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In this paper, Petri net models for flexible manufacturing systems (FMS) are constructed. A firing sequence of the Petri net from an initial marking to a final one can be seen as a schedule of the modeled FMS. By using the branch-and-bound algorithm, an optimal schedule of the FMS can be obtained. Timed marked graphs, a special class of timed Petri nets, are then used to analyze the long-term performance of the job-shop systems. For a job shop system, a procedure is proposed to derive the marked graph from the initial Petri net model after the schedule is determined. The branch and bound algorithm and proposed procedure are illustrated through a job-shop system.