This thesis presents a solution method for the machine-part grouping problem which incorporates relevant production requirements such as routing sequence, production volume, unit handling size, unit processing time, intercell distance and cell size. We formulate the machine grouping problem as a generalized quadratic assignment(GQA) problem whose objective is to minimize the total intercell movements. To solve the GQA problem, a solution method is developed. It is based on genetic algorithm and greedy heuristic. Once machine cells are identified, the part family identification procedure is employed to find the associated part families. To evaluate the performance of the proposed method, twelve different problem sets taken from the previous research works are solved. The computational results show that the proposed method is substantially better than two existing algorithms in terms of such measures as global efficiency, group efficiency, intercell move factor and grouping effectiveness.