Abstract
Online and semi-online scheduling problems on a single machine with an availability constraint are considered in this paper. The machine has one unavailable interval in which jobs cannot be processed. Preemption is not allowed. Jobs arrive over time. The objective is to minimize makespan. First we discuss the online version of the problem. After giving its lower bound, we prove that Earliest Release Date (ERD) algorithm is an optimal algorithm. Then we study some semi-online problems in which the largest processing time, the total processing time, the largest release date, or the optimal makespan is known in advance. For these semi-online problems, we give their lower bounds, design semi-online algorithms and prove their competitive ratios, respectively.
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