Cost index equals time cost divivded by fuel cost. Given that, do the airlines in Middle East generally use higher cost indexes because fuel costs are much cheaper?
Not all of the Middle East countries are oil rich. And recent developments highlight that there's a shift away from an oil-based economy. Most recently Saudi Arabia introduced taxes for the first time, with a 83-127% hike in petrol prices. And Dubai introducing VAT also for the first time.
An in-depth analysis of Emirates' financials as of Jan 2017 can be found here, in an article titled, 'Is Emirates in trouble?'.
Jet fuel is still the highest operational cost item but has declined sharply since 2014/15.
They also had issues with yield and load factors. It's a business like any business, if you can't fill the seats, you're not making money.
Here are the latest fuel prices from IATA as of 2 Feb 2018:
A metric-ton is \$17.7 cheaper than the most expensive region. So for a long-haul that needs say 100 tonnes of fuel, that's a saving of \$1,770. But, don't forget that when a Gulf carrier flies to anywhere outside the region, they'll fill up their tanks there, likewise for say a European carrier filling up in the Middle East.
It may be more beneficial to a regional low-cost carrier though. But since short flights are not as affected, any little saving will help towards a profit. Also note a high cost index is not just about cheap fuel, but also expensive maintenance. It is used when the flight-hours need cutting down as the plane ages. A low cost-index could also be used to delay the arrival to let a storm subside (even with cheap fuel on board). It's complicated.
Taking Emirates for example, when they fly westbound with the cheaper fuel, they could use a higher cost index to offset the headwind, and on the return, a low cost index to offset the more expensive fuel they picked up, but since now they are in tailwind, the time penalty won't be big.
As for the exact cost indexes, that information is not public, and with the aforementioned developments and putting the fuel costs in perspective, I hope that helps.