The problem that you are trying to solve is not that your body is not producing melatonin, it's that it is producing it at the wrong time. Melatonin is produced in a cycle pertaining to your bodies waking/resting periods. This is why you get jet lag, your hormones (melatonin is a hormone) are on daily cycles from the old location, that do not match up with the days from your new location. Supplementing with melatonin before going to bed will create a large spike in your melatonin levels and your body will see that as the peak of its melatonin cycle and reset accordingly.