A Bender’s Decomposition Algorithm for Multi-objective Hub Location Problem Considering Stochastic Characteristics

Document Type : Research Paper


1 School of Industrial Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, I.R. Iran

2 Dept. of Industrial Engineering, Shahed University, Tehran, I.R. Iran


In this paper, a multi-objective hub location problem considering stochastic links and candidate nodes characteristics is modeled. The first objective is to minimize total costs, including setup and transportation costs. The second one is to minimize network risks. Characteristics such as weather conditions, safety, exchange rate, crisis, are defined as uncertainty parameters and considered as different scenarios. Due to the size of the numbers of scenarios, it is assumed that the distribution of their risks is considered to be normal. Also reliability levels associated to candidate hub nodes and links are considered as chance constraints. Moreover a Bender’s decomposition algorithm is utilized to solve the proposed model. In order to evaluate the performance of the proposed model, the results of this algorithm are compared to those of Cplex solver. The comparison shows that Cplex solver can solves small size problems but the Bender’s decomposition algorithm is capable of solving problems of large scale as well as small ones.


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