Theory of complexity – How can I develop a pseudo-polynomial time algorithm for a non-integer problem?

I have a scheduling problem with a set of jobs $ J, with a setting & # 39; & # 39; non integer & # 39; & # 39; $ beta_j $, that is, the parameter is a real number and $ beta_j leqslant 0.5, exists in J $.

Since the problem will be trivial if $ beta_j> 0.5, forall j in J $, I can not assume we can turn an instance into an entire instance. By the way, I'm looking for the computer complexity of the problem.

My question is therefore: how can I develop a pseudo-polynomial time algorithm for the problem (to indicate that it is at most NP-hard in the ordinary sense), although the problem is not an integer value ?