Delivery Time Improvement Auction Market

In high school and during college breaks, I worked at a local pizza place (as I've mentioned all too frequently here). As an overzealous engineering student, I was always looking for ways to do things more efficiently. One of our biggest problems: inefficient allocation of human capital (a.k.a. delivery boys).

Alas, I never had the time to come up with anything fancy, until now (years later). I decided to start a pet project to develop a web-based "Pizza Delivery Route Optimizer" using as much open source software as possible.

I'm still designing the system, and don't plan on selling it, but a thought occurred to me:

What if people could bid in a live auction on how quickly their orders could arrive? Let's say it's a busy Friday night, and you want your pizza there in 30 minutes or less. In a fair world, even with a fancy Pizza Delivery Route Optimizer running, this would be an unrealistic expectation.

But what if it weren't? What if you could see approximately when your order would arrive, how many orders were ahead of you, and could either bid against other orders to move up in the pecking order or pay a small fee to do the same? What would be a fair price? I'd imagine it would be tailored to current supply (number of drivers) and demand (number of orders). For example, if there are 20 orders ahead of you and only 15 drivers on staff, the fee would be higher than it would be if there were 10 orders and 12 drivers.

To do an auction, the customer would need to set up an account and would only be billed if their expected (not actual) delivery time were made earlier. It'd be unfair to the delivery guy (and probably unsafe) to guarantee a time of arrival. Remember Domino's "30 Minute Guarantee"? Domino's ended it when a delivery guy killed someone trying to make it in the 30 minute window.

I think there may be a market for the auction format, but the implementation would be tough. For one, you wouldn't likely have people stay on a website to actually bid in real time (they are, after all, not willing to spend the time picking the pizza up in the first place). Therefore, a simple fee would probably be easier to implement. This would, however, not necessarily do well for the delivery guy, since the customer would feel no reason to tip the delivery guy if they've already paid more for the delivery in the first place. Perhaps you could split the fee with the delivery guy? It's a tough one to do if you want things to be fair to all parties.