Even without medication, that routine is the basic thing to do. Try to catch some sleep on the plane; sudifed, mask & ear plugs help don't drink caffine, alchol or cola. When you arrive at your port city, tour as long as you can without sitting down for any great length of time; short lunch or light breakfast is fine. Go to your hotel or board ship mid to late afternoon and nap; get up and get refreshed for dinner.
Andee is correct. Jet lag has been a major problem for me in the past - walking zombie! Then I started taking Ambien during the long flight, timed to awake about an hour before landing, and now I have no jet lag problems.