You said b can't be billed after B. But it sounds like it can't be billed 
before. 

Say b is ready at 1,  can you bill it at 1 and then B at 2?

Anyway, my first thought was using weights on the edges equal to the duration 
between the dependencies and use a max cost on the graph. But calculating the 
duration for each edge may not gain you anything compared to your current 
solution. 
If it ain't broke ...

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