This thesis is concerned with the development of two generalized set covering models. The first model is formulated for the total set covering problem where cost is minimized subject to the constraint that each customer must be served by at least one facility. The second model is constructed for the partial set covering problem in which customer coverage is maximized subject to a budget constraint. The conventional formulations of both the total set covering and partial set covering problems are shown to be special cases of the two generalized models that arc developed. Appropriate solution strategies arc discussed for each generalized model. A specialized algorithm for a particular case of the partial covering problem is constructed and computational results are presented.