10.1007/s40096-021-00386-5

Estimation of cost efficiency with piecewise linear cost function in integer-valued data envelopment analysis

  • Fatemeh Mirzaeian1,
  • Reza Fallahnejad*1,
  1. Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, IR

Published in Issue 2021-02-27

How to Cite

Mirzaeian, F., & Fallahnejad, R. (2021). Estimation of cost efficiency with piecewise linear cost function in integer-valued data envelopment analysis. Mathematical Sciences, 16(1 (March 2022). https://doi.org/10.1007/s40096-021-00386-5
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Abstract

Abstract The cost efficiency is one of the types of the used efficiency concepts in the data envelopment analysis (DEA). In the literature of the cost efficiency, the prices are often applied to the units in a fixed and linear form, while in some cases, as the subjects of the savings and observance of the consumption patterns, the prices are usually considered in terms of stepwise (piecewise linear) and not fixed (linear). This paper proposes the new models to evaluate of the cost efficiency in the fully competitive setting by using the costs in a piecewise linear form. The models are developed for the non-fully competitive and integer-valued inputs cases. Finally, the proposed models are used to determine the cost efficiency of the confectioneries in Islam Abad Gharb city from Iran country in the case study.

Keywords

  • Data envelopment analysis,
  • Piecewise linear functions,
  • Cost efficiency,
  • Mixed integer programming

References

  1. Alirezaee and Rafiee Sani (2011) An enumeration algorithm for integer-valued data envelopment analysis 18(6) (pp. 729-740) https://doi.org/10.1111/j.1475-3995.2011.00822.x
  2. Camanho and Dyson (2005) Cost efficiency measurement with price uncertainty a DEA application bank branch assessments (pp. 432-446) https://doi.org/10.1016/j.ejor.2003.07.018
  3. Camanho and Dyson (2008) A generalisation of the Farrell cost efficiency measure applicable to non-fully competitive settings (pp. 147-162) https://doi.org/10.1016/j.omega.2005.12.004
  4. Charnes et al. (1978) Measuring the efficiency of decision making units 2(6) (pp. 429-441) https://doi.org/10.1016/0377-2217(78)90138-8
  5. Färe et al. (1985) Kluwer Nijhoff https://doi.org/10.1007/978-94-015-7721-2
  6. Farrell (1957) The measurement of productive efficiency (pp. 253-351) https://doi.org/10.2307/2343100
  7. Jahanshahloo et al. (2008) A simplified version of the DEA cost efficiency model (pp. 814-815) https://doi.org/10.1016/j.ejor.2006.11.043
  8. Karimi and Khorram (2016) Identification of congestion by means of integer-valued data envelopment analysis (pp. 513-521) https://doi.org/10.1016/j.cie.2016.06.017
  9. Kazemi Matin and Emrouznejad (2011) An integer-valued data envelopment analysis model with bounded outputs (pp. 741-749) https://doi.org/10.1111/j.1475-3995.2011.00828.x
  10. Kuosmanen and Kazemi (2009) Theory of integer valued data envelopment analysis 192(2) (pp. 658-667) https://doi.org/10.1016/j.ejor.2007.09.040
  11. Kuosmanen, T., Keshvari, A., Kazemi Matin, R.: Discrete and integer valued inputs and outputs in data envelopment analysis. In: Zho, J., (eds) Data Envelopment Analysis. International Series in Operational Research & Management Science, 221, 67–103. (2015)
  12. Kuosmanen and Post (2001) Measuring economic efficiency with incomplete price information: with an application to European commercial banks 134(1) (pp. 43-58) https://doi.org/10.1016/S0377-2217(00)00237-X
  13. Lozano and Villa (2006) Data envelopment analysis of integer-valued inputs and outputs 33(10) (pp. 3004-3014) https://doi.org/10.1016/j.cor.2005.02.031
  14. Mostafaee and Saljooghi (2010) Cost efficiency measures in data envelopment analysis with data uncertainty 202(2) (pp. 595-603) https://doi.org/10.1016/j.ejor.2009.06.007
  15. Murty (1983) Wiley
  16. Sahoo et al. (2012) Returns to growth in a non-parametric DEA approach 19(3) (pp. 463-486) https://doi.org/10.1111/j.1475-3995.2012.00841.x
  17. Sahoo et al. (2014) Cost, revenue and profit efficiency measurement in DEA: a directional distance function approach (pp. 921-938) https://doi.org/10.1016/j.ejor.2014.02.017
  18. Sahoo and Tone (2009) Decomposing capacity utilization in data envelopment analysis an application to banks in India 195(2) (pp. 575-594) https://doi.org/10.1016/j.ejor.2008.02.017
  19. Sahoo and Tone (2009) Radial and non-radial decompositions of profit change with an application to indian banking 196(3) (pp. 1130-1146) https://doi.org/10.1016/j.ejor.2008.04.036
  20. Sahoo and Tone (2013) Non-parametric measurement of economies of scale and scope in non-competitive environment with price uncertainty 41(1) (pp. 97-111) https://doi.org/10.1016/j.omega.2011.11.008
  21. Sueyoshi (1997) Measuring efficiencies and returns to scale of Nippon telegraph and telephone in production and cost analyses (pp. 779-796) https://doi.org/10.1287/mnsc.43.6.779
  22. Tone (2002) A strange case of the cost and allocative efficiencies in DEA (pp. 1225-1231) https://doi.org/10.1057/palgrave.jors.2601438
  23. Tone and Sahoo (2005) Evaluating cost efficiency and returns to scale in the life insurance corporation of India using data envelopment analysis (pp. 261-285) https://doi.org/10.1016/j.seps.2004.06.001
  24. Tone and Sahoo (2006) Re-examining Scale Elasticity in DEA 145(1) (pp. 69-87) https://doi.org/10.1007/s10479-006-0027-6
  25. Tone, K., Tsutsui, M.: Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons. Socio-Economic Planning Sciences, 91–106 (2007)