Online scheduling of unit length jobs on a batching machine to maximize the number of early jobs with lookahead

This paper studies online scheduling of unit length jobs on a parallel hatching machine with the help of lookahead. The objective is to maximize the number of early jobs. Denote by b the size of each batch with b = infinity in the unbounded hatching and b < infinity in the bounded hatching. In the LKL lookahead model, at a time instant t, an online algorithm can foresee all jobs that will arrive in the time segment (t, t + L). When 0 <= L < 1, we show that a simple greedy online algorithm (independent of the value of L) has a best possible competitive ratio of 1/min{n, b + 1}, where n is the number of jobs. This means that lookahead is useless when 0 <= L < 1. When 1 <= L < 2, we establish the upper bounds 0.39 (for b = infinity) and 2/3 (for b < infinity) of competitive ratios, and provide an online algorithm of competitive ratios 1/4 (for b = infinity) and 1/5 (for b < infinity). (C) 2009 Elsevier B.V. All rights reserved