0
$\begingroup$

Assuming I have two 0-1 decision variables X[a,b] and Y[i,j,e,d] where :

X[a,b] = 1 if a is in b 0 otherwise

Y[i,j,e,d] = 1 if (i,j) is matched with (e,d) 0 otherwise.

I need to ensure that if two elements say k and l are both in f respectively i.e X[k,f] == 1 and X[l,f]==1 then no matching i.e for each (e,d) Y[k,l,e,d] = 0.

Knowing that my mathematical program is of type ILP, how do I write a constraint expressing the earlier statement ? Like I need to monitor both the value of the decision variables and the indices at the same time, is that possible to come up with a constraint ?

Highly appreciate your help.

Improve this question
$\endgroup$
4
  • $\begingroup$ At first you wrote, that variable Y accepts 4 'arguments' and then you write with only 2. What does it mean? $\endgroup$ Commented Nov 3, 2017 at 9:44
  • $\begingroup$ @SzymonStankiewicz You are right ! It was a mistake of typing. I corrected it now. Is that clear now ? $\endgroup$ Commented Nov 3, 2017 at 14:37
  • $\begingroup$ Maybe something like this? $$\underset{f}{\forall}\;\;\underset{k,l}{\forall}\;\;\underset{e,d}{\forall}\;X_{k,f}+X_{l,f}+Y_{k,l,e,d}<3$$ $\endgroup$ Commented Nov 4, 2017 at 14:05
  • $\begingroup$ @SzymonStankiewicz it worked well ! thanks a lot :). The thing is that instead of <3 I put <= 2 ;). $\endgroup$ Commented Nov 4, 2017 at 23:58

0

Reset to default

Your Answer

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

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.