Mixed-Integer Linear Programing : get the maximum constant associated to a non null variable

96 Views Asked by At

Does anyone know a way get the maximum constant associated to a non null variable using Mixed-Integer Linear Programing ?

I would like to get the variable $a$ in this description :
$$ i = 1,\ldots,m $$ $$ C_{i}, B : constants $$ $$ x_{i} : variables $$ $$ C_{i}, B \gt 0 $$ $$ x_{i} \in 0 \cup [B; +\infty] $$ $$ a = \max_i (C_i \text{ when } x_{i} > 0) $$ $$ a = 0 \quad \text{if there is no } x_{i} > 0 $$

Getting $a$ must not change the validity of an existing objective function.

Thanks for your help