Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model |
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Authors: | Saber Shiripour M. Amiri-Aref M. Mohammadnia-Otaghsara Nezam Mahdavi-Amiri |
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Affiliation: | 1. Department of Industrial Engineering , Mazandaran University of Science &2. Technology , Babol , Iran;3. Faculty of Mathematical Sciences , Sharif University of Technology , Tehran , Iran |
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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. |
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Keywords: | multi-facility location problem quadratic programming rectilinear distance probabilistic line barrier |
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