Weighted Scheduling with one overlap

[nik88]

The reason I post this is because I am working on a project that is meant to allocate vehicles to people in a household.

Basically, I need to figure out, given a group of peoples schedule, who should get the car at what times?

more specifically, if there are 4 people in a household each with a set of trips which trips should get the car (all trips start from home and end at home) ... I could go into further detail, but I translated the problem to an activity scheduling problem described in my above post.

This is not a homework assignment!

I am not looking for a solution, just an idea if dynamic programming can work somewhat efficiently (polynomial time) for this problem. And if it can't, any suggestions on what kind of problem this resembles?

If more detail is needed on the specifics of Vehicle allocation for household activities ... I can do this ...

Thanks in advance.