# Tag Info

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$, and$...