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In the constraints below, why have they used the big M? What do we look for in order to identify the big M in other questions?

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    $\begingroup$ big M constraints are used to model constraints with implications (e.g. $y=0 \implies x=0$) so you can start by identifying where you have implications in your model. $\endgroup$
    – Kuifje
    Commented Oct 13, 2023 at 15:12

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This is a common modeling techniques in operations research.

Another interpretation is if-then relationship or indicator. When you have to count how many days you have to setup to produce then you can introduce this big-M formulation.

In this case, you can imagine that the big-M value is your maximum production capacity, since you never hope the value of $x$ would exceed your production capacity.

Of course this big-M value should be always valid for your entire problem, otherwise you would obtain wrong counting number on setup variables.

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