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Cone ratio models with shared resources and nontransparent allocation parameters in network DEA

Author

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  • Jingjing Ding
  • Chenpeng Feng
  • Gongbing Bi
  • Liang Liang
  • M. Khan

Abstract

Many studies have examined the performance of production systems with shared resources through the application of data envelopment analysis (DEA). The present models are based on the multiplier-type frameworks and resource allocation variables (RAVs) in simple yet edifying network settings, such as multi-component and two-stage structures. Two issues associated with RAVs, however, are relevant to both the theory and practice. First, the existing models with RAVs are nonlinear in general. Second, a potential conflict of interest between a central evaluator (CE) and the managers of decision-making units (DMUs), due to the unknown allocation parameters, has not been addressed. The current study contributes to the resolution of these issues by presenting conflict free models (CFMs). Two striking features of the proposed models include their convenient transformation into linear programs and that they are conflict free. Thus, the manager of a DMU has no basis to argue against the evaluation results by simply claiming that faulty information regarding the split of shared resources has been used, as no such information relating to the CE’s preference or pertaining to RAVs is included in the model formulation. Furthermore, we investigate the relations between CFMs and the existing models, strengthening the interpretations of the existing models. Finally, the proposed models incorporate partial ordering preferences expressed as the cone ratio constraints, which are suitable for a wide range of real life applications. A dataset extracted from literature is used to illustrate the main concept that drives this research. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Jingjing Ding & Chenpeng Feng & Gongbing Bi & Liang Liang & M. Khan, 2015. "Cone ratio models with shared resources and nontransparent allocation parameters in network DEA," Journal of Productivity Analysis, Springer, vol. 44(2), pages 137-155, October.
    • Handle: RePEc:kap:jproda:v:44:y:2015:i:2:p:137-155
    DOI: 10.1007/s11123-014-0420-0
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    References listed on IDEAS

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    Cited by:

    1. Victor V. Podinovski & Ole Bent Olesen & Cláudia S. Sarrico, 2018. "Nonparametric Production Technologies with Multiple Component Processes," Operations Research, INFORMS, vol. 66(1), pages 282-300, January.
    2. Antonio Peyrache & Maria C. A. Silva, 2019. "The Inefficiency of Production Systems and its decomposition," CEPA Working Papers Series WP052019, School of Economics, University of Queensland, Australia.
    3. Giannis Karagiannis & Panagiotis Ravanos, 2023. "On Value Efficiency Analysis and Cone-Ratio Data Envelopment Analysis models," Discussion Paper Series 2023_03, Department of Economics, University of Macedonia, revised Mar 2023.
    4. Antonio Peyrache & Maria C. A. Silva, 2022. "Efficiency and Productivity Analysis from a System Perspective: Historical Overview," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 173-230, Springer.
    5. Ding, Jingjing & Dong, Wei & Liang, Liang & Zhu, Joe, 2017. "Goal congruence analysis in multi-Division Organizations with shared resources based on data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 263(3), pages 961-973.
    6. Majid Azadi & Balal Karimi & William Ho & Reza Farzipoor Saen, 2022. "Assessing green performance of power plants by multiple hybrid returns to scale technologies," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1177-1211, December.
    7. Mahdiloo, Mahdi & Ngwenyama, Ojelanki & Scheepers, Rens & Tamaddoni, Ali, 2018. "Managing emissions allowances of electricity producers to maximize CO2 abatement: DEA models for analyzing emissions and allocating emissions allowances," International Journal of Production Economics, Elsevier, vol. 205(C), pages 244-255.

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    More about this item

    Keywords

    Cone ratio; Data envelopment analysis; Shared resource; Multi-component; Two-stage; Conflict of interest; Partial ordering; Network; D21; D24;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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