The Toilet Paper Problem

During my first year in grad school I came across this paper on "The Toilet Paper Problem" which divides the population into "little choosers" and "big choosers." In trying to find it again to share with all of you, I also came across an essay which is perhaps more useful: "Toilet Paper Algorithms."

Math, answering the important questions in life.

Everything is a trade-off

I recently attended a project management workshop run by an Ann Arbor company (Menlo Innovations). While their company does software development, the techniques we learned are useful pretty much any time you can't do everything you need to, by yourself, in a day. The main takeaway was that by doing any particular thing, you are implicitly choosing not to do other things. Instead, you should try to make those choices explicit.

The tool he gave us for this purpose was to write every possible task on index cards along with estimated time to complete them. The idea is that now you have a physical representation of the trade-offs. You can choose card A which takes one week, or you can choose cards B and C which also add up to one week. He also talked a bit about what our brains are naturally good at:

• Making an initial plan is hard. Poking holes in a plan is easy. Therefore, you should do whatever you can to not work with a blank page.
• If you scale the size of the card to the length of the task (i.e., set your scale as one card = one day of work, so a task that takes half a day you use half a card for), our brains intuitively do the trade-offs.
• Taking away the technology leaves our brains free to just focus on the other aspects. There are definitely advantages to using technology some of the time. But most of the difficulty of project management is these trade-offs, not software giving you a better estimate of how long a particular task will take. Pretty much any estimate will be bad, but some estimates will be useful.

In implementing this approach for my thesis, I am finding that the most critical thing to be working on in the moment is obvious to me. But before I had this system I had no good way to lay out everything left for all of my projects. It would still be nice to have twice as many hours to get everything done, but I am finding a lot of peace in seeing how my current task specifically fits together with the bigger picture.

Comparing alternatives

A few years ago I took a systems engineering course and one of the topics we covered was how to compare different options you might need to choose between. There were two tips that stuck with me, so I thought I would share them here.

1. Compare actual alternatives. When you are considering different options, it is really easy to compare one specific possibility versus the entire world of other possibilities. Do we want pizza for dinner tonight? Well, pizza is cheap and easy, but it isn't exactly healthy, and there are things that are more delicious... But how many things are both healthier and more delicious at the same time as they cost the same amount of money and time? Pizza versus spaghetti however is an actual comparison.
2. Include an evolutionary alternative in addition to revolutionary alternatives. An evolutionary alternative involves doing more or less what you have been doing, but perhaps better. A revolutionary alternative involves a completely new way of accomplishing your goal. The idea being that typically revolutionary ideas will be a lot more costly to implement, and it is easy to get carried away with planning something totally new and lose sight of what you are really trying to accomplish. One example is the repair or replace decision for a car.

Do you have any other tricks for choosing the best alternative?

Next Generation 911

Yesterday the Diane Rhem Show had a piece on the 9-1-1 emergency phone system which itself was motivated by the recent NYT opinion column written by the chairman of the FCC. The basic point in both stories was that our 9-1-1 system is horribly out of date, and it will take a lot of effort and money to get it up to speed.

I have known for a while that cellphones were sort of a problem for 9-1-1 since it is hard to track the location the call is coming from. I had also heard that some areas are upgrading to accept text messages, though it was not until the story yesterday that I learned at least one reason that would be desirable (to silently notify police of an intruder). The thing that I had not considered before is all the benefits we could have if 9-1-1 were fully modernized including pictures and video (send a picture of the intruder, have a paramedic be able to see the injury, probably countless other things).

One of the guests on the Diane Rhem show commented that he expects the number itself to be about the only thing that is still the same five years from now. According to David Furth from the FCC, the US system is still pretty good on a global scale, but we have a lot of work to do if we want the system to perform in the best way possible.

Stupid Users

Fundamentally, humans are error prone. I just came across the "e-counting game" where you ask a class to count the number of letter "e"s in a 400 word document and offer $20 to the first person who shouts out the correct number. The author mentions that if you're ok missing 10-25% of the "e"s, you're fine. But most times we try to have people inspect things we really want the missed number to be a lot closer to zero.

There are many ways people try to reduce the error rate. Standards (righty tighty, lefty loosey) can help some. So can visual instructions (A giant "Pull" sign on a door). But the best tools focus on how the user actually interacts with whatever it is. The Toyota Production System has "Poka-yoke" which asks you to design something that cannot be put together wrong (think of the children's shape sorter boxes). An example of good visual implications is that newer stoves often have the knobs in the same arrangement as the burners themselves.

In short, there are some tasks humans are naturally bad at. And so if you find yourself paying for something online and the website asks you to enter your account number twice, you really should actually type it out each time.

Multi-objective decision making

In optimization we like to provide The Optimal Solution and as an OR person I like to apply the same principles to my daily life. However, any time there are multiple goals, the meaning of The Optimal Solution get fuzzier. Deciding the best nut butter to buy is one example of multi-objective decision making. As a company, we can say that a particular decision is objectively better if it leads to higher profits. But once you have more than one goal (taste and cost in the nut butter example, though you could add others like effort to make your own or nutrition), things get trickier. 

The linked post tries to get at this by having a region of worthwhile choices and a region of not-worthwhile choices. That is more or less what most optimization algorithms do. Generally if you have multiple objectives, you give them all weights and choose the option that maximizes the weighted sum. However, those weights are fundamentally subjective. The Pareto frontier attempts to partially get around this by capturing all possible sets of weights and identifying the set of good solutions. But you still typically have to choose one of those options, which takes us back to a subjective decision.

Making a subjective decision is not a bad thing, and weights are a pretty good way to formalize the subjectivity. But it still helps to recognize that taste and cost aren't truly substitutes for each other.

What causes slowdowns on the interstate?

This week I attended a talk which talked about flow rate and traffic slowdowns. The speaker mentioned that when the number of cars per hour traveling on a highway reached a certain level, we find that sometimes the traffic will be able to happily keep moving at the speed limit, but usually it cannot. I found Figure 1 in this article which shows the phenomenon. A couple other things that can contribute to a traffic slowdown include:

• Drivers needing to make a decision.
• An existing slowdown. In this old link the author experimentally found that he could reduce the amount of backed up traffic by driving slower but at a constant speed.

Avoiding traffic jams is then about ensuring your traffic network has enough capacity, minimizing decision points, and helping recover from a slowdown if it happens.