My theory (which is a theory what is, for those of you who know what I am referring to) is that it should be at the last possible minute before the airline are forced to do some Op Ups. So it is when the airline realises that they have oversold economy and may need to do some Op Ups. So this would mean before or at airport check in. Now, having said that, if you are proactively offered an online upgrade (before or at OLCI) at what you consider to be a decent price, you may wish to take it then rather than wait until you get to the airport. Reason for that is that there may only a need for the airline to move a few people, so if they all buy all the available upgrades before you, then you stay in whatever class you booked.