Online scheduling of equal-length jobs with incompatible families on multiple batch machines to maximize the weighted number of early jobs

Abstract

This paper studies the online scheduling of equal-length jobs with incompatible families on multiple batch machines which can process the jobs from a common family in batches, where each batch has a capacity b with b=∞ in the unbounded batching and b<∞ in the bounded batching. Each job J has an equal-length integral processing time p>0, an integral release time r(J)⩾0, an integral deadline d(J)⩾0 and a real weight w(J)⩾0. The goal is to determine a preemptive schedule with restart which maximizes the weighted number of early jobs. When p=1, we show that a simple greedy online algorithm has a competitive ratio 2, and establish the lower bound 2−1/b. This means that the greedy algorithm is of the best possible for b=∞. When p is any positive integer, we provide an online algorithm of competitive ratio 3+22 for both b=∞ and b<∞. This is the first online algorithm for the problem with a constant competitive ratio.