This paper presents a linear assignment algorithm for machine-cell and part-family formation for the design of cellular manufacturing systems. The present approach begins with the determination of part-family or machine-cell representatives by means of comparing similarity coefficients between parts or machines and finding a set of the least similar parts or machines. Using the group representatives and associated similarity coefficients, a linear assignment model is formulated for solving the formation problem by allocating the remaining parts or machines and maximizing a similarity index. Based on the formulated linear assignment model, a group fort-nation algorithm is developed. The results of a comparative study based on multiple performance criteria and many existing data sets show that the present approach is very effective and efficient, especially in dealing with large-sized problems. (C) 2003 Elsevier Ltd. All rights reserved.