Toilet Paper Operations Research
2023.01.28
I still remember my first encounter with Operations Research, OR, when I was a part of Fuji Xerox’s planning department. Back then, I was assigned to study OR under the section chief.
The section chief was well-versed in OR, and I learned many things from him. The first story that he told me to teach me about OR was about toilet paper:
Users should not be inconvenienced by running out of toilet paper in public restrooms, offices, and hotels, he explained. For this reason, most toilet paper holders have a spare roll of toilet paper attached to the dispenser.
However, if two rolls are installed in a way that makes either accessible, users will use whichever roll they prefer, and thus the extra roll is meaningless since both rolls will run out.
At what point should the rolls be switched out to prevent the situation of having no toilet paper? It is uneconomical to replace them when there are still enough rolls left- yet, there is nothing worse than having no toilet paper left because both rolls run out.
How can restroom upkeepers ensure that users don’t run out of toilet paper, but simultaneously replenish the rolls in the most economical and effective way possible?
My confident (and simple) answer at the time was to leave one roll in its wrapper so that the user will finish the unwrapped roll before opening the spare, wrapped one. Once the restroom upkeeper sees that the wrapped role is now unwrapped, they can simply add another wrapped roll to the stall.
The section chief shut down my answer right away. He explained that in practice, many people decide to take home the full roll of toilet paper when it is wrapped!!!
The correct answer that my section chief gave me was to make a special toilet paper holder that only dispensed the new roll after the first roll is used entirely.
Since this interaction with my then-section chief, toilet paper holders often cross my mind.
Now that I think about it, I saw two types of toilet paper holders at the World Economic Forum Annual Meeting in Davos this year.
Anyway……
