We consider multi-period part selection and loading problems in flexible manufacturing systems with the objective of minimizing subcontracting costs. The part selection problem is to select sets of part types and to determine their quantities to be produced during the upcoming planning horizon while satisfying due dates of all orders for the parts, and the loading problem involves allocation of operations and required tools to machines. Production demands should be satisfied for periods through subcontracting if production demands cannot be satisfied by the system due to machine capacity or tool magazine capacity constraints. For the part selection and loading problems, we develop three iterative algorithms, called the forward algorithm, the backward algorithm and the capacity approximation algorithm, that solve the part selection and loading problems iteratively for each period. To compare the three algorithms, a series of computational experiments is done on randomly generated test problems.