Once you learn about certain models used in operations research and industrial engineering, you start seeing them everywhere. I see the umbrella problem and its variants everywhere (read about the umbrella problem in this post).
I try to keep a few pens in my laptop bag at all times. These pens will drift in and out of my bag when I work. Every now and then, the pens entirely move out of my bag and I am left without a much needed pen. This happened earlier in March when I was on a trip and had planned to review a paper on my flight.
It has been a very cold winter in Wisconsin. I learned the hard way that it’s useful to keep a spare sweater or two in my office. I often forget to wear them home, and so sweaters and scarves have been accumulating in my office.
The city of Madison tries to be pedestrian friendly. They have these pedestrian flags (see picture below) that are supposed to help you cross the street safely. Each intersection has a bunch of flags in two bins with on either side of the street. I drive by a few of these intersections on the way home, and sometimes I see an intersection where all the flags are in one of the two bins. It always makes me smile.
This isn’t exactly the umbrella problem since the same pedestrian doesn’t go from one side of the street to the other indefinitely as in the umbrella problem, but the umbrella problem only needs to be slightly modified to capture the real problem here and to provide insight into how many flags should be stocked to maintain a certain reliability level.
Look for a few posts about March Madness next week!