Big-M in model notation?

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?

• 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.
– prubin
May 3 at 18:59

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.