DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications Ozren Despic ´ Æ Mladen Despic ´ Æ Joseph C. Paradi Published online: 22 May 2007 Ó Springer Science+Business Media, LLC 2007 Abstract We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea—Ratio Analysis. Our model, called DEA-R, treats all possible ratios ‘‘output/input’’ as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for effi- ciency, the two measures are comparable. Our mathemat- ical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts’ opinions via flexible restrictive conditions on individual ‘‘output/input’’ pairs. Keywords DEA  Efficiency  Ratio analysis  Weight restrictions JEL Classifications C61  C14 1 Introduction The main reason we are interested in the DEA-R model is the flexibility it creates for the analyst to incorporate var- ious experts’ opinions within a DEA-based relative effi- ciency model—this is also one of the method’s main advantages over other DEA approaches. Modeling experts’ opinions is a very important issue in the practical appli- cations of DEA even though it is of a rather controversial nature. From a theoretical perspective, according to Dyson et al. (2001), controversy is there because there are diffi- culties arising from the ‘pure’ DEA model as well as the problems arising from augmenting the ‘pure’ model by various weight restrictions, representing mathematical translations of experts’ opinions. From a practical per- spective, adding subjective restrictions to the DEA model is undesirable since without them DEA can be claimed to be a remarkably unbiased evaluation tool (assuming the appropriate selection of the inputs and the outputs). Without these restrictions, however, the only thing we can claim with certainty is that none of the inefficient pro- duction units is declared as one of the most efficient ones. In general, as concluded in Pedraja-Chaparro et al. (1997), the results obtained by DEA improve considerably by introducing reasonable restrictions on the weights. In the DEA literature, there is no lack of research when it comes to modeling experts’ opinions. An excellent sur- vey on various methods can be found in Allen et al. (1997). More recently, Sarrico and Dyson (2004) gave an in-depth analysis on restricting virtual weights in DEA. Many dif- ferent approaches have been proposed to deal with this issue using some types of weight restrictions, but also through some other means such as adding unobserved units to the existing set of units as in Thanassoulis and Allen (1998). Due to a vast variety of possible experts’ opinions, This work was made possible by the generous financial support of NSERC, Canada. O. Despic ´(&) Aston Business School, Aston University, Birmingham B4 7ET, UK e-mail: o.despic@aston.ac.uk M. Despic ´ Agricore United, Winnipeg, MB, Canada R3C 3A7 e-mail: mdespic@agricoreunited.com J. C. Paradi Centre for Management of Technology and Entrepreneurship, University of Toronto, 200 College Street, Toronto, ON, Canada M5S 3E5 e-mail: paradi@mie.utoronto.ca 123 J Prod Anal (2007) 28:33–44 DOI 10.1007/s11123-007-0050-x