Fast approximation algorithms to minimize a special weighted flow-time criterion on a single machine with a non-availability interval and release dates

摘要

This paper is the first attempt to successfully design efficient approximation algorithms for the single-machine weighted flow-time minimization problem when jobs have different release dates and weights equal to their processing times under the assumption that one job is fixed (i.e., the machine is unavailable during a fixed interval corresponding to the fixed job). Our work is motivated by an interesting algorithmic application to the generation of valid inequalities in a branch-and-cut method. Our analysis shows that the trivial FIFO sequence can lead to an arbitrary large worst-case performance bound. Hence, we modify this sequence so that a new 2-approximation solution can be obtained for every instance and we prove the tightness of this bound. Then, we propose a fully polynomial-time approximation algorithm with efficient running time for the considered problem. Especially, the complexity of our algorithm is strongly polynomial.