While there are plenty of suggestions in this topic on how to fix this problem, they only address the effect (zone jumping), and not the cause (unassigned overhead bins). What is needed are overhead bin sections preassigned to each passenger. (A seat for you and a "seat" for your stuff.) If your bag meets the airline size requirements, you are guaranteed a place to stow it. No more rush to be the first onboard.

Since there would be more passengers than bin sections, there would probably have to be a fee associated with it. While this would be a disruptive change to the way fliers have always used overhead bins, it would restore order to an increasingly disorderly process.

Waiting to get ripped on this one.