This research aims at solving an engineering design problem encountered in the field of wireless communication systems using mathematical programming techniques. The problem addressed is an indispensable part of micro-cellular radio system design. It involves an optimal location of radio transmitters, given a distribution of receivers and desired signal characteristics. The study has been conducted with the intent of making this problem an integral part of a CAD system for designing radio communication systems. The tool that has been developed for locating a transmitter in such a context is sensitive to different needs of coverage at different locations in the design space. The physical nature of this problem enables it to be conceptualized as a traditional facility location problem. The transmitter is a service facility responsible for serving all the receivers in the design space. A cost is incurred in terms of path-loss, delay spread, and other separation-based measures, whenever service is extended to a receiver. The objective is to place this transmitter in such a way that it optimally serves all the receivers, as measured according to some merit function. However, the nature of the latter merit or objective function, and the nature of the acceptable region for transmitter placement, imparts a special structure to the problem that distinguishes it from traditional facility location problems. The aim of this research effort is to construct a suitable representative mathematical model for this problem, and to design and compare various solution methodologies that are computationally competitive, numerically stable, and accurate. / Master of Science