I would like to adjust my constraint so that the x are only ever added for the weekend of a week, i.e. days 6,7 and then 13,14 and 20,21 etc.. That would be my previous formulation, but how can I formulate it more beautifully?

$\sum_{i\in I}^{}x_{jit}\le 2~~~\forall j\in J,b\in B,t\in\{6,7\}\cup\{13,14\}\\ $


1 Answer 1


I would just define another set, $T^{Weekends} = \{t \in T | t\mod 7 =6 \;\vee t \mod 7=0\}$. Here I have assumed that you have a set $T$ with all relevant days.

Then you can write your constraint like this:

$\sum_{i\in I}^{}x_{jit}\le 2~~~\forall j\in J,t\in T^{Weekends}\\ $

I have removed $b\in B$, since $b$ is unused.

  • 1
    $\begingroup$ I think you meant that the $\mod 7$ values are $6$ and $0$. $\endgroup$
    – RobPratt
    Commented Nov 19, 2023 at 12:25
  • $\begingroup$ @RobPratt , oh, sorry, yes. I will make an edit to my answer. $\endgroup$
    – gmn
    Commented Nov 19, 2023 at 12:58

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