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Partial input to output impacts in DEA: Production considerations and resource sharing among business subunits

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  • Raha Imanirad
  • Wade D. Cook
  • Joe Zhu

Abstract

Data envelopment analysis (DEA) is a methodology for evaluating the relative efficiencies of peer decision‐making units (DMUs), in a multiple input/output setting. Although it is generally assumed that all outputs are impacted by all inputs, there are many situations where this may not be the case. This article extends the conventional DEA methodology to allow for the measurement of technical efficiency in situations where only partial input‐to‐output impacts exist. The new methodology involves viewing the DMU as a business unit, consisting of a set of mutually exclusive subunits, each of which can be treated in the conventional DEA sense. A further consideration involves the imposition of constraints in the form of assurance regions (AR) on pairs of multipliers. These AR constraints often arise at the level of the subunit, and as a result, there can be multiple and often inconsistent AR constraints on any given variable pair. We present a methodology for resolving such inconsistencies. To demonstrate the overall methodology, we apply it to the problem of evaluating the efficiencies of a set of steel fabrication plants. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

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  • Raha Imanirad & Wade D. Cook & Joe Zhu, 2013. "Partial input to output impacts in DEA: Production considerations and resource sharing among business subunits," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(3), pages 190-207, April.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:3:p:190-207
    DOI: 10.1002/nav.21528
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    1. Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity and intermediate products: A frontier approach," Economics Letters, Elsevier, vol. 50(1), pages 65-70, January.
    2. Pulley, Lawrence B & Braunstein, Yale M, 1992. "A Composite Cost Function for Multiproduct Firms with an Application to Economies of Scope in Banking," The Review of Economics and Statistics, MIT Press, vol. 74(2), pages 221-230, May.
    3. A. Bessent & W. Bessent & J. Elam & T. Clark, 1988. "Efficiency Frontier Determination by Constrained Facet Analysis," Operations Research, INFORMS, vol. 36(5), pages 785-796, October.
    4. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    6. Cook, Wade D. & Hababou, Moez, 2001. "Sales performance measurement in bank branches," Omega, Elsevier, vol. 29(4), pages 299-307, August.
    7. Wade Cook & Moez Hababou & Hans Tuenter, 2000. "Multicomponent Efficiency Measurement and Shared Inputs in Data Envelopment Analysis: An Application to Sales and Service Performance in Bank Branches," Journal of Productivity Analysis, Springer, vol. 14(3), pages 209-224, November.
    8. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    9. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    10. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
    11. Cook, Wade D. & Zhu, Joe & Bi, Gongbing & Yang, Feng, 2010. "Network DEA: Additive efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1122-1129, December.
    12. Panzar, John C & Willig, Robert D, 1981. "Economies of Scope," American Economic Review, American Economic Association, vol. 71(2), pages 268-272, May.
    13. Cook, Wade D. & Liang, Liang & Zhu, Joe, 2010. "Measuring performance of two-stage network structures by DEA: A review and future perspective," Omega, Elsevier, vol. 38(6), pages 423-430, December.
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    Cited by:

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    7. Hao Cai & Ling Liang & Jing Tang & Qianxian Wang & Lihong Wei & Jiaping Xie, 2019. "An Empirical Study on the Efficiency and Influencing Factors of the Photovoltaic Industry in China and an Analysis of Its Influencing Factors," Sustainability, MDPI, vol. 11(23), pages 1-22, November.
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    9. Avilés-Sacoto, Sonia Valeria & Cook, Wade D. & Güemes-Castorena, David & Zhu, Joe, 2020. "Modelling Efficiency in Regional Innovation Systems: A Two-Stage Data Envelopment Analysis Problem with Shared Outputs within Groups of Decision-Making Units," European Journal of Operational Research, Elsevier, vol. 287(2), pages 572-582.
    10. Josef Jablonský, 2019. "Data Envelopment Analysis Models in Non-Homogeneous Environment," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 67(6), pages 1535-1540.
    11. Rita Shakouri & Maziar Salahi & Sohrab Kordrostami & Jie Wu, 2019. "Flexible measure in the presence of the partial input to output impacts process," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(3), pages 77-98.
    12. Touati-Tliba, Mohamed, 2024. "Comparative performance of Algeria's education districts: The Influence of colonial legacy through cultural capital," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).
    13. Huang-Ping Yen & Po-Chi Chen & Kung-Cheng Ho, 2021. "Analyzing Destination Accessibility From the Perspective of Efficiency Among Tourism Origin Countries," SAGE Open, , vol. 11(2), pages 21582440211, April.
    14. Avilés-Sacoto, Estefanía Caridad & Avilés-Sacoto, Sonia Valeria & Güemes-Castorena, David & Cook, Wade D., 2021. "Environmental performance evaluation: A state-level DEA analysis," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    15. Mohammad Nemati & Reza Kazemi Matin & Mehdi Toloo, 2020. "A two-stage DEA model with partial impacts between inputs and outputs: application in refinery industries," Annals of Operations Research, Springer, vol. 295(1), pages 285-312, December.
    16. Lívia Torres & Francisco S. Ramos, 2024. "Allocating Benefits Due to Shared Resources Using Shapley Value and Nucleolus in Dynamic Network Data Envelopment Analysis," Mathematics, MDPI, vol. 12(5), pages 1-23, February.
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    18. Xiong, Xi & Yang, Guo-liang & Guan, Zhong-cheng, 2020. "A parallel DEA-based method for evaluating parallel independent subunits with heterogeneous outputs," Journal of Informetrics, Elsevier, vol. 14(3).
    19. Fukuyama, Hirofumi & Song, Yao-yao & Ren, Xian-tong & Yang, Guo-liang, 2022. "Using a novel DEA-based model to investigate capacity utilization of Chinese firms," Omega, Elsevier, vol. 106(C).
    20. Fukuyama, Hirofumi & Liu, Hui-hui & Song, Yao-yao & Yang, Guo-liang, 2021. "Measuring the capacity utilization of the 48 largest iron and steel enterprises in China," European Journal of Operational Research, Elsevier, vol. 288(2), pages 648-665.

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