New answers tagged integer-programming
4
Well, you did not define and detail well the problem, hence, I will first write formally the problem definition based on my understanding of what you have written, and then I will propose an Integer Programming formulation.
Problem definition
Let's first define formally the problem.
Let:
$t$ be the number of tasks to be serviced;
$T = \mathbb{N}_{\leqslant ...
7
Introduce binary variables $z_1$, $z_2$, and $z_3$, and impose linear constraints
\begin{align}
z_1+z_2 +z_3&= 1 \tag1\\
1z_1+bz_2+(b+1)z_3 \le y &\le (b-1)z_1+bz_2+Uz_3 \tag2\\
z_2&\le x\tag3
\end{align}
Constraints $(1)$ and $(2)$ enforce the three disjoint cases $y<b$, $y=b$, and $y>b$. Constraint $(3)$ enforces $x=0\implies z_2=0$, and $...
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