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Apr 10, 2022 at 13:57 vote accept Fabius Wiesner
Apr 9, 2022 at 20:08 comment added prubin $\dots \le -2$ would be appropriate if you omitted $x_{31}.$ Rob's model includes it. You could fix $x_{31}=1,$ but there is no need to.
Apr 9, 2022 at 19:11 comment added Fabius Wiesner Rethinking about it, I think that $\ldots-s_i<=-2$, since I consider $x_{31}=1$ and $x_0=0$ in my "simplification". Thus we have $0$ objective value with non-integer $x_i$, and we can't conclude anything.
Apr 9, 2022 at 18:34 comment added RobPratt Yes, $\dots -s_i \le -1$.
Apr 9, 2022 at 18:32 history edited RobPratt CC BY-SA 4.0
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Apr 9, 2022 at 18:32 comment added Fabius Wiesner I think I have to replace $\ldots<=-2$ with $\ldots-s_i<=-1$ in my inequalities right?
Apr 9, 2022 at 18:29 comment added Fabius Wiesner Wait, I must retry, I didn't consider the empty set in Rob Pratt formulation, I have to check it again.
Apr 9, 2022 at 18:28 comment added RobPratt If the objective value is $0$ and the $x$ variables take integer values, you have a counterexample. Otherwise, you can't conclude anything.
Apr 9, 2022 at 18:26 comment added prubin If the objective value is zero, the solution should provide a counterexample to the conjecture. Does it?
Apr 9, 2022 at 18:14 comment added Fabius Wiesner Unfortunately, with slack variables, the result is $0$. So we can say nothing in this case?
Apr 9, 2022 at 17:20 history answered RobPratt CC BY-SA 4.0