Issue |
RAIRO-Oper. Res.
Volume 58, Number 3, May-June 2024
|
|
---|---|---|
Page(s) | 2393 - 2419 | |
DOI | https://doi.org/10.1051/ro/2024029 | |
Published online | 18 June 2024 |
Approximation schemes for scheduling jobs on identical parallel machines to minimize the maximum lateness and makespan
1
University of Gezira, Wad-Madani, Sudan
2
Université de Lorraine, LCOMS EA7306, Metz 57000, France
3
Sudan University of Science and Technology, Khartoum, Sudan
* Corresponding author: pierre.laroche@univ-lorraine.fr
Received:
24
January
2022
Accepted:
30
January
2024
We consider a multiobjective scheduling problem, with the aim of minimizing the maximum lateness and the makespan on identical machines, when the number of machines is fixed. This paper proposes an exact algorithm (based on a dynamic programming) to generate the complete Pareto Frontier in a pseudo-polynomial time. Moreover, four heuristics have been proposed in order to optimize our algorithm. Then, we present a Polynomial Time Approximation Scheme (PTAS) to generate an approximate Pareto Frontier. In this scheme, we use a simplification technique based on the merging of jobs. Furthermore, we present a Fully Polynomial Time Approximation Scheme (FPTAS) to generate an approximate Pareto Frontier, based on the conversion of the dynamic programming algorithm. The proposed FPTAS is strongly polynomial. Finally, some numerical experiments are provided in order to compare the proposed approaches.
Mathematics Subject Classification: 90C59 / 90C39 / 90C29
Key words: Approximation / multiobjective scheduling / maximum lateness / Makespan / dynamic programming / PTAS / FPTAS
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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