Integrated data envelopment analysis: Global vs. local optimum

Sungmook Lim, Joe Zhu

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European Journal of Operational Research 201, 477-489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.'s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm.

Original languageEnglish
Pages (from-to)276-278
Number of pages3
JournalEuropean Journal of Operational Research
Volume229
Issue number1
DOIs
StatePublished - 16 Aug 2013

Keywords

  • Efficiency
  • Global optimum
  • Integrated data envelopment analysis
  • Local optimum
  • Two-stage

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