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In this paper, new plane curves (multidirectorial curves as counterpart to multifocal curves; and focal-directorial curves as curves of a transitory type) are considered through geometric genesis, and their form variation for special choices of foci and directrices disposition. Furthermore, the form variation of Weberian focal-directorial curves (WFDC) for different values of accompanying parameter S and Weberian coefficients is considered. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]