A new mathematical model for the Weber location problem with a probabilistic polyhedral barrier |
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Authors: | Mehdi Amiri-Aref Nikbakhsh Javadian Reza Tavakkoli-Moghaddam Armand Baboli |
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Affiliation: | 1. Department of Industrial Engineering, Mazandaran University of Science &2. Technology, Babol, Iran.m.a.aref@ustmb.ac.ir;4. Technology, Babol, Iran.;5. Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.;6. INSA-Lyon, DISP Laboratory, F-69621, Villeurbanne, France. |
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Abstract: | With the wide application of location theory in a variety of industries, the presence of barriers ?merits the attention of managers and engineers.? In this paper, we assess the Weber location problem in the presence of a polyhedral barrier which probabilistically occurs on a given horizontal barrier route in the rectilinear space. A left triangular distribution function is used for the starting point of the barrier and therefore an expected rectilinear barrier distance function is formulated. In addition, a modification of the polyhedral barrier is presented which is equivalent to the original problem. Therefore, a mixed integer nonlinear programming model, which has a nonconvex solution space, is presented. Furthermore, by decomposing the feasible space into a finite number of convex solution spaces, an exact heuristic solution method is proposed. Then, a lower bound problem based on the forbidden region is applied. Some theorems and an example are reported. |
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Keywords: | Weber location problem polyhedral barrier mixed integer nonlinear programming optimisation |
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