Mahdi Bashiri - Phd candidate, Department of Industrial Engineering, Shahed University, Tehran, Iran
Hamid Reza Hamid Reza - MSc, Department of Industrial Engineering, Shahed University, Tehran, Iran

In this paper, a novel approach to multi response optimization is presented. In the proposed approach, response variables in treatments combination occur with a certain probability. Moreover, we assume that each treatment has a network style. Due to the probabilistic nature of the treatment combination, the suggested approach can compute the efficiency of each treatment under the desirable reliability. The approach has been constructed based on a network data envelopment analysis and the chance constraint method. Finally, a numerical example shows applicability of the proposed method to a multi response problem. The results indicate that the proposed approach is a capable method for analyzing the best treatment and compared to other existing methods, it performs better in efficient treatment determination.

Multi Response Optimization; Chance Constraint; Network Data Envelopment Analysis; Knapsack Approach