PRODUCTION PLANNING PROBLEMS FOR FLEXIBLE MANUFACTURING SYSTEMS

A flexible manufacturing system (FMS) is an automated, batch manufacturing system consisting of a set of numerically controlled machine tools with automatic tool interchange capabilities. A computer-controlled material handling system transports parts from machine to machine. This research is concerned with certain production planning problems associated with FMS\u27s. In particular, the grouping and loading problems are examined and solved. The solution to the machine grouping problem is a partition of the machines such that each machine in a particular group is able to perform the same operations. The loading problem is to allocate the operations and associated tools of a set of selected part types among the machine groups, subject to the technological and capacity constraints of the FMS. The measure used to evaluate solutions is the expected production rate. The approach to solving these problems uses a closed network of queues (CNQ) model. A stochastic model was chosen to take into consideration variability caused by the occurrence of random events and congestion during real-time scheduling. Within the context of a CNQ, the expected production rate is defined as a function of the number of parts in the system, the number and sizes of machine groups (the solution to the grouping problem) and the workload assigned to each group (the solution to the loading problem). Several alternative definitions of the production function are developed over different state spaces. These alternatives provide tools which can be used to prove properties of the function for optimization purposes. The CNQ model is used to solve a relaxed version of the grouping problem. The relaxation permits all possible partitions of m machines to be ordered with respect to expected production rate. The solution to the loading problem is a set of optimal allocation ratios, or relative ratios at which each group should be loaded to maximize expected production. In particular, we show that for systems with equal numbers of machines in each group, the optimal loading procedure is to balance the assigned workload, i.e., to equalize the total assigned processing time on each machine. However, we also show that there are better partitions into the same number of groups such that the expected production is maximized by assigning unequal workloads to the machines. This result differs from virtually all previous solutions of various loading problems, which assume an objective of balancing the workload. Having considered the grouping and loading problems in the context of the CNQ model, we next consider more realistic models. The solution of a particular grouping problem with additional constraints is the best feasible grouping as defined by the CNQ results. Alternative loading objectives are defined in addition to the balancing and unbalancing objectives examined using the CNQ model. Application of the alternative objectives can produce better results (with respect to production rate) than balancing, despite a highly unbalanced resultant system. Several nonlinear mixed integer formulations of the loading problem are developed, linearized in various ways, and applied to data from an existing FMS. Because some formulations are too large to solve, several heuristics are suggested