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I am currently writing my first paper and I was wondering whether it is usual to list Big-$M$ or Small-$m$ in the model notation, or are these values that can be regarded as standard? If so, do you have to explain in the text how to parameterize these values or can you skip that?

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    $\begingroup$ Although it's not commonly done, I'm a fan of using a subscript on $M$ to indicate a parameter large enough for a particular constraint instance. Some people (especially students?) seem to think the usual notation means a single parameter value used throughout the model ... which means picking a value that is perhaps unnecessarily large for some constraints. $\endgroup$
    – prubin
    May 3 at 18:59

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I think this depends a lot on why you provide the model. You might not even have to linearise in the first place if the mathematical formulation is there just to state the problem unambiguously, but you have no intention of solving it exactly.

However, if you provide the mathematical formulation with the intent of solving it (or you provide it for readers to use it for this purpose), you must have made some determination of a suitable value for $M$. There are two situations I can think of:

  • The value of $M$ depends on the properties of the data in a non-obvious way. In particular, there is no unambiguous bound you can select without resorting to experimentation using actual data. In this case, I would report the actual value of $M$ you select in the numerical section.
  • The value of $M$ can be bounded based on reasoning about the problem setting. In particular, you can state a bound in the form of some formula or procedure. If this is the case, I would definitely report on the formula or procedure. Anyone working with your model will be able to use this bound, so it's helpful if they don't have to rederive it themselves. This is especially important if you find that the value of $M$ matters significantly for the performance of your formulation, or when you can prove your bound is tight.
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In general, I would say using M for a large enough constant is quite standard in operations research literature and therefore, most people do not declare them in the notation section. However, you should explain in the methodology section how this big-Ms are tuned for your particular application.

Not sure what you mean by small-m. Usually, the symbol epsilon is used for a small enough number, especially for tolerances to stop iterative algorithms, for instance.

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