Scheduling with cardinality dependent unavailability periods

TL;DR

This paper studies non-preemptive scheduling on identical machines with cardinality-dependent unavailability periods, proposing approximation schemes for minimizing makespan and the number of machines needed under fixed deadlines.

Contribution

It introduces approximation schemes for scheduling problems with cardinality-dependent unavailability, a novel aspect in machine scheduling research.

Findings

Developed an EPTAS for minimizing makespan with cardinality-dependent unavailability.

Created an AFPTAS for minimizing the number of machines under a fixed deadline.

Established the theoretical foundations for scheduling with cardinality-dependent unavailability.

Abstract

We consider non-preemptive scheduling problems on parallel identical machines where machines change their status from being available to being unavailable and vice versa along the time horizon. The particular form of unavailability we consider is when the starting time of each downtime depends upon the cardinality of the job subset processed on that machine since the previous downtime. We consider the problem of minimizing the makespan in such scenarios as well as its dual problem where we have a fixed common deadline of $1$ and the goal is to minimize the number of machines for which there is a feasible schedule. We develop an EPTAS for the first variant and an AFPTAS for the second variant.