I have a model involving constraints of the form $$d(i) = a \cdot W(i) + b \cdot B(i)$$ where $W(i)$ is binary and $d(i), B(i)$ are positive reals.
The objective function is $\max\sum B(i)$.
While solving the problem, the solver sets some $W(i)$ to $1$ but keeps the corresponding $B(i)$ at zero. In other words the solver 'prefers' to fulfill the constraint $d(i) = a \cdot W(i) + b \cdot 0$. Advancing towards the optimum is extremely slow.
The question is, how can I "persuade" the solver to set $B(i)$ well above $0$ whenever it decides to set $W(i)$ to $1$? Because I am asking to maximize $\sum B(i)$ I would expect that the solver does what I am asking. The solver should understand that it can only reach the optimum, if it set the values $B(i)$ to appropriate values $> 0$.