1
$\begingroup$

I have two specific types of bilinear terms in the problem. The first type involves the multiplication of an integer variable and a continuous variable, while the second type involves the multiplication of two continuous variables. I'm currently exploring the possibility of linearizing this problem using the Benders technique. However, I'm unsure if it is feasible in my particular case, which is why I have posed this question. I'm aware that numerous papers have been published on this topic, but I may have overlooked some of them. Therefore, I believe it would be beneficial to seek input from this community, particularly from individuals well-versed in Benders. Would you kindly provide me with any relevant papers in the field of Benders that pertain to my query?

Best,

Samira

$\endgroup$
3
  • $\begingroup$ Welcome to OR SE. Unfortunately, Benders does not handle bilinear constraints, so I don't see how it would apply to your case. $\endgroup$
    – prubin
    Jul 5, 2023 at 17:47
  • $\begingroup$ What do you think about this paper? mdpi.com/1996-1073/14/20/6503 $\endgroup$ Jul 5, 2023 at 19:01
  • $\begingroup$ It's a bit hard to read, but it seems to handle bilinear constraints. One catch is that it uses an approximation to the cuts. Benders is already what is known as an "outer approximation" (feasible region a superset of the true feasible region), and now you are doing an outer approximation of the outer approximation. So how quickly it converges (assuming it does converge) is an open question. You could certainly try it. $\endgroup$
    – prubin
    Jul 5, 2023 at 23:05

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.