Dynamic concept of returns to scales and its characteristics on production frontier in intersection form

Quan ling Wei, Hong Yan

Research output: Journal article publicationJournal articleAcademic researchpeer-review


This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale (RTS) of economic units with multiple inputs and outputs. It is frequently noticed that when we increase the input of a decision making unit (DMU) with a certain status of RTS, different status of RTS is observed. For example, when we increase the input of a DMU with constant RTS under the traditional method, a decreasing RTS is often observed instead of the expected constant RTS. We thus define the RTS of each DMU in both input expansion and contraction regions respectively. The research starts from transferring the production possibility set into the intersection form, by giving the explicit linear inequality representation of production frontiers. The RTS structural characteristics of DMUs' on the production frontier are described. Status of RTS of those DMUs on the production frontier include increasing RTS, constant RTS, decreasing RTS, saturated RTS and evidence of congestion. Necessary and sufficient conditions for RTS evaluation are provided. The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.
Original languageEnglish
Pages (from-to)355-366
Number of pages12
JournalActa Mathematicae Applicatae Sinica
Issue number3
Publication statusPublished - 21 Jul 2011


  • DEA
  • production possibility set
  • returns to scale

ASJC Scopus subject areas

  • Applied Mathematics

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