TY - JOUR
T1 - Integrated data envelopment analysis
T2 - Global vs. local optimum
AU - Lim, Sungmook
AU - Zhu, Joe
PY - 2013/8/16
Y1 - 2013/8/16
N2 - 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.
AB - 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.
KW - Efficiency
KW - Global optimum
KW - Integrated data envelopment analysis
KW - Local optimum
KW - Two-stage
UR - http://www.scopus.com/inward/record.url?scp=84876412473&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2013.02.023
DO - 10.1016/j.ejor.2013.02.023
M3 - Article
AN - SCOPUS:84876412473
SN - 0377-2217
VL - 229
SP - 276
EP - 278
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 1
ER -