Maryam Salami - Department of Mathematics, Shiraz University, Shiraz, Iran
Mohammad Bagher Ahmadi - Department of Mathematics, Shiraz University, Shiraz, Iran

In this paper a Bilevel Programming approach as a tool for modeling hierarchical and decentralized systems, is proposed for measuring efficiency of two-stage network structure by Data Envelopment Analysis (DEA). In twostage network structure case, each of Decision Making Units (DMUs) is comprised of two stages: a leaders and a follower. The first level of Bilevel Programming is devoted to maximize the efficiency of the leader and that is of the follower at the second level simultaneously. This approach will help decentralized and hierarchical systems to optimize each of their subsystems performance by distinguishing inefficient units and implementing possible improvements. For solving the proposed model a Hierarchical Genetic Algorithm (HGA) is implemented.

Data Envelopment Analysis, Bilevel Programming Problem, Two-Stage Network Structure، Genetic Algorithm