This study addresses a multi-period part selection problem for flexible manufacturing systems in which processing times are controllable. The problem is to determine the set of parts and their processing times while satisfying the processing time and the tool magazine capacities in each period of a planning horizon. The objective is to minimize the sum of processing, earliness/tardiness, subcontracting and tool costs. Practical considerations such as available tool copies and tool lives are also considered. An integer programming model is developed, and two-phase heuristics are proposed in which an initial solution is obtained by a greedy heuristic under initial processing times and then it is improved using local search methods while adjusting processing times. Computational experiments were done on a number of test instances, and the results are reported.