Optimization of location of interconnected facilities on parallel lines with forbidden zones

An overview of statements, models and methods for solving location problem of interconnected rectangular facilities on parallel lines with forbidden zones is given. The centers of the facilities are connected by communications with each other and with forbidden zones. It is necessary to place facilities outside the zones in such a way that the total cost of communications facilities to each other and to the zones was minimal. The main focus is on the problem on the line. For several lines communication are through a viaduct. Models of graph–theoretic formulation and partially integer programming with Boolean variables are constructed. Properties are found that allow us to consider the problem as discrete and decompose it into a number of problems of smaller dimension. Algorithms for finding exact and approximate solutions are developed, and polynomial solvable cases are identified. The results of numerical experiments are presented. Bibliogr. 32.