IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/92617.html
   My bibliography  Save this paper

Model and measure the relative efficiency of a four-stage production process. An NDEA multiplier relational model under different systems of resource distribution preferences between sub-processes

Author

Listed:
  • Pinto, Claudio

Abstract

Measuring the relative efficiency of a production process with the DEA considers the production process as a “black box” that uses inputs to transform them into outputs. In reality, many production processes are carried out by carrying out several interconnected activities that are usually grouped into phases that are in turn interconnected. For this reason, measuring the relative efficiency of a production process within the DEA technique requires shaping it as a network system (in others words to consider the production process as interconnected sub-process). In the case of network systems, the NDEA approach has developed many models to measure their relative efficiency: independent models, connected models and relational models. In particular, the relational model allows to measure at the same time both the efficiency of the system and the efficiency of the sub-process once the operations between the latter have been considered. In our opinion, many real production processes can be modelled as a network of four sub-processes that are differently interconnected with each other. In this paper we will model a production process as a network of four sub-processes with shared variables and fixed preferences about the allocation of system resources between them. To measure the relative efficiency of the process and its parts we will develop an input-oriented NDEA model in the multiplier version. To solve the model we will use virtual data under several resources allocation preference’s structure. Then we will conclude that 1) a production process with four interconnected sub-processes can represent a large number of real production processes, so the NDEA model developed here can potentially be used for many applications, 2) the resource allocation preference system inter-sub-process influences the measurement of relative efficiency.

