Journal of Productivity Analysis

, Volume 44, Issue 2, pp 137–155 | Cite as

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

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


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.


Cone ratio Data envelopment analysis Shared resource Multi-component Two-stage Conflict of interest Partial ordering Network 

JEL classification

D21 D24 



The authors are indebted to Professor Podinovski and two anonymous reviewers for their thoughtful comments and suggestions. This research is supported by National Natural Science Funds of China (No. 71301155), National Natural Science Funds of China for Innovative Research Groups (No.71121061), and the Fundamental Research Funds for the Central Universities (J2014hgbz0172).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jingjing Ding
    • 2
  • Chenpeng Feng
    • 1
    • 3
  • Gongbing Bi
    • 1
  • Liang Liang
    • 2
  • M. Riaz Khan
    • 4
  1. 1.School of ManagementUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2.School of ManagementHefei University of TechnologyHefeiPeople’s Republic of China
  3. 3.Laboratory of IBISCUniversity of Evry-Val d’EssonneEvryFrance
  4. 4.Manning School of BusinessUniversity of Massachusetts LowellLowellUSA

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