Reduction from an assignment problem to an independent set problem: NP-hard
If you want to show that your problem is NP hard, your reduction should go in the other direction. You have to show:
$\exists L \in NPH: L \le_M yourProblem$ 
where $NPH$ is the Set of NP-hard languages. 

Your try looks like you wan't to reduce from your problem to Independent Set.