Raziyeh Shamsi - Department of Mathematics, Evaz Centre, Larestan Branch, Islamic Azad University, Evaz, Iran
Safdar Ghasami Shahvari - Department of Statistics, Bandare Jask Branch, Islamic Azad University, Bandare Jask, Iran
Kamran Yeganegi - Department of Industrial Engineering , Zanjan Branch, Islamic Azad University, Zanjan, Iran

In this paper, we obtain the projection of inefficient units indata envelopment analysis (DEA) in the case of stochasticinputs and outputs using the multi-objective programming(MOP) structure. In some problems, the inputs might bestochastic while the outputs are deterministic, and viceversa. In such cases, we propose multi-objective DEA-Rmodel, because in some cases (e.g., when unnecessary andirrational weights by the BCC model reduces the efficiencyscore), an efficient DMU is introduced as inefficient by theBCC model, whereas the DMU is considered efficient by theDEA-R model. In some other case, only the ratio ofstochastic data may be available (e.g.; the ratio ofstochastic inputs to stochastic outputs). Thus, we providemulti objective DEA model without explicit outputs andprove that in-put oriented MOP DEA-R model in theinvariable return to scale case can be replacing by MOPDEAmodel without explicit outputs in the variable return toscale and vice versa. Using the interactive methods forsolving the proposed model, yields a projectioncorresponding to the viewpoint of the DM and the analyst,which is nearer to reality and more practical. Finally, anapplication is provided.

Dea-r, multi-objective programming, stochastic data, dataenvelopment analysis