A friend of mine who’s an economics prof told me once that his entire discipline can be summarised by answering the question “How far would you drive out of your way to buy fuel at a discount of n%?”
Today’s invention is a vehicle which will be aware from moment-to-moment of its current fuel load and consumption rate as well as the distribution of petrol stations (and prices) within driving range.
This, together with the driver’s input of his/her destination and urgency allows an approximate optimisation to be undertaken, so that the car can be rerouted to take on board fuel -if the combination of detour shortness, low price and urgency justifies this.
This analysis would involve evaluation of the cost/benefit ratio of a detour ie (extra time and extra fuel used) vs (fuel cost saving).
(If the price were sufficiently low at a particular location, it would be worth driving there in a car with a specially enlarged tank. This approach could be further augmented by making predictions about the future price of fuel. In other words, is it worth driving for x km today for a discount of n% when the price in three days’ time will be discounted by n+m% ?)