An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown

摘要

We consider a semi-online scheduling problem on a single machine with an unexpected breakdown period. In the problem, each job has a processing time and a subsequent delivery time. All these data are known in the beginning. The scheduler has to determine a sequence S of these jobs for processing. After S is given, a machine unavailability period may occur where its starting time and length are not known in advance. The objective is to minimize the time by which all jobs are delivered. We present an online algorithm with a competitive ratio of 5+12 approximate to 1.618pprox 1.618$$end{document}, which improves the previously known algorithm with 2+22 approximate to 1.707$$rac{2+sqrt{2}}{2}pprox 1.707$$end{document}-competitive.