One option is to have clients enter their source, destination, bid, and the range of times when they'd be willing to travel, and to have an algorithm for selecting the highest revenue path (which won't always mean accepting the highest bid, if slightly lower bids can chain together destinations and sources). (There could also be a secondary market to fill any otherwise-empty legs in this path.) The operations problem of creating this algorithm seems related to the traveling salesman problem (it's a different problem, but may involve similar math).

But I expect that, to maximize revenue, satisfying the highest-paying clients will be more important than efficiency in maximizing the number of paying clients per hour. Prices of trips are likely to vary by more than an order of magnitude, and trips with a fixed source, destination, and time would tend to get lower bids. He might even want to give some of these otherwise-empty trips away for free, (e.g., as "upgrades" to airline passengers who were scheduled on that route, in order to build goodwill with airlines who are now sharing the airport with him, and who may be able to do him favors like transporting passengers who he has to cancel on).

There are complications in terms of the timing of booking (regardless of whether there are secondary auctions), because some high-paying clients will want to book at the last minute and get a trip ASAP, while others will want to book in advance and have a guarantee that the trip will go as scheduled. So the revenue-maximizing strategy would probably involve a mix of trips booked in advance and trips booked closer to the departure time, with some preference for clients who are more flexible about timing or cancellations.