIS

This paper considers a proposal, by Chang and Guh, that the non-archimedean infinitesimal in the CCR data envelopment analysis model be replaced with a data-dependent finite magnitude. Whilst the intention of the proposal is clear: to reduce the CCR efficiency rating of certain problematic DMUs, it is found not to work in practice. An alternative implementation, which puts the CCR model into a mixed-binary linear programming framework, is developed. Chang and Guhs proposal is also related to the earlier modification to the CCR model, Constrained Facet Analysis. Both are seen as providing bounds on the relative efficiency of DMUs which are not properly enveloped in the CCR model.

Multicomponent efficiency measurement and core business identification in multiplant firms: A DEA model ☆

Performance modelling, across a set of similar decision making units (DMUs), has generally been directed toward the derivation of a single measure of efficiency. Data envelopment analysis (DEA) is often a tool of choice in arriving at such a measure. In the current paper, performance is viewed from a multi-functional perspective, with the ultimate goal being to identify for each DMU, the function or component of the business that should be deemed that DMUs core business. We present a modified version of the DEA model to accommodate this core business selection. The model is applied to a set of manufacturing plants in the steel molding and sheet steel industry.

Strategic choice and data envelopment analysis: comparing computers across many attributes

A linear programming approach (Data Envelopment Analysis) is described to determine the relative merits of a set of multi-input, multi-output systems, in which more output for less input is considered good. The method is applied to benchmarks of microcomputers, and is contrasted with a multiple regression analysis of the same data. It is also argued that the essence of two opposing strategic outlooks can be captured within the method.