Abstract
The capacitated single machine scheduling problem arises from a manufacturing system. The machine works periodically and is capacitated in each period. This is a variant of the bin packing problem. We theoretically compare two types of production settings: in the first type, the machine processes each demand without splitting and in the second, splitting is allowed but a setup time occurs. From the worst case viewpoint, we show that the optimal schedule length of the production without splitting may be nearly twice as long as that of the production with splitting. The ratio of two is asymptotically tight. Then we adapt the well-known bin packing heuristics for the on-line version of the capacitated single machine scheduling problem and give their worst case analysis.
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