Public-private interests collide in an elevator moment

I just got out of an elevator - one of those "smart" ones in which there are barely any buttons inside the elevator itself. You press the floor number on the outside, and are assigned to one of the elevators.

Two of us got inside this one elevator, one going to the 8th floor, the other 16th. Those two floors were dutifully displayed on the side panel of the elevator. The doors did not close for about 20 seconds. Two ladies came in and then the doors closed.

Immediately one of the latecomers realized she entered the wrong one; presumably she didn't wanted either 8 or 16. There was no button to press so she got off on the 8th floor.

***

I wonder whether the automated operations of these "smart" elevators are beneficial to me or not. To understand that more, one can consider the alternate world. What would have happened if those elevators were the old-school, regular ones?

The other man and I would have entered the elevator and pressed 8 and 16 respectively. Within the next 20 seconds, we would have pressed the "close door" button - or most likely, the doors would have shut after a few seconds, as most elevator doors do.

The two ladies would arrive around the 20-second mark, and they would take a different elevator from the two of us. There might be one available immediately, or they might have had to wait for their turn.

The confused lady would not have had to detour because she would just press the button of the floor she wanted to go to after entering the elevator.

***

This elevator moment brings out the differences between the regular and "smart" operating modes:

• It is possible but not certain (depending on how long the ladies would have had to wait) that the total waiting times of all four of us were shortened by automation
• It is certain that individually, the waiting times did not all decrease due to automation. The other man and I waited longer than in the old world while the two ladies probably would have waited less
• Not quite, because the confused lady certainly ended up with a longer journey time under automation because she could only exit at floor 8 (no buttons), and because she would have to wait again for another elevator ride. So three out of four individuals incurred a cost of automation

***

This type of automation belongs to a class of problems in the operations research field known as scheduling. Given a set of demands (people needing to get to specific floors), a set of supplies with a fixed capacity (elevators), an arrival process (when passengers show up), and a service model (speed of the elevator, time it takes on each stop, etc.), we want to determine the best way to operate the elevator.

But what does it mean by "best"? In most such formulations, "best" is defined as the lowest average waiting time.

"Best" for whom? When we program the operation to minimize the average waiting time, we optimize for the average user. One might think that if it is best for the average, it should be best for the individual user. But that's a fallacy: what is best for the average user is not necessarily best for each individual user. In our example, three of the four individuals end up with longer wait times than in the regular operating mode. 

The opposite fallacy is also true: if we optimize each individual user, the outcome is not necessarily the best solution on average. A New York subway scenario illustrates this: the late-arriving passenger who forces his/her way into the train by obstructing the door is optimizing his/her individual objective but in so doing, imposes an additional delay on everyone else in the train already.

In general, the best private solutions do not need to coincide with the best public solution. User optimization and system optimization may not produce the same outcome.

For another example of this phenomenon, read Chapter 1 of Numbers Rule Your World, on ramp meters. 

 

Comments

[Michael Schettler]

I think we might disagree on what is being optimized for.

My assumption as I was reading was that the algorithm would be optimized for cost/energy expenditures, therefore the fewest trips with no regard for passenger waiting times.

[Kaiser]

MS: Good point. It's more than likely that most businesses are optimizing for their own benefits first before customers'. There's probably some regularizing constraint or multiple objectives because the minimal energy setting would probably involve a higher occupancy rate, which means making passengers wait a lot longer.

[James Kingsbery]

This analysis ignores the people who pressed the "9" "12" and "14" buttons, who didn't have to share an elevator with you as a result.

[Kaiser]

JK: My point is that what is good for individuals may not be good for the average. If optimizing for the average, there will be individual "winners" and "losers." There was one clear winner in the example I gave.