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I'm looking at a problem that seems quite like flexible jobshop, but as I understand it jobshop is basically all about finding the order/sequence of tasks (across multiple machines potentially), however as far as I can tell it doesn't consider times. The problem I'm looking at has some jobs that will only be available to start at a specific time (earliest start time) and also may have their own deadlines for completion.

I could approach this just by setting constraints on those tasks not starting until t>earliest start time, but it seems like that would be potentially limiting?

Can anyone point me to what this may be called if its not a version of jobshop, or if it is jobshop how to best approach the differences?

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  • $\begingroup$ Welcome to OR.SE. The (flexible) job-shop scheduling actually needs to have a specific route for each job. And these routes basically should be different for at least two jobs. $\endgroup$
    – A.Omidi
    Commented Sep 29, 2023 at 12:20

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It's definitely a job-shop variant. Usually we use the terms "release time" and "deadline". See the job characteristics list here: https://en.wikipedia.org/wiki/Optimal_job_scheduling . The triplet notation there will help you search for papers that have similar job shop formulations. Adding the additional constraints is what you need to do; it will further reduce the feasible solution count but that shouldn't slow the (already slow) computation. Be sure to use the indicator constraint functions for the disjunctive constraints.

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