TY - JOUR
T1 - Robust Russell and enhanced Russell measures in DEA
AU - Salahi, Maziar
AU - Toloo, Mehdi
AU - Hesabirad, Zeynab
N1 - Funding Information:
The first author would like to thank University of Guilan for supporting his research and the second author would like to thank the Czech Science Foundation [GACR≤ 17-23495S] for all support.
Publisher Copyright:
© 2018, © The Operational Research Society 2018.
PY - 2019/8/3
Y1 - 2019/8/3
N2 - Russell measure is among non-radial measures for efficiency evaluation of decision making units in data envelopment analysis. Due to the nonlinearity of its objective function, an enhanced version of it is proposed that can be linearized using the known Charnes–Cooper change of variables. In this article, we give equivalent formulations of the robust Russell measure and its enhanced models under interval and ellipsoidal uncertainties in their best- and worst-cases. We show that the built formulations stay convex for both best- and worst-cases under interval uncertainty as well as worst-case with ellipsoidal uncertainty. In other words, these formulations are nonconvex only for ellipsoidal uncertainty in their best-case. Some illustrative examples are provided to validate the new models.
AB - Russell measure is among non-radial measures for efficiency evaluation of decision making units in data envelopment analysis. Due to the nonlinearity of its objective function, an enhanced version of it is proposed that can be linearized using the known Charnes–Cooper change of variables. In this article, we give equivalent formulations of the robust Russell measure and its enhanced models under interval and ellipsoidal uncertainties in their best- and worst-cases. We show that the built formulations stay convex for both best- and worst-cases under interval uncertainty as well as worst-case with ellipsoidal uncertainty. In other words, these formulations are nonconvex only for ellipsoidal uncertainty in their best-case. Some illustrative examples are provided to validate the new models.
KW - Data envelopment analysis
KW - data uncertainty
KW - enhanced Russell measure
KW - Russell measure
KW - second order cone program
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U2 - 10.1080/01605682.2018.1489353
DO - 10.1080/01605682.2018.1489353
M3 - Article
AN - SCOPUS:85056434561
SN - 0160-5682
VL - 70
SP - 1275
EP - 1283
JO - Journal of the Operational Research Society
JF - Journal of the Operational Research Society
IS - 8
ER -