The Challenges of Trip Planning; or, How Do We Make This Decision?

A little over a month ago, Patrick Honner, a math teach I follow on Twitter (@MrHonner), wrote a blog post about his Saturday morning trip to the grocery store. He took a simple question, what’s the best way to maximize the one-time 20% discount he’d earned from his local grocery store, and explored it as a constrained optimization problem. (If you want to read more about it, his post is here.)

I was reminded of this post the other day as my wife and I were talking about a part of our upcoming trip that had been challenging to plan. We wanted to go to Yellowstone and Grand Teton National Parks during our trip, but we were having trouble making the timing and logistics work. After talking for a while and getting completely frustrated that we couldn’t resolve the issues, my math brain finally kicked in and I remember to ask the question I always tell my students to ask: what if?

Original Trip

Twenty minutes later, we had decided to ditch these widely-recognized national parks in favor of a different route, one that would allow us to see more, do more, and avoid the conflicts that had been plaguing us earlier. Yes, we were giving up the chance to see two the country’s most famous parks, but what we were getting in return made the sacrifice worth it.

Revised Trip
So what does this have to do with Mr. Honner’s groceries? Like his grocery shopping, our trip planning dilemma fits quite nicely into a useful area of mathematics. Unlike his problem, though, which dealt with mathematics covered in multivariable calculus, our problem’s solution can be found in a far less taught topic: multiple-criteria decision making (MCDM).

MCDM is a sub-discipline of operations research that focuses on making decisions when there are several criteria involved, and is especially valuable when the criteria are in conflict with each other. When we were trying to make a decision about our trip, we were weighing one criteria (our desire to see these parks