In this paper we consider a critical production scheduling problem, the part selection problem, for the effective utilization of a flexible manufacturing system (FMS). The problem is to determine how to split up the production requirement given for a certain period into a number of subsets in order to minimize the number of tool changeovers and the sum of maximum workloads. First, we describe the part selection problem and show that, although the problem can be formulated as an integer programming problem, the number of integer variables is too large to obtain optimal solutions for realistic problems. Then, we develop a heuristic method and carry out the computational experiments to test its efficiency and validity. The computational results show that our heuristic method is efficient and can be used to solve large-scale problems.