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Using input–output orientation model for determining most productive scale size in DEA. (English) Zbl 1101.90366

Summary: One of the existing approaches for determining mpss is \(\alpha -\beta\) model proposed in W. W. Cooper, R. G. Thompson and R. M. Thrall’s article [Ann. Oper. Res. 66, 3–45 (1996; Zbl 0863.90003)]. 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 E. Thanassoulis, Introduction to the Theory and Applications of Data Envelopment Analysis, a foundation text with integrated software, Kluwer Academic Publishers (2001); R. D. Banker, Eur. J. Oper. Res. 17, 35–44 (1984; Zbl 0538.90030)]. 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.

MSC:

90B50 Management decision making, including multiple objectives
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
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