An epsilon-based measure of efficiency in DEA – A third pole of technical efficiency

A multivariate statistical approach to reducing the number of variables in data envelopment analysis

Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction

This paper is primarily concerned with data envelopment analysis (DEA) of systems where negative outputs and negative inputs arise naturally. Examples of situations in which both negative inputs and negative outputs occur are given. More attention has been paid, in the literature, to the former type of problem. Most available DEA software does not solve this type of problem or copes with negative outputs and possibly negative inputs by assigning zero weights to them. A modified slacks-based measure (MSBM) model is presented, in which both negative outputs and negative inputs occur. The MSBM model overcomes the lack of translation invariance in the slacks-based measure model by drawing on the ideas from the range directional model (RDM). The MSBM model takes into account individual input and output slacks, which provides more precise evaluation of inefficient decision-making units (DMUs). It therefore, generally leads to lower efficiencies for inefficient DMUs than the RDM.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2602318.pdf

A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs

This research further develops the combined use of principal component analysis (PCA) and data envelopment analysis (DEA). The aim is to reduce the curse of dimensionality that occurs in DEA when there is an excessive number of inputs and outputs in relation to the number of decision-making units. Three separate PCA–DEA formulations are developed in the paper utilising the results of PCA to develop objective, assurance region type constraints on the DEA weights. The first model applies PCA to grouped data representing similar themes, such as quality or environmental measures. The second model, if needed, applies PCA to all inputs and separately to all outputs, thus further strengthening the discrimination power of DEA. The third formulation searches for a single set of global weights with which to fully rank all observations. In summary, it is clear that the use of principal components can noticeably improve the strength of DEA models.

Including principal component weights to improve discrimination in data envelopment analysis

In Data Envelopment Analysis (DEA), when there are more inputs and outputs, there are more efficient Decision Making Units (DMus). For example, if the specific inputs or outputs advantageous for a particular DMU are used, the DMU will become efficient. Usually the variables used as inputs or outputs are correlated. Therefore, the inputs and outputs should be selected appropriately by experts who know their characteristics very well. People who are less familiar with those characteristics require tools to assist in the selection. We propose using principal component analysis as a means of weighting inputs and/or outputs and summarizing parsimoniously them rather than selecting them. A basic model and its modification are proposed. In principal component analysis, many weights for the variables that define principal components (PCs) have negative values. This may cause a negative integrated input that is a denominator of the objective function in fractional programming. The denominator should be positive. In the basic model, a condition that the denominator must be positive is added. When the number of PCs is less than the number of original variables, a part of original information is neglected. In the modified model, a part of the neglected information is also used.

/pdf/application-of-principal-component-analysis-for-parsimonious-4m9tpibq3l.pdf

Yoko Hoshiai

Papers

Application of principal component analysis for parsimonious summarization of dea inputs and/or outputs