Flow-shop scheduling in the metal industry
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abstract
In the metal industry, the processing of a part (from an ingot, say) requires first the heating of the ingot. Then, when the ingot has reached the desired temperature, it is launched in the shop and processed by the machines. In a flow-shop environment, a part cools down and its processing time on each machine is increased, to a point where it may be necessary to stop the operations on that part, and reheat it before processing can be resumed. This introduces a state dependence in the processing times, i.e. processing times are no longer given by a constant, but, rather, by a function of the time a part has spent into the shop before it is processed. Since the scheduling problem requires the knowledge of the processing times of the jobs, i.e we need to know whether the processing time of job j on machine 2 is f(j2) or f(j22+j2), a.s.o for all machines, which actually depends on whether j2>0 or j2 = 0 (which depends on jobs j-1, j-2, ..., 1), then the processing times themselves depend on the schedule. Then how can we schedule the jobs if the processing times are schedule dependent? We review here the main results in the literature in a deterministic environment.
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Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104)
