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Two-stage DEA model with complex numbers: a case study of power plants in Iran

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Abstract

The two-stage DEA models have been developed to evaluate the efficiency of two-stage processes. One of the challenging issues in two-stage DEA models is to incorporate complex numbers. Complex numbers are often used in problems related to different industries, such as the power industry. Electrical energy, as the product of the power plant industry, consists of two main components: active power, i.e. the real part, and reactive power, i.e. the imaginary part. When we use conventional two-stage DEA models to evaluate the efficiency of the power plants, the measurement of efficiency is limited to real numbers, i.e. the active power and reactive power are thus ignored. In this paper, novel two-stage DEA models under CRS and VRS assumptions are proposed to incorporate complex numbers. The developed models are applied to a dataset for steam power plants in Iran and the results are compared with traditional two-stage DEA models. The analysis of the results shows that the use of complex numbers in measuring efficiency provides more reliable results compared to traditional two-stage DEA models. The results of the analysis also indicate that among technical, managerial and scale efficiencies, the scale efficiency has the greatest influence on the technical efficiency.

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Acknowledgements

The authors would like to thank the Iran Electricity Management, Distribution, Transfer, and Production Company (known as Tavanir Company) for collecting data and consultation.

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Authors and Affiliations

  1. Department of Industrial Engineering, Sari Branch, Islamic Azad University, Sari, Iran

    Mahmood Esfandiari

  2. Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

    Saber Saati

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  1. Mahmood Esfandiari
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  2. Saber Saati
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Esfandiari, M., Saati, S. Two-stage DEA model with complex numbers: a case study of power plants in Iran. OPSEARCH (2024). https://doi.org/10.1007/s12597-024-00801-0

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