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Improving the discrimination power with a new multi-criteria data envelopment model

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Abstract

Data envelopment analysis (DEA) allows evaluation of the relative efficiencies of similar entities, known as decision making units (DMUs), which consume the same types of resources and offer similar types of products. It is known that under certain circumstances, when the number of DMUs does not meet the DEA Golden Rule, that is, this number is not sufficiently large compared to the total number of inputs and outputs, traditional DEA models often yield solutions that identify too many DMUs as efficient. In fact, this weak discrimination power and unrealistic weight distribution presented by DEA models remain a major challenge, leading to the development of models to improve this performance, such as: multiple criteria data envelopment analysis (MCDEA), bi-objective multiple criteria data envelopment analysis, goal programming approaches to solve weighted goal programming (WGP–MCDEA) and extended–MCDEA. This paper proposes a new MCDEA model which is based on goal programming, with and without super efficiency concepts, and presents test results that show its advantages over the above cited models. A set of problems from the literature and real-world applications are used in these tests. The results show that the new MCDEA model provides better discrimination of DMUs in all tested problems, and provides a weight dispersion that is statistically equal to that obtained by other MCDEA models. An additional feature of the proposed model is that it allows the identification of the input and output variables that are most important to the problem, to make it easier for the decision maker to improve the efficiency of the DMUs involved. This is very useful in practice, because in general, the available resources are scarce, so it is a further advantage of the proposed MCDEA model over the others tested.

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Acknowledgements

This study was partially supported by the National Council for Scientific and Technological Development (CNPq-302730/2018-4; CNPq-303350/2018-0), and the São Paulo State Research Foundation (FAPESP-2018/06858-0; FAPESP-2018/14433-0).

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Authors and Affiliations

  1. Department of Production, São Paulo State University, São Paulo, Brazil

    Aneirson Francisco da Silva, Fernando Augusto S. Marins & Erica Ximenes Dias

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  1. Aneirson Francisco da Silva
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  2. Fernando Augusto S. Marins
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  3. Erica Ximenes Dias
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Correspondence to Aneirson Francisco da Silva.

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Appendices

Appendix A

See Tables 11, 12, 13, 14, 15 and 16.

Table 11 The most cited papers about MCDEA Models
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Appendix B

Table 12 The results for \(\hbox {P}_{1}\) with \(\varepsilon = 0\)
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Appendix C

Table 13 The results for \(\hbox {P}_{2}\) with \(\varepsilon = 0\)
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Appendix D

Table 14 The most important input and output variables
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Table 15 The results for \(\hbox {P}_{2}\) with \(\varepsilon = 0.00033434\)
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Appendix E

Table 16 Data of 30 OECD countries
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da Silva, A.F., Marins, F.A.S. & Dias, E.X. Improving the discrimination power with a new multi-criteria data envelopment model. Ann Oper Res 287, 127–159 (2020). https://doi.org/10.1007/s10479-019-03446-1

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