Online scheduling with chain precedence constraints of equal-length jobs on parallel machines to minimize makespan

Abstract

We study the online scheduling problem on m identical parallel machines to minimize makespan, i.e., the maximum completion time of the jobs, where m is given in advance and the jobs arrive online over time. We assume that the jobs, which arrive at some nonnegative real times, are of equal-length and are restricted by chain precedence constraints. Moreover, the jobs arriving at distinct times are independent, and so, only the jobs arriving at a common time are restricted by the chain precedence constraints. In the literature, a best possible online algorithm of a competitive ratio 1.3028 is given for the case $m=2$. But the problem is unaddressed for $m\ge 3$. In this paper, we present a best possible online algorithm for the problem with $m\ge 3$, where the algorithm has a competitive ratio of 1.3028 for $3\le m\le 5$ and 1.3146 for $m\ge 6$.