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arXiv · 2412.10760

Fixed Order Scheduling with Deadlines

Andre Berger·Arman Rouhani·Marc Schröder
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Abstract

This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the number of machines while ensuring deadlines are met and the fixed order is maintained. We show that the first-fit algorithm solves the problem optimally with unit processing times and is a 2-approximation in the following four cases: (1) the order aligns with non-increasing slacks, (2) the order aligns with non-decreasing slacks, (3) the order aligns with non-increasing deadlines, and (4) the optimal solution uses at most 3 machines. For the general problem we provide an $O(\log n)$-approximation.

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Andre Berger, Arman Rouhani, Marc Schröder. 2024-12-14. Fixed Order Scheduling with Deadlines. https://arxiv.org/abs/2412.10760

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