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Weber problem for rectangles on lines with forbidden gaps

The location problem of interconnected facilities on the parallel lines with forbidden gaps is considered. Location in forbidden gaps is not allowed. The located facilities are connected among themselves and with gaps. The rectangular metric is used. It is need to minimize the total cost of connections between facilities and between facilities and gaps. The problem is an adequate model of many practical applications from various fields of science and engineering. The mathematical model of nonlinear programming of the problem is proposed. The overview of decision's methods and the properties of the problem are provided. The decision's scheme for one line and the algorithm of an approximate solution of the problem for several lines are proposed.