Is Time scheduling problem np hard or np complete?

Question

I have a set of courses and each courses have a set of classes. Each classes have a set of timings available with some penalty. I wanted to schedule each classes to any of the timings of its with a minimum value of penalty and minimum violation pf soft constraints (because each soft constraints violation gives some penalty). I am not sure whether this problem is np hard or np complete.

Thanks in advance

Answer 1

NP-complete problems are decision problems by definition. NP-hard problems include decision problems but also encompass search and optimization problems like yours.