Until now i formulated some Linear Programming problems with integer constraints and some with continuous constraints. Now, i've written a linear programming model that both contains variables with integer constraints and with continuous constraints. Is it possible ?
$max \sum_{i=1}^{n} p_{i}x_{i}$
$ \sum_{i=1}^{n} a_{ij}x_{i}=b_{j}-s_{j}+s_{j-1}$ , $j=1..T$
$x_{i}\in \left \{ 0,1 \right \}$ , $i=1..n$
$s_{j}>=0$ , $j=1..T$
Is this a valid linear programming model ? (x and s are variables)
Best Answer
Yes, that's perfectly possible. The criterion is whether it is a linear optimization problem if you replace $x_i \in \{0,1\}$ with $0 \leq x_i \leq 1$.