Application of the facility location problem to the problem of locating concentrators on an FAA microwave system

Abstract

The FAA has decided to install, operate, and maintain its own national microwave network called the Radio Communications Link (RCL) network. With this network and its capability to provide concentration points at any one of its microwave repeater locations, the FAA can substantially reduce its leased line budget. This paper addresses the problem of determining the most cost-effective mix of point-to-point leased lines and “tail circuits” to RCL concentrators for connecting communicating pairs of FAA facilities. The problem, formulated as an integer programming (IP) problem, is shown to be similar to the facility location problem. Also, like the facility problem, integral optimal solutions are frequently obtained. (The reason integral optimal solutions are frequently obtained for the facility location problem is not known.) Thus it is an example, more complex than the facility location problem, where such a phenomenon occurs. Also, the dimensionality of the problem precludes its being solved all in one piece. In this paper we formulate the problem, relate it to the facility location problem, and provide the partitioning and reduction techniques used to solve it in a reasonable amount of time. The partitioning and reduction techniques are independent of any particular formulation for this type of problem, and the solution methodology that would be applied to any subproblem.