The maximum principle analysis conducted in the previous chapter yields qualitative information about the extremal behavior of flexible manufacturing systems. Until now we examined typical elements (regimes) of optimal “scheduling trajectories” and the production conditions necessary for their appearance. It was easy to predict that the analytical information would be insufficient for developing the optimal schedule for the large class of FMS modeled and studied in the previous chapters. The calculation of the optimal schedule can be done analytically only for special cases of small-dimensional manufacturing systems. For example, assuming constant demand rate and linear or quadratic surplus/backlog cost dependencies, the limit cycles and transition corridors can be found analytically for one-machine, two-product scheduling problems. In section 7.2, we present an analytical solution approach to solving one-machine, multiple-part-type problems under constant-in-time demand.
KeywordsSchedule Problem Optimal Control Problem Setup Time Planning Horizon Optimal Schedule
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