Scheduling on Identical Machines with Setup Time and Unknown Execution Time

TL;DR

This paper studies online scheduling on identical machines with setup times depending on job sets and unknown job durations, proposing algorithms with optimal competitive ratios across various scenarios.

Contribution

It introduces online algorithms for scheduling with setup times and unknown job durations, achieving asymptotically optimal competitive ratios in multiple scenarios.

Findings

Algorithms achieve optimal competitive ratios for all scenarios.

Setup time modeled as a monotone function of job sets.

Effective handling of unknown job execution times.

Abstract

In this study, we investigate a scheduling problem on identical machines in which jobs require initial setup before execution. We assume that an algorithm can dynamically form a batch (i.e., a collection of jobs to be processed together) from the remaining jobs. The setup time is modeled as a known monotone function of the set of jobs within a batch, while the execution time of each job remains unknown until completion. This uncertainty poses significant challenges for minimizing the makespan. We address these challenges by considering two scenarios: each job batch must be assigned to a single machine, or a batch may be distributed across multiple machines. For both scenarios, we analyze settings with and without preemption. Across these four settings, we design online algorithms that achieve asymptotically optimal competitive ratios with respect to both the number of jobs and the number of machines.