Online and semi-online scheduling on two hierarchical machines with a common due date to maximize the total early work
Man Xiao, Xiaoqiao Liu, Weidong Li, Xin Chen, Malgorzata Sterna, Jacek, Blazewicz

TL;DR
This paper develops optimal online and semi-online algorithms for scheduling jobs on two hierarchical machines with a common due date, aiming to maximize early work, and provides competitive ratio guarantees.
Contribution
It introduces new optimal algorithms for various online and semi-online scheduling scenarios with hierarchical machines and common due date.
Findings
Optimal online algorithm with a competitive ratio of √2.
Semi-online algorithm with a competitive ratio of 4/3.
Algorithms for specific cases with known largest processing time.
Abstract
In this study, we investigated several online and semi-online scheduling problems on two hierarchical machines with a common due date to maximize the total early work. For the pure online case, we designed an optimal online algorithm with a competitive ratio of . For the case when the total processing time is known, we proposed an optimal semi-online algorithm with a competitive ratio of . Additionally, for the cases when the largest processing time is known, we gave optimal algorithms with a competitive ratio of if the largest job is a lower hierarchy one, and of if the largest job is a higher hierarchy one, respectively.
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Taxonomy
TopicsOptimization and Search Problems · Scheduling and Optimization Algorithms
