Are measures taken to mitigate the effect of jet lag on pilot performance?
Well, if we use a quote from a Jetstar management pilot, to pilots who complained about fatigue, "harden up princesses", then I'd have to say that fatigue is not treated seriously by many airlines. One major airline was paxing crew into Australia, and then they would immediately put on their uniform and operate the aircraft out...having supposedly had sufficient rest to do so in the cabin on that previous flight.
And are simulator training exercises done in a way that has pilots in a jet-lagged mode?
My licence, and so right to work, depends upon my performance in the simulator. I will not even turn up if I haven't had a decent sleep beforehand. Plus, you are supposed to learn things in the sim...what would you even remember if you went there jet lagged.
There have been exercises run with jet lagged pilots. We participated in a study on the effects of fatigue a few years ago, and part of that study was to run sim exercises just after pilots had arrived back in Sydney from long trips. Those sims were 'no jeopardy'....otherwise nobody would have turned up. The aim of the study was to come up with a fatigue management system, that would be applied to the way trips were built and crewed. As far as I know, no system is in use anywhere in the world, and many jurisdictions (EU) have actually been increasing crew work limits.
A number of years back now, CASA were actually going to hand the management of flight time limits over to the airlines, on the basis that 'they would not do anything dangerous', and 'there has never been a fatigue related accident'. At about the same time, NASA released a real report on fatigue, that related the levels of fatigue to blood alcohol concentrations...and the results were not pretty. Saner heads perhaps realised that the airlines would do anything for a buck (they only have to say they are safe, not actually be safe), and they perhaps realised that there were probably liability issues that could affect them, and so they rules were not changed. But a number of exemptions still exist, which were not based on any form of scientific study, one way or the other. And for the 'no fatigue related accidents', well they perhaps realised that there have been an awful lot of 'pilot error' accidents, and perhaps, just perhaps, some of them might have been fatigued. Possibly even most....