Minimal pulse width to actuate a solenoid
The energy you need for the move of the solenoid core depend on several factors, such as:


mass to move, its way, initial friction and time to move. 


As you see there are too many variables and these could be voltage and temperature dependent. 

Thus a feedback is needed to signal that the move is accomplished. This could be a reed or Hall-switch or optical switch and could be quite an effort and maybe if you can define the maximum force needed it is simpler to have a driver circuit with fixed current profile. Since the initial force needed is highest(due to friction) an intelligent solenoid drive can be applied. You find more details here: http://www.ichaus.de/wp8_whitepaper_en .

This intelligent drive can also involve a microcontroller if needed.