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A multiplicative method for estimating the potential gains from two-stage production system mergers

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Abstract

In this study, a data envelopment analysis-based approach is proposed for estimating and decomposing the potential gains from the horizontal integrations of two-stage production systems. In the first tier, the gains of the potential merger are measured by a composite efficiency index. The potential efficiency gains are then decomposed as the product of coordination efficiency and two divisional potential efficiency gains. In the second tier, the divisional potential efficiency gains are decomposed into scope, size, and learning efficiencies. We develop a multiplicative framework for decomposing potential efficiency gain in mergers of the two-stage production systems, and the coordination efficiency is considered. In the case study of commercial banks in mainland China, we develop an algorithm for estimating and decomposing potential efficiency gain for a two-stage bank production system.

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Funding

Funding was provided by National Science Foundation of China (Grant No. 71701220).

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Authors and Affiliations

  1. International School of Business Finance, Sun Yat-Sen University, Zhuhai Campus, Tangjiawan, Zhuhai, 519082, People’s Republic of China

    Jianhui Xie

  2. School of Economics, Hefei University of Technology, No.190, Tunxi Road, Hefei, 230026, Anhui, People’s Republic of China

    Xiaoxuan Zhu & Liang Liang

  3. School of Management, Hefei University of Technology, No. 193, TunXi Road, Hefei, 230009, Anhui, People’s Republic of China

    Liang Liang

Authors
  1. Jianhui Xie
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Correspondence to Xiaoxuan Zhu.

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Appendix

Appendix

Table 4 reports the outputs orientation potential efficiency gains and their decompositions of the first 20 mergers in CRS case. We can find that the equation \( ME^{K} = CE^{K} *SCE_{1}^{K} *LE_{1}^{K} *SCE_{2}^{K} *LE_{2}^{K} \) is supported by the result of each K. Table 5 reports the outputs orientation potential efficiency gains and their decompositions of the first 20 mergers in VRS case. The equation \( ME^{K} = CE^{K} *SIE_{1}^{K} *SCE_{1}^{K} *LE_{1}^{K} *SIE_{2}^{K} *SCE_{2}^{K} *LE_{2}^{K} \) is supported by the result of each K.

Table 4 Potential efficiency gains and their decompositions of the first 20 mergers in CRS case
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Table 5 Potential efficiency gains and their decompositions of the first 20 mergers in VRS case
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Xie, J., Zhu, X. & Liang, L. A multiplicative method for estimating the potential gains from two-stage production system mergers. Ann Oper Res 288, 475–493 (2020). https://doi.org/10.1007/s10479-020-03530-x

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