Research minimax and minisum Weber problems on a plane with forbidden zones

Abstract

Abstract Weber problem is a well–known location problem of connected facilities. Two optimality criteria are considered. The first criterion is minimization of the total cost of connections among facilities. The second criterion is minimization of the maximum connection between facilities. This article deals with Weber problems on a plane with rectangular forbidden zones. Location inside in the forbidden zones is not allowed. The sides of forbidden zones are parallel to the coordinate axes. To measure distances rectangular metric is used. An overview of studies for these problems is provided. Some properties of the problems are described. For example, the possibilities of reduction of admissible areas in the search for an optimal solution are presented. Variants of different bounds of the objective functions are provided. Models of integer linear programming with Boolean variables are given. Computational experiments with using the branch and bound algorithms, the constructed models and IBM ILOG CPLEX package were carried out. Usage of the properties of reductions of admissible areas is promising both in solving of the problems by combinatorial methods and using the integer optimization apparatus.