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.
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.