Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model

Abstract

We consider a multi-facility location problem in the presence of a line barrier with the starting point of the barrier uniformly distributed. The objective is to locate n new facilities among m existing facilities minimising the summation of the weighted expected rectilinear barrier distances of the locations of new facilities and new and existing facilities. The proposed problem is designed as a mixed-integer nonlinear programming model, conveniently transformed into a mixed-integer quadratic programming model. The computational results show that the LINGO 9.0 software package is effective in solving problems with small sizes. For large problems, we propose two meta-heuristic algorithms, namely the genetic algorithm and the imperialist competitive algorithm for optimisation. The numerical investigations illustrate the effectiveness of the proposed algorithms.

Keywords:

• multi-facility location problem
• quadratic programming
• rectilinear distance
• probabilistic line barrier

Acknowledgements

The fifth author thanks the Research Council of Sharif University of Technology, and the other authors thank Mazandaran University of Science and Technology for supporting this work. The authors are also grateful to the Editor and two anonymous referees for their constructive comments and suggestions in improvement of the presentation.