Software Deployment

Hello All - I am new to SCCM and would like to clear few of my doubts.
We are supporting different geographical areas viz US ,INDIA and UK and other parts of Asia. And almost all of our Sites are located in US and UK and honkong and not in India.
Scenario -: We create an advertisement to deploy a particular package to all systems covering US, UK and Asia , the package installs successfully (most of them will be US)to some systems and fails on others. I see that the advertisements expires well before running.
What we do is we put the start time, mandatory assignments and then we expire it after 5 to 6 hours.(Start time 06:00 PM , Mandatory assignment = 06:30PM and expire at 11:30 PM - These timings are based on the time I see on the SCCM console which comes automatically)
How do I ensure that the advertisement runs on all the systems at a particular timing i.e., I want the advertisement to run exactly at 6:30 PM on local system timings with the expiry as mentioned as above????