Fixed order scheduling with deadlines

André Berger; Arman Rouhani; Marc Schröder

doi:10.1016/j.orl.2025.107306

Fixed order scheduling with deadlines

André Berger
, Arman Rouhani^*
, Marc Schröder

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

This paper studies a scheduling problem where machines must follow a predetermined fixed order for processing jobs. Given n jobs, each with processing times and deadlines, we aim to minimize the number of machines used while meeting deadlines and maintaining the order. We show that the first-fit algorithm is a 2-approximation when the order aligns with non-increasing slacks, non-decreasing slacks, or non-increasing deadlines. In general, we provide an O(log?n)-approximation.

Original language	English
Article number	107306
Journal	Operations Research Letters
Volume	61
DOIs	https://doi.org/10.1016/j.orl.2025.107306
Publication status	Published - 1 Jul 2025

Keywords

Approximation algorithms
Bin packing
Fixed order
Scheduling
Set cover

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10.1016/j.orl.2025.107306Licence: CC BY

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abstract = "This paper studies a scheduling problem where machines must follow a predetermined fixed order for processing jobs. Given n jobs, each with processing times and deadlines, we aim to minimize the number of machines used while meeting deadlines and maintaining the order. We show that the first-fit algorithm is a 2-approximation when the order aligns with non-increasing slacks, non-decreasing slacks, or non-increasing deadlines. In general, we provide an O(log?n)-approximation.",

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N2 - This paper studies a scheduling problem where machines must follow a predetermined fixed order for processing jobs. Given n jobs, each with processing times and deadlines, we aim to minimize the number of machines used while meeting deadlines and maintaining the order. We show that the first-fit algorithm is a 2-approximation when the order aligns with non-increasing slacks, non-decreasing slacks, or non-increasing deadlines. In general, we provide an O(log?n)-approximation.

AB - This paper studies a scheduling problem where machines must follow a predetermined fixed order for processing jobs. Given n jobs, each with processing times and deadlines, we aim to minimize the number of machines used while meeting deadlines and maintaining the order. We show that the first-fit algorithm is a 2-approximation when the order aligns with non-increasing slacks, non-decreasing slacks, or non-increasing deadlines. In general, we provide an O(log?n)-approximation.

KW - Approximation algorithms

KW - Bin packing

KW - Fixed order

KW - Scheduling

KW - Set cover

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DO - 10.1016/j.orl.2025.107306

M3 - Article

SN - 0167-6377

VL - 61

JO - Operations Research Letters

JF - Operations Research Letters

M1 - 107306

ER -

Fixed order scheduling with deadlines

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Keywords

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