Equitable colouring and scheduling on identical machines Online publication date: Tue, 14-Nov-2023
by Sarah Nouri; Mourad Boudhar
International Journal of Mathematics in Operational Research (IJMOR), Vol. 26, No. 3, 2023
Abstract: This paper deals in the first place with the problems of two-equitable colouring of a union of complete bipartite graphs and three-equitable colouring of connected bipartite graphs, where their NP-completeness is proved. In the second place, it studies the scheduling problem of conflicting jobs on identical machines, while distributing the load evenly between them. Jobs with conflicting constraints cannot be executed on the same machine, these constraints are modelled by a conflict graph. Such problem with identical processing times can be seen as an m-equitable colouring. If the conflict graph is a star graph or a union of chains, this paper demonstrates that the addressed scheduling problem remains NP-hard. Furthermore, the paper describes mixed integer linear programming formulations, followed by some heuristics. The computational experiments show that one of the MILPs can optimally solve some instances with 100 jobs, and the proposed heuristics perform well.
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Mathematics in Operational Research (IJMOR):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email subs@inderscience.com
Our Blog 
Follow us on Twitter 
Visit us on Facebook