Abstract One of the existing approaches for determining mpss is α− β model proposed in Cooper, Thompson and Thrall’s article [Annals of Operations Research 66 (1996) 3]. The direct solving of that model is rather difficult because the objective function is fractional. Hence in this paper besides introducing a model with output–input orientation, the previous model difficulties will be removed because the new objective function is linear. And also it is proved that both models are the same in determining mpss. Furthermore by solving this model it is not necessary to scaling the data as it is necessary in CCR model so that figurative DMU move in the joint frontier of BCC and CCR models [see Introduction to the Theory and Applications of Data Envelopment Analysis, a foundation text with integrated software, 2001; European Journal of Operational Research 17 (1984) 35]. So we can consider this as another merit for this model in determining mpss. We obtain the smallest and the most mpss corresponding with the evaluating DMU and also we present necessary and sufficient condition for boundedness of this model by dual model and numerical example confirms validity of this model as a means for determining mpss.