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In the world of manufacturing, different strategies could be followed to handle the rapidly changing consumer needs and desires in order to remain competitive, and enable their manufacturing systems to respond quickly to new demand and handle the fluctuation in demand. Since the cellular manufacturing system is an important part of the manufacturing system, a new design method, multi-stage cellular manufacturing system design, is proposed in this dissertation. Three performance measures, total number of machines, total machine cost, and %actual risk level, are utilized to evaluate the performance of the proposed design. Considering the uncertainty in the product demand and processing times, two types of the multi-stage cellular manufacturing system are studied. The first type is a deterministic multi-stage cellular manufacturing system. This type of system is propounded to improve the flexibility of the system where the possibility of adding new machines, mini-cells, and stages is existent. Based on the similarity coefficient type used to group the operations into a stage, two design methods are introduced. The first design method is the multi-stage cellular manufacturing system based on the similarity among machines. A new mathematical model is developed to group the machines into stages by maximizing the similarity coefficient among machines. The second design method is the multi-stage cellular manufacturing system based on the similarity among products. A novel heuristic algorithm and mathematical model are proposed to assign machines to stages based on the newly similarity coefficient “cumulative similarity coefficient among products”. In the two design methods, two mini-cell types, regular and flexible flowshop mini-cells, are used in a stage considering the type of products and the possibility to duplicate the machine type. Additionally, the number of stages and product families is un-predetermined and predetermined to minimize the total number of machines. The single-stage and multi-stage cellular manufacturing system performances are compared. The total machines cost is also taken into consideration to evaluate the performance of the proposed design methods in terms of the total number of machines. It is concluded that the flexible mini-cells with a predetermined number of stages and product families could obtain the minimum total number of machines. Forming the stages based on the cumulative similarity coefficient among products using the mathematical model plays a significant role in reducing the total machines. The number of machines in the system decreases as the number of stages increases, also. However, the decreasing number of machines does not guarantee to reduce the total machine cost. The second type is a stochastic multi-stage cellular manufacturing system in uncertain product demand and processing times. Based on the possibility to mix the product families in the stage, two design methods are proposed to handle the uncertainty of the capacity requirements. The first design method is the stochastic multi-stage cellular manufacturing system with regular mini-cell. The second design method is the stochastic multi-stage cellular manufacturing system with layered mini-cell. Three types of layered mini-cells are created in a stage considering the number of product families processed in a mini-cell. In the two design methods, the machines are assigned to a stage(s) based on the “average processing time variability” by a novel heuristic algorithm. Additionally, two design approaches are created in each design method based on the similarity coefficient used in a stage to calculate the similarity coefficient among products. In the first design approach, the products are grouped into product families depending on the hybrid similarity coefficient based on demand variability. In the second design approach, the product families are formed based on a new similarity coefficient, which is a hybrid similarity coefficient based on the processing times and demand. However, it is observed that an increase in the total number of stages does not always lead to reducing the total number of machines. Additionally, increasing the %risk level does not guarantee to increased %actual risk level.

In many cellular manufacturing systems, cells have flowshop scheduling characteristics. Most flowshop scheduling methods appeared in the literature assume that products are processed in batch or mixed mode. However, it has been observed that processing products in mixed mode (Batch-Cyclic Scheduling) improves the production rates as long as setup times are negligible. In this study, three phases are proposed to solve this problem. The first phase determines the product families based on processing similarity coefficients between products. Then in the second phase a new dissimilarity coefficient among products is used to divide the product family into subfamilies. Even though products in the same family are similar, we are attempting to create subfamilies where products in a subfamily have different bottleneck machines and wide difference between processing times. The production rate improvement observed when running products in batch-cyclic-mode was higher when bottleneck machines shifted and difference in processing times was higher. Finally, in the third phase, the products in each subfamily are scheduled in their corresponding cells using batch-cyclic and batch scheduling methods. However, the results show the efficiency of the batch-cyclic scheduling method to minimize the makespan, reduce the number of cells, and improve capacity parameter in the system.