A handy idea would be to write an app to schedule meetings between people's calendars (no idea if this already exists though).
Other than the obvious constraint to find an available slot for everyone involved, people could set other constraints, e.g., "busy 60 mins before and after I meet people out of my organisation", or "is there an available conference room".
The way we tend to set up meetings by email is a bit of back and forth where everyone provides a range and we narrow it down, but this can be done automatically.
You could even add weights to your objective in order to make sure that the schedule attempts to fulfill people's wishes/preferences, e.g., "all my meetings must be in a contiguous 3-hour block every day, if possible".
This can get interesting from an OR point of view because as the number of people and constraints increases, it can quickly become non-trivial to generate the schedule.
It could also be really interactive and make suggestions, e.g., "I detected that the only way to schedule this meeting this month is the 17.00-18.00 slot on Monday. Are you willing to attend a meeting after working hours?"