Veloo
Well ..... let's take a B747-400 burning approximately 10 tonnes of fuel per hour in the criuise travelling at 480 kts tas. That means it travels 8 nm per minute. So if you can shorten its track by 8nm it will save one minutes worth of fuel. 1/60th of 10 tonnes = 166 kgs of fuel. I am guessing that Jet A1 presently costs US$300 per tonne, so an 8nm track shortcut would save about US$50 in fuel costs alone.
For other types adjust the fuel burn accordingly.
HTH