In this paper, we develop a mixed integer program for the design of cellular manufacturing systems. We assume that there are alternate process plans for each part and that each operation in these plans can be performed on alternate machines. The objective of the model is to minimize the sum of investment, processing and material handling costs. Processing times, capacities of machines and cell size restrictions are considered in the process. Part families, machine groups and part plans are identified concurrently. For the efficient solution of the relaxed linear program an efficient column generation scheme is provided. In the problem under consideration columns are generated by solving simple semi-assignment problems. Three different strategies are tested for generating the columns and the best scheme is selected for subsequent use in the branch and bound procedure developed. Finally, computational experience is provided for randomly generated test problems.