Suggested Citation

  • Pinto, Claudio, 2019. "Model and measure the relative efficiency of a four-stage production process. An NDEA multiplier relational model under different systems of resource distribution preferences between sub-processes," MPRA Paper 92617, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:92617
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/92617/1/MPRA_paper_92617.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kao, Chiang, 2009. "Efficiency decomposition in network data envelopment analysis: A relational model," European Journal of Operational Research, Elsevier, vol. 192(3), pages 949-962, February.
    2. Rolf Färe & Shawna Grosskopf & Gerald Whittaker, 2014. "Network DEA II," International Series in Operations Research & Management Science, in: Wade D. Cook & Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 0, pages 307-327, Springer.
    3. Thomas Sexton & Herbert Lewis, 2003. "Two-Stage DEA: An Application to Major League Baseball," Journal of Productivity Analysis, Springer, vol. 19(2), pages 227-249, April.
    4. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "A survey of DEA applications," Omega, Elsevier, vol. 41(5), pages 893-902.
    5. Kao, Chiang & Hwang, Shiuh-Nan, 2008. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan," European Journal of Operational Research, Elsevier, vol. 185(1), pages 418-429, February.
    6. Lorenzo Castelli & Raffaele Pesenti & Walter Ukovich, 2010. "A classification of DEA models when the internal structure of the Decision Making Units is considered," Annals of Operations Research, Springer, vol. 173(1), pages 207-235, January.
    7. Chien Wang & Ram Gopal & Stanley Zionts, 1997. "Use of Data Envelopment Analysis in assessing Information Technology impact on firm performance," Annals of Operations Research, Springer, vol. 73(0), pages 191-213, October.
    8. Wanke, Peter & Maredza, Andrew & Gupta, Rangan, 2017. "Merger and acquisitions in South African banking: A network DEA model," Research in International Business and Finance, Elsevier, vol. 41(C), pages 362-376.
    9. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
    10. Hiroyuki Kawaguchi & Kaoru Tone & Miki Tsutsui, 2014. "Estimation of the efficiency of Japanese hospitals using a dynamic and network data envelopment analysis model," Health Care Management Science, Springer, vol. 17(2), pages 101-112, June.
    11. Emrouznejad, Ali & Parker, Barnett R. & Tavares, Gabriel, 2008. "Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA," Socio-Economic Planning Sciences, Elsevier, vol. 42(3), pages 151-157, September.
    12. Kao, Chiang, 2009. "Efficiency measurement for parallel production systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1107-1112, August.
    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.
    14. Bruce Hollingsworth, 2008. "The measurement of efficiency and productivity of health care delivery," Health Economics, John Wiley & Sons, Ltd., vol. 17(10), pages 1107-1128, October.
    15. Chen, Yao & Du, Juan & David Sherman, H. & Zhu, Joe, 2010. "DEA model with shared resources and efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(1), pages 339-349, November.
    16. Castelli, Lorenzo & Pesenti, Raffaele & Ukovich, Walter, 2001. "DEA-like models for efficiency evaluations of specialized and interdependent units," European Journal of Operational Research, Elsevier, vol. 132(2), pages 274-286, July.
    17. Rolf Färe & Gerald Whittaker, 1995. "An Intermediate Input Model Of Dairy Production Using Complex Survey Data," Journal of Agricultural Economics, Wiley Blackwell, vol. 46(2), pages 201-213, May.
    18. 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.
    19. Prieto, Angel M. & Zofio, Jose L., 2007. "Network DEA efficiency in input-output models: With an application to OECD countries," European Journal of Operational Research, Elsevier, vol. 178(1), pages 292-304, April.
    20. Kao, Chiang, 2014. "Efficiency decomposition for general multi-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 232(1), pages 117-124.
    21. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Claudio Pinto, 2021. "Measure the Relative Efficiency of a Four-Stage Production Process with NDEA," International Journal of Business and Management, Canadian Center of Science and Education, vol. 15(10), pages 1-35, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    2. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min, 2016. "Research fronts in data envelopment analysis," Omega, Elsevier, vol. 58(C), pages 33-45.
    3. AGRELL, Per & HATAMI-MARBINI, Adel, 2011. "Frontier-based performance analysis models for supply chain management; state of the art and research directions," LIDAM Discussion Papers CORE 2011069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Huang, Tai-Hsin & Chen, Kuan-Chen & Lin, Chung-I, 2018. "An extension from network DEA to copula-based network SFA: Evidence from the U.S. commercial banks in 2009," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 51-62.
    5. Tavakoli, Ibrahim M. & Mostafaee, Amin, 2019. "Free disposal hull efficiency scores of units with network structures," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1027-1036.
    6. Sotiros, Dimitris & Koronakos, Gregory & Despotis, Dimitris K., 2019. "Dominance at the divisional efficiencies level in network DEA: The case of two-stage processes," Omega, Elsevier, vol. 85(C), pages 144-155.
    7. Tatiana Bencova & Andrea Bohacikova, 2022. "DEA in Performance Measurement of Two-Stage Processes: Comparative Overview of the Literature," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 5, pages 111-129.
    8. Mohammad Amirkhan & Hosein Didehkhani & Kaveh Khalili-Damghani & Ashkan Hafezalkotob, 2018. "Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1429-1467, September.
    9. Claudio Pinto, 2021. "Measure the Relative Efficiency of a Four-Stage Production Process with NDEA," International Journal of Business and Management, Canadian Center of Science and Education, vol. 15(10), pages 1-35, July.
    10. Mirdehghan, S. Morteza & Fukuyama, Hirofumi, 2016. "Pareto–Koopmans efficiency and network DEA," Omega, Elsevier, vol. 61(C), pages 78-88.
    11. Halkos, George & Tzeremes, Nickolaos & Kourtzidis, Stavros, 2011. "The use of supply chain DEA models in operations management: A survey," MPRA Paper 31846, University Library of Munich, Germany.
    12. Pinto, Claudio, 2018. "Performances management when modelling internal structure," MPRA Paper 87923, University Library of Munich, Germany.
    13. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "Data envelopment analysis 1978–2010: A citation-based literature survey," Omega, Elsevier, vol. 41(1), pages 3-15.
    14. Kao, Chiang, 2020. "Decomposition of slacks-based efficiency measures in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 283(2), pages 588-600.
    15. Fukuyama, Hirofumi & Mirdehghan, S.M., 2012. "Identifying the efficiency status in network DEA," European Journal of Operational Research, Elsevier, vol. 220(1), pages 85-92.
    16. Kao, Chiang, 2014. "Efficiency decomposition for general multi-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 232(1), pages 117-124.
    17. Li, Yongjun & Lei, Xiyang & Dai, Qianzhi & Liang, Liang, 2015. "Performance evaluation of participating nations at the 2012 London Summer Olympics by a two-stage data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 243(3), pages 964-973.
    18. Kao, Chiang & Hwang, Shiuh-Nan, 2011. "Decomposition of technical and scale efficiencies in two-stage production systems," European Journal of Operational Research, Elsevier, vol. 211(3), pages 515-519, June.
    19. Tone, Kaoru & Tsutsui, Miki, 2009. "Network DEA: A slacks-based measure approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 243-252, August.
    20. Li, Yongjun & Chen, Yao & Liang, Liang & Xie, Jianhui, 2012. "DEA models for extended two-stage network structures," Omega, Elsevier, vol. 40(5), pages 611-618.

    More about this item

    Keywords

    network DEA; performances management; internal structure; inputs-outputs system.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • M0 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:92617. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.