Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 463976, 40 pages
Research Article

A Nonlinear Multiobjective Bilevel Model for Minimum Cost Network Flow Problem in a Large-Scale Construction Project

1State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610064, China
2Uncertainty Decision-Making Laboratory, Sichuan University, Chengdu 610064, China

Received 3 January 2012; Revised 9 March 2012; Accepted 19 March 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Jiuping Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this study is to deal with a minimum cost network flow problem (MCNFP) in a large-scale construction project using a nonlinear multiobjective bilevel model with birandom variables. The main target of the upper level is to minimize both direct and transportation time costs. The target of the lower level is to minimize transportation costs. After an analysis of the birandom variables, an expectation multiobjective bilevel programming model with chance constraints is formulated to incorporate decision makers’ preferences. To solve the identified special conditions, an equivalent crisp model is proposed with an additional multiobjective bilevel particle swarm optimization (MOBLPSO) developed to solve the model. The Shuibuya Hydropower Project is used as a real-world example to verify the proposed approach. Results and analysis are presented to highlight the performances of the MOBLPSO, which is very effective and efficient compared to a genetic algorithm and a simulated annealing algorithm.