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I'm looking to identify a problem in the literature that I'm currently solving.

I have a set of jobs each having a set of operations. Each operation has a duration. An operation may be done by a machine, from a set of machines, that can process the operation type. Machines only process one type of operation and have a run-time capacity. Operations of each job may be done in any order. Of course each machine may only do one operation at a time. The objective is to find a feasible allocation of operations to machines so as to finish all jobs within an allotted maximum time.

I'd appreciate help identifying the problem and references to papers you know of.

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  • $\begingroup$ Welcome to OR-MS. As you mentioned "Operations of each job may be done in any order" it sounds like open shop scheduling model. Whatever, you could try solving your model using flexible job shop by defining the specific route for each job. There are many useful related questions which could be found on "or.stackexchange". E.g. this, this, this and this links would be interested. $\endgroup$
    – A.Omidi
    Jan 9, 2020 at 9:54

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This is a production planning/production scheduling problem (Google scholar these for many relevant hits), some nice references to get you started include this one and this one.

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