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Merge pull request #2 from nnadeau/patch-1
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Citation fix
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KingZee committed Sep 26, 2019
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# Problem definition

There are three types of scheduling problems : Flow-shop, job-shop, and open-shop scheduling. Each one of them has many subsets and variations, (which are generally quite more complex, making them prone to anomalies and edge cases [@Panwalkar2020; Rustogi2013]) but we are going to restrict the scope of our definition at problems with fixed, known-beforehand processing times, that will execute on a single available machine, with no setup-times, due dates or release dates. They remain NP-hard problems even with these constraints [@applegate1991computational].
There are three types of scheduling problems : Flow-shop, job-shop, and open-shop scheduling. Each one of them has many subsets and variations, (which are generally quite more complex, making them prone to anomalies and edge cases [@Panwalkar2020; @Rustogi2013]) but we are going to restrict the scope of our definition at problems with fixed, known-beforehand processing times, that will execute on a single available machine, with no setup-times, due dates or release dates. They remain NP-hard problems even with these constraints [@applegate1991computational].

We have a set of $n$ jobs $J_1, J_2, ..., J_n$. Within each job there is a set of operations $O_1, O_2, ..., O_m$ that need to be executed on $m$ machines $M_1, M_2, ..., M_m$. These different types of problems have the optimization objective, and some constraints in common:

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While our software is a real-life application of the concepts above, its goal is to provide a framework for other researchers to build and improve upon. In its current state, our software is feature complete, but there is still a lot of room for further improvement. Our long-term research goal includes adding more algorithm implementations for completion, and possibly include different problem subtypes and optimization goals. A practical goal is also making the software more accessible for research through improving thread management code and implementing features like GPU computation.

# References
# References

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