The first step towards implementing Group Technology in manufacturing is the decomposition of the manufacturing system into manufacturing cells consisting of various machines and part-families assigned to it. We formulate the problem as a Quadratic Integer Program. This formulation offers considerable flexibility to the system designer in deciding the number and size of cells. The formulation can also handle situations where there are multiple machines of the same type. A simple heuristic is developed to solve the problem. Computational tests reveal that the heuristic algorithm obtains solutions that are as good or better than other methods for simultaneous formation of machine cells and part-families.