Integrated data envelopment analysis: Global vs. local optimum

Sungmook Lim and Joe Zhu

European Journal of Operational Research, 2013, vol. 229, issue 1, 276-278

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.

Keywords: Integrated data envelopment analysis; Efficiency; Two-stage; Local optimum; Global optimum (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:229:y:2013:i:1:p:276-278

DOI: 10.1016/j.ejor.2013.02.023

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