Proportional Production Trade-Offs in Dea

Abstract

The "trade-offs Data envelopment analysis (DEA)" model is built by adding an extra axiom to the traditional production possibility set. The axiom introduces some replacement relations as production rules between inputs and outputs and leads to some extensions to the production possibility set. It provides more discriminatory power of decision-making units (DMUs) in DEA models, and the results are more adaptable to real conditions. In this paper, these variations are defined in proportional forms, which make the variation proportionate to DMUs' sizes. So we call them proportional tradeoffs, and they offer some advantages in comparison with simple trade-off vectors, which depend on input or output units of measurements. First of all, the proportional trade-offs vectors can fairly consider the DMUs' abilities and their strengths in adapting to the proposed changes. Secondly, it will be seen that proportional trade-off vectors can be used as a generalization of usual returns to scales (RTS), and finally the proportional trade-offs models cover the basic DEA models and their related production possibility set (PPSs) as special cases.Keywords: Data envelopment analysis (DEA); production possibility set (PPS); proportional trade-offs (PTO); returns to scale (RTS). 1250035-1 Asia Pac. J. Oper. Res. 2012.29. Downloaded from www.worldscientific.com by THE UNIV OF WESTERN ONTARIO on 02/07/15. For personal use only. 1250035-2 Asia Pac. J. Oper. Res. 2012.29. Downloaded from www.worldscientific.com by THE UNIV OF WESTERN ONTARIO on 02/07/15. For personal use only. Proportional Production Trade-Offs in DEA Simple Trade-Offs VectorsThe trade-offs model is created by extending the PPS axioms based on trade-offs, which are replacement relations between inputs and outputs (Podinovski, 2004a).

Selective proportionality and integer-valued data in DEA: an application to performance evaluation of high schools

“…Kazemi Matin and Emrouznejad ( 2011 ) utilized a variant of the HRS assumption and developed a bounded technology set by taking into account integer-valued data. Alirezaee and Boloori ( 2012 ) proposed a proportional model of trade-offs in the DEA framework by modifying the proportionality axiom and by considering some input–output replacement. Huang et al ( 2012 ) considered a hybrid DEA model and evaluated proportionate and non-proportionate inputs with radial and non-radial measures in an application to Taiwanese international tourist hotels.…”