Returns to Scale in DEA

  • Rajiv D. Banker
  • William W. Cooper
  • Lawrence M. Seiford
  • Joe ZhuEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 164)


This chapter discusses returns to scale (RTS) in data envelopment analysis (DEA). The BCC and CCR models described in Chap. 1 of this handbook are treated in input-oriented forms, while the multiplicative model is treated in output-oriented form. (This distinction is not pertinent for the additive model, which simultaneously maximizes outputs and minimizes inputs in the sense of a vector optimization.) Quantitative estimates in the form of scale elasticities are treated in the context of multiplicative models, but the bulk of the discussion is confined to qualitative characterizations such as whether RTS is identified as increasing, decreasing, or constant. This is discussed for each type of model, and relations between the results for the different models are established. The opening section describes and delimits approaches to be examined. The concluding section outlines further opportunities for research and an Appendix discusses other approaches in DEA treatment of RTS.


Data envelopment analysis Efficiency Returns to scale 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Rajiv D. Banker
    • 1
  • William W. Cooper
    • 2
  • Lawrence M. Seiford
    • 3
  • Joe Zhu
    • 4
    Email author
  1. 1.Fox School of Business and ManagementTemple UniversityPhiladelphiaUSA
  2. 2.Red McCombs School of BusinessUniversity of Texas at AustinAustinUSA
  3. 3.Department of Industrial and Operations EngineeringUniversity of Michigan at Ann ArborAnn ArborUSA
  4. 4.School of BusinessWorcester Polytechnic InstituteWorcesterUSA

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