Best advice I got and I used and continue to use is this. If you flight is during the day take your dose on your starting time zone. Once you arrive at your destination stay on the time zone you just came from till you go to bed. When you get up take meds at the new time zone to the schedule you where using. Then do the reverse when you go back.
I did this when I flew to Iceland and it worked well for me. (5 hour change) my flight was overnight. I took my last pills boarded the plane and then tried to sleep. Once we arrived in Iceland I took my regular morning dose at 7am Iceland time. I found I had no issue doing it that way. When we came home I stayed on the Iceland time zone and took an extra pill because we gained 5 hours. When I went to bed that night I made sure to go to bed at my regular time. Then put my self on my regular schedule the following morning.
Hope this helps