Find non-overlapping scheduled jobs with maximum cost
The graph of overlapping jobs is an interval graph. Interval graphs are perfect graphs. So what you are trying to do is find a maximum weight independent set (i.e., no two overlap) in a perfect graph. This can be solved in polynomial time. The algorithm is given in "Polynomial Algorithms for Perfect Graphs", by M. Grötschel, L. Lovász, and A. Schrijver. 

There are a number of special cases of perfect graphs for which people have discovered simpler and more efficient algorithms for this task. I don't know whether interval graphs fall into one of these special cases.