Fixed Order Scheduling with Deadlines
Andre Berger, Arman Rouhani, Marc Schr\"oder

TL;DR
This paper investigates a fixed order scheduling problem on parallel machines with deadlines, demonstrating optimality and approximation bounds for the first-fit algorithm under various conditions, and providing an $O( ext{log } n)$-approximation for the general case.
Contribution
It establishes the optimality of first-fit for unit processing times and provides approximation guarantees in specific scenarios, along with an $O( ext{log } n)$-approximation for the general problem.
Findings
First-fit is optimal with unit processing times.
First-fit is a 2-approximation under certain order conditions.
An $O( ext{log } n)$-approximation algorithm is proposed for the general problem.
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 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 -approximation.
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Taxonomy
TopicsScheduling and Optimization Algorithms
