Kianoosh Kianfar - Department of Industrial Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran.
Mahnaz Ahadzadeh Namin - Department of Mathematics, Shahr Qods Branch, Islamic Azad University, Tehran, Iran.
Akbar Alam Tabriz - Department of Management, Shahid Beheshti University, Tehran, Iran.
Esmaeil Najafi - Department of Industrial Engineering, Science and Research branch, Islamic Azad University, Tehran,

Finding efficient target for Decision Making Unit (DMU) is one of the important targets of data envelopment analysis (DEA). However, in some issues and models, obtained efficient target has negative indexes. Negative efficient target input (projected point) shortcoming is overcome using a single-stage DEA model with weight restriction according to previous researches. In this paper, a two-stage network unit with weight restrictions is considered. Models for each stage of the unit under assessment and the unit itself are presented in order to overcome negative target input problem at each stage of the unit under assessment and the unit itself. Then, an efficient target with positive indexes is introduced. The performance of the proposed model is explained with a numerical example. Eventually, at the end of this research, efficient projected point of each DMU is approved by new proposed single stage model. This proposed extended model can be used in two-stage network and is considered as an innovation in this study. Using the proposed single-stage model of previous research and its use in two-stage networks indicated that some projected points that have negative indexes in input, are converted to positive indexes in input.

Data envelopment analysis; productions trade-offs; weight restrictions; efficient target