Think about it. Fast food restaurants are already equipped to put up and change prices for standard items, like a hamburger of cheeseburger, or double cheeseburger. Besides that fact, lets look at the economics of cheeseburgers. Cheeseburgers from chain restaurants are created in centers of mass production, where the supplies (buns, patties, cheese). These ingredients must be transported to the fast food joints, which costs money (refrigeration of the truck, gas, etc). These same factors come into play with the business of petroleum.
By using a fluctuating system, retailers are able to keep their prices on their product as low as possible, while still maintaining a profit. Say McDonalds is losing to Wendys in a certain town - the branch would be able to cut under Wendy's prices, perhaps temporarily, perhaps permanently, as their profit at that location allows, to attract more customers. Consumers benefit from having the companies compete more for our cheeseburger cravings.
Some might decry that in some places, far from production centers, the prices would become extravagantly high. An Alaskan Cheeseburger may in fact be higher priced after all this - but incentives by government and compensation in standards of living will eventually balance the demand. Alaskans get paid to live up there anyways I hear, and when you think about it, a dollar cheeseburger up there is a fucking steal compared to a dollar cheeseburger in Arkansas.