Mark
Do you speak from experience or merely looking at the books?
The payload/range tables usually are fairly light on for arrival fuel and I don't know anyone that would arrive with bare bones fuel.
Adelaide only really has Melbourne as a destination alternate, Edinburgh really doesn't help you much and taking a foreign registered aeroplane into that port would be a time consuming exercise.
It has been a while since I flew a 737-800 but it never did as well as book and I never took min fuel. I don't doubt there will be some days where departing with a full load won't be an issue but there will be days when it is.
That said I doubt they will fill it up so the point may well be moot.
The other thing worth looking at is the weight that comes with a full load. You have picked 15.5 tonnes for 160 pax. I generally use 100 kg per punter and then for predominantly holiday traffic that tends to be a bit on the light side - ok for business routes. I don't see many 77kg adults on board these days..
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