Can you solve this problem of effortlessly increasing worker productivity?

Of course. But the increase only works if one person is moved from “B” to “A”. There isn’t any way to improve “B” by sending one of the people from “A” – at their current level of productivity – to “B”.

If we move Person 4 (selling 4 cars a week) from “B” to “A”, then per capita productivity at “A” moves from 2 cars per week to 2.5 cars per week per person, and the per-person productivity at “B” will also increase from 5 to 5.5.

Demote the head of department A to a salesman in Department B and promote the 6 car a week sales person in Department B to head of Department A. That should shake things up nicely.

@CWOTUS – Correct me if I’m wrong, but that leads only to a perceived increase in productivity based on fuzzy math.

Person 6 is still selling 6 cars regardless of whether he does so in Location A or Location B.

The same number of cars are being sold, regardless, at least hypothetically, and for now.

I’d ask what is wrong with Department A’s cars, that customers are flocking to Department B?

@Seek “Person 6 is still selling 6 cars regardless of whether he does so in Location A or Location B.”

Where in the OP do you glean this as happening? My take away is department B has a top selling team because they are in Department B and not in Department A. Department A is under-performing for one reason only and that they are in Department A which tells me Department A is managed by a poorly performing manager and Department B is led by a result oriented manager.

In the OP’s hypothetical, the “average sales per person” can be improved in both locations by moving the least productive person in Dept. B to Dept. A.

I’m agreeing with you that this is fuzzy math and not realistic.

If Dept. A has an inferior product or bad management, then the move of one of Dept B’s members to Dept A is going to hurt both departments in the long run. Sure, your “average sales per person” will rise momentarily, but then Dept. B is left with more sales to be handled by fewer people, and Dept A will be overstaffed and sitting around twiddling their thumbs.

(edit, got letters mixed up)

@Seek I disagree that moving top performer to the under performing dept will hurt both departments. 6 car a week sales guy will sell 6 cars a week no matter where you move her/him or even if she/he crosses over to the competition. Any other sales person on his team will benefit from their tutelage. The under performing manager upon demotion will either wake up and smell the coffee or be let go if they continue to not meet sales goals. As owners of a company these are the necessary shuffling of the deck we have to do to meet sales goals we set and require.

I am facing this very situation at my work where my secretary who is simply in charge of our social media is now generating more sales leads than my Director of Sales who has access to the same technology.

@Cruiser , @CWOTUS mentioned moving the lowest performer of the top-performing department.

@Seek you are correct that it’s only a perceived increase in productivity and not an actual increase – since only a real increase in production (in this case, sales) would lead to a real increase in productivity.

That’s one of the illustrations of Will Rogers’ genius: moving the Oklahoman to California would not actually increase anyone’s real intelligence, but anyone who believes exclusively in these types of statistics would easily be fooled.

@Seek I am not talking about @CWOTUS answer and re-reading your last comment ( I am assuming was directed towards my last comment directed towards yours) there is no reference to @CWOTUS… I am referring to the OP…He did not mention nor suggest moving low performer to top performer department…he asked “Do you see a way of moving a person from one department to the other which will cause average sales per person to increase in both departments?” and thus the crux of my answers.

@CWOTUS You are missing the point and genius of the Will Rogers effect where in this scenario to have Dept A which is under performing and for obvious reasons…they are complacent in their performance which is supported by leaders of Dept A who accept this level of performance. I call it coasting and collecting a paycheck. Dept B is excelling not just because of good leadership (though cruicial to their overall performance) but because of the desire of the sales team to not only sell more cars but because of individual drive, motivation and desire to make more money. Again a high performer will always perform above expectations no matter where you put them because they have learned the ways to success from their leaders and their hard work discipline which then can thusly inspire those on their team. Shuffling the deck is smart management and so is discarding the cards you see you don’t need. IMO why our country is struggling because we now support mediocrity instead of championing success.

A to B, B to A, Obi Wan, Charlie fuckin Chan…bolllocks to that carry on.
Fire the slackers, it’s the only sound way

Close both departments. We don’t need any more fucking cars on the roads. They pollute. They consume energy and resources. They produce negative externalities. They are contributing to anthropogenic global warming.

And fuck sales people too. Do something that contributes intellectually and culturally to the world—or do nothing at all. Fucking parasites. And don’t even get me started on the “heads of the departments”—managers are some of the worst.

And to answer the OP. You move the 4 sales per week person from department B to A. Now deparment B will average 5.5 sales per person per week, and deparment A will average 2.5 sales per person per week. And then close them down.

@CWOTUS got it right.

@Seek, I was hoping my use of the word “effortlessly” hinted at a kind of sleight of hand. Nothing substantive has been accomplished, but it is counter-intuitive, to me at least, that the averages of both departments can be increased by simply moving a person from one to the other.

Here is a nice Wikipedia article on the subject. If you are not interested in the math, skip down to the section titled “Stage migration”, which shows how improved detection of a disease leads to a perceived increase in the lifespan for both people with the disease and also for those who don’t have it.

I might move an employee to try to figure out what’s going on. Why is there such a difference? The chances of all three people in one department being more productive than another department is very unlikely. I would think it has to do with the supervisor, or the shift, or something besides just the employees themselves.

What if you were the manager of Department A? Would you suggest to the manager of Department B that an employee be moved so that you could both report productivity gains?

I’m going to revise my answer. I would interview all the employees and managers and try to figure out what the hell is going on.