A new mathematical model for the Weber location problem with a probabilistic polyhedral barrier

作者：Amiri Aref Mehdi^*; Javadian Nikbakhsh; Tavakkoli Moghaddam Reza; Baboli Armand

来源：International Journal of Production Research, 2013, 51(20): 6110-6128.

DOI：10.1080/00207543.2013.796422

• Weber location problem
• polyhedral barrier
• mixed integer nonlinear programming
• optimisation

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.

• 出版日期2013-10-15