I am searching for a keyword that describes a machine scheduling problem in which machines are allowed to process multiple jobs at a time. Each job requires a given capacity on the machine. At any point in time, the sum of the capacity required by the jobs processed at that time must not exceed a given limit.

Particularly, I am searching for MILP formulations for problems with this property. However, I only find parallel machine scheduling problems in which the processing of only one job at a time is allowed.

New contributor
yolothan is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
  • $\begingroup$ Do you have any stages or routes in the jobs that should be considered prior? Or the environment is just a parallel machine? $\endgroup$
    – A.Omidi
    May 27 at 20:48

1 Answer 1


The keyword is "resource constrained scheduling problem".

Here is a book chapter about the classical mixed-integer programming models for the standard version of the problem:

  • Artigues, Christian, Oumar Koné, Pierre Lopez, et Marcel Mongeau. 2015. « Mixed-Integer Linear Programming Formulations ». In Handbook on Project Management and Scheduling Vol.1, édité par Christoph Schwindt et Jürgen Zimmermann, 17‑41. International Handbooks on Information Systems. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-05443-8_2.

Your Answer

yolothan is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.