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This paper presents a new heuristic scheduling algorithm for flexible manufacturing systems (FMSs) with partially overlapping machine capabilities. Unlike traditional 'routing then sequencing' methods, the algorithm solves routing and sequencing sub-problems of FMS scheduling simultaneously by combining several dispatching rules. The primary objective is to take advantage of the system flexibility provided by partially overlapping machine capabilities and various processing speeds associated with different machines in FMS. Simulation results show that for the class of FMS scheduling problems modeled in this paper, the algorithm generate valid schedules and improve solution quality at an average of 30% compared to a variation of the longest processing time first (LPT) rule.