In the Flow/Job Shop problems, and other related scheduling problems, a common assumption is that at any given time, a particular job will be being processed on at most one machine (usually... none).

Now imagine a scheduling problem in which a particular job requires multiple "machines" simultaneously, e.g. multiple "resources" instances which are modelled as separate machines. For example, producing a particular type of widget requires 1x human resource A and 1x lathe B and 1x computer server C, at the same time, during which those particular resource instances are locked and cannot work on any other jobs.

What class of scheduling problem is this? (One-to-many job-to-machine model)

ANSWER: "Resource constrained scheduling" seems to be the idea, e.g. as discussed in Chapter 17 of "Principles of Sequencing and Scheduling" by Baker/Trietsch.

  • $\begingroup$ Did you try search with "resource constrained scheduling" keyword? $\endgroup$ – kur ag Aug 5 '19 at 8:26
  • $\begingroup$ Thank you - yes this is the idea I was looking for. $\endgroup$ – Brendan Hill Aug 5 '19 at 10:18

The sequencing models (flow/job shops or hybrid too) are the basic (concept) in the scheduling. It means that to use them into the real world scheduling problems you will have to modify them. (adding some constraints to the model which represent your limitations).

AFAIK, as you mentioned constraints, it can be expressed as a specific project scheduling with resource constraints. would you search for some of the practical scheduling software such as SAP-APO, ASPROVA or some of the online sequencing software? (some of them have a trial version)

They have some nice features such as resource leveling, flexible Gantt chart, exact or heuristic algorithms and other facilities that might be useful.

  • $\begingroup$ Sorry I should have clarified - I am trying to understand how the one-job-multiple-servers-simultaneous constraint is referred to within literature, rather than find a software product to solve it. I.e. where does it fit within the standard taxonomy of scheduling problems. $\endgroup$ – Brendan Hill Aug 5 '19 at 10:03

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