•We provide a new interpretation of optimal weights in DEA models with weight restrictions.•Such weights may not represent the given unit in the best light in comparison to all observed units.•The ...optimal weights are however the most favorable when the unit is benchmarked against the entire technology.•This interpretation also applies to conventional DEA models without weight restrictions.
According to a conventional interpretation of a multiplier DEA model, its optimal weights show the decision making unit under the assessment, denoted DMUo, in the best light in comparison to all observed DMUs. For multiplier models with additional weight restrictions such an interpretation is known to be generally incorrect (specifically, if weight restrictions are linked or nonhomogeneous), and the meaning of optimal weights in such models has remained unclear. In this paper we prove that, for any weight restrictions, the optimal weights of the multiplier model show DMUo in the best light in comparison to the entire technology expanded by the weight restrictions. This result is consistent with the fact that the dual envelopment DEA model benchmarks DMUo against all DMUs in the technology, and not only against the observed DMUs. Our development overcomes previous concerns about the use of weight restrictions of certain types in DEA models and provides their rigorous and meaningful interpretation.
•We consider nonparametric polyhedral technologies with undesirable outputs.•Examples of marginal characteristics include different rates and elasticity measures.•We solve a single linear program for ...each one-sided marginal characteristic.•This produces exact estimates of the minimal and maximal marginal values.•This avoids finding the ratio of shadow prices which are not uniquely defined.
There is extensive literature on the estimation of marginal characteristics of nonparametric production frontiers, including various marginal rates and elasticity measures. It has recently been shown that all such characteristics can be evaluated by a unifying linear programming approach applicable to any polyhedral production technology. In this paper we show how this approach can be applied to polyhedral technologies incorporating undesirable outputs. In particular, we derive a linear programming method for the direct assessment of the marginal rate of transformation between a bad and a good output often used for the estimation of the unobserved price of the bad output. In contrast with the existing methods based on a conventionally specified directional distance function, the new approach does not require the assessment of two shadow prices of the good and bad outputs. It also correctly estimates one-sided marginal rates in all cases in which the shadow prices on nonsmooth production frontiers are not unique.
In data envelopment analysis, a conventional procedure for testing efficiency of decision making units (DMUs) consists of two stages, each requiring solution of a linear program. The first stage ...identifies the input or output radial efficiency of a DMU, and the second stage maximizes the sum of component input and output slacks. A traditional alternative is the single-stage approximation of the two-stage procedure in which the objective functions of the first and second stages are combined, with the latter multiplied by a small positive constant epsilon. A known drawback of such approach is that very small values of epsilon may cause computational inaccuracies and large values do not allow a good approximation. In this paper, we develop a new single-stage linear programming approach that does not require the specification of a small constant epsilon and is completely equivalent to the conventional two-stage solution procedure. It produces exactly the same sets of primal and dual optimal solutions as the two separate stages of the two-stage approach. The new single-stage procedure is applicable to any convex polyhedral technology.
•We develop a single-stage solution approach for data envelopment analysis.•The new approach does not require the specification of a small constant epsilon.•The single-stage approach is equivalent to the conventional two-stage procedure.•The new approach is applicable to any convex polyhedral technology.
•We develop a model of technology with volume and ratio inputs and outputs.•We assume that the denominators of ratio measures are within some known bounds.•Information about the bounds improves the ...discriminating power of the models.•We consider both cases of variable and constant returns to scale.
Applications of data envelopment analysis often incorporate inputs and outputs stated as proportions or percentages, which are typically used to represent socio-economic and quality characteristics of the production process. As is well known, the use of such ratio measures is inconsistent with the assumption of convexity required by the conventional variable and constant returns-to-scale (VRS and CRS) technologies, and with the additional assumption of scalability in the case of CRS. Several existing approaches to modelling technologies with ratio data assume that either we know the exact volume numerators and denominators of all ratio measures or, alternatively, that we do not have such information. The former approaches are not always realistic and the latter are equivalent to benchmarking each decision making unit against a significantly reduced subset of observed units, which has a negative impact on the discriminating power of the model. In this paper, we develop new technologies under the assumptions of VRS and CRS that bridge the gap between the two known approaches. They are applicable in a general scenario in which we can specify some lower and upper bounds for the numerators or denominators of the ratio measures, which should be unproblematic in most practical settings. We demonstrate the usefulness and advantages of the developed approach by an application in the context of school education.
•We develop production technologies with groups of closely related inputs or outputs.•Closely related inputs or outputs are assumed to satisfy joint weak disposability.•The inputs and outputs that ...are not closely related are strongly disposable.•We develop the notion of returns to scale for the selectively disposable technology.•The usefulness of the suggested model is demonstrated by a computational example.
The conventional constant and variable returns-to-scale models of data envelopment analysis (DEA) incorporate the assumption of strong, or free, disposability. According to this assumption, each input can be increased and each output can be reduced independently of the other measures. In this paper we argue that this assumption may not be suitable in applications in which some inputs or outputs are closely related to each other. Assuming strong disposability of such closely related measures may lead to unrealistic input and output profiles, and result in meaningless efficiency scores. Examples include inputs and outputs that are strongly correlated, represent overlapping measures or situations in which one measure is a subset of another. In this paper we develop production technologies that allow the specification of groups of closely related inputs and outputs which are only jointly weakly disposable. This assumption does not change the existing proportions between the closely related measures in the same group. We demonstrate the usefulness of the suggested approach by computational experiments.
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.
In this paper we consider the use of data envelopment analysis (DEA) for the assessment of efficiency of units whose output profiles exhibit specialisation. An example of this is found in agriculture ...where a large number of different crops may be produced in a particular region, but only a few farms actually produce each particular crop. Because of the large number of outputs, the use of conventional DEA models in such applications results in a poor efficiency discrimination. We overcome this problem by specifying production trade-offs between different outputs, relying on the methodology of Podinovski (J Oper Res Soc 2004;55:1311–22). The main idea of our approach is to relate various outputs to the production of the main output. We illustrate this methodology by an application of DEA involving agricultural farms in different regions of Turkey. An integral part of this application is the elicitation of expert judgements in order to formulate the required production trade-offs. Their use in DEA models results in a significant improvement of the efficiency discrimination. The proposed methodology should also be of interest to other applications of DEA where units may exhibit specialization, such as applications involving hospitals or bank branches.
•Efficiency assessment of units with specialised production profiles is considered.•The use of production trade-off in DEA is demonstrated by an application to agriculture.•Expert judgements are used to assess production trade-offs.•The trade-off approach yields a significant improvement to the efficiency discrimination.
Pitfalls and protocols in DEA Podinovski, V. V; Sarrico, C. S; Dyson, R. G ...
European journal of operational research,
07/2001, Letnik:
132, Številka:
2
Journal Article
Recenzirano
The practical application of data envelopment analysis (DEA) presents a range of procedural issues to be examined and resolved including those relating to the homogeneity of the units under ...assessment, the input/output set selected, the measurement of those selected variables and the weights attributed to them. Each of these issues can present difficulties in practice. The purpose of this paper is to highlight some of the pitfalls that have been identified in application papers under each of these headings and to suggest protocols to avoid the pitfalls and guide the application of the methodology.
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