Even as most flights are packed these days, some planes still take off with plenty of vacant seats, including in First and Business Class, effectively losing the airlines hundreds of thousands of dollars. Offering lower last-minute fares on undersold flights seems a logical solution, and carriers do it sometimes, but those attempts are utterly insufficient.

Let’s look at a recent international flight — most U.S. airlines give away free upgrades on domestic routes to fill their premium cabins. I picked a United Airlines flight on a route with traditionally heavy demand in Business Class: San Francisco to Sydney. As the above image shows, on June 19, that Boeing 747 left with 18 empty seats in Business Class, including on the upper deck…