We consider a part-mix allocation problem in a hybrid manufacturing system (HMS) composed of a flexible manufacturing cell (FMC) and a conventional jobshop with the objective of minimizing makespan. The problem is to find the best part-mix allocation to the FMC and the conventional jobshop for a given set of part types to be produced during the upcoming planning horizon. For the problem, we should solve the jobshop and the FMC scheduling problems for each part-mix allocation alternative. Because of the computational difficulty of each of the scheduling problems, we use heuristics: list scheduling method for the jobshop scheduling problem and a part grouping algorithm called the maximal intersection minimal union heuristic for the FMC scheduling problem. Then, for the entire part-mix allocation problem, we develop a branch and fathoming algorithm that uses the two scheduling heuristics. These algorithms, when combined, give a good part-mix allocation and production schedules in the FMC and the conventional jobshop at the same time. Computational results show that the branch and fathoming algorithm requires much shorter computation time than a full enumeration method and can solve problems of a practical size in a reasonable amount of time.