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UBC Theses and Dissertations

The cost minimization of machining operations using geometric programming Freedman, Paul


The cost minimization of a machining operation can be described as a non-linear constrained optimization problem. Geometric Programming (GP) is a relatively new technique well-suited to this class of problems. In this thesis, three GP methods are described that are practical for real-time microprocessor controllers; numerical examples are presented based on three machining operations. For high volume production, several machines can be serially linked with buffers in between to form an Automatic Transfer Line (ATL). The minimization of the combined costs is accomplished in a new way by modelling the cost of each machine as a polynomial function of cycle time, the machining time per workpiece. A new control strategy is described that dynamically re-assigns the cycle times of working machines when others in the ATL fail. To implement this strategy, a two level hierarchy is proposed with a local controller associated with each machine, and a single supervisory controller. Simulation of some typical ATL configurations is used to compare the performance of this strategy with the strategy of no change in cycle time. For the cases studied, modest savings in cost and substantial savings in mean in-process buffer level are obtained when the machines are arranged in the appropriate order.

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