Suppose we consider budgeted uncertainty (Bertsimas and Sim, 2002) for the following scenario. We have a binary decision variable $x_{i,j}$, where $i \in I$ and $j \in J$ (two sets). We then have the following constraint:

$\sum_i x_{i,j} \geq b_j$ for all $j \in J$

The value $b$ comes from a separate set, say $B$, where each element is associated with an element from $J$.

Now we assume, up to $\Gamma$ elements from $B$ are uncertain. How can we derive the robust counterpart or move the uncertainty to left-hand side? Alternatively, can someone point me to relevant literature.

Note: There is similarity to question: Gamma uncertainty set

However, the information provided here is more specific. Alternatively, I seek better explanation or other relevant literature, since the linked paper is not easily accessible.

  • 2
    $\begingroup$ If the constraint is for every i,j then why do we have a summation and what is its index? $\endgroup$ Feb 21, 2023 at 17:57
  • $\begingroup$ @evrenguney I have updated the description for some reason stackexchange does not allow me to put it using \limits $\endgroup$
    – Pia MiA
    Feb 21, 2023 at 23:29
  • 1
    $\begingroup$ @PiaMiA, RO webinar this Friday, mobile.twitter.com/JannisK13/status/1628036347104489473 $\endgroup$ Feb 22, 2023 at 12:47


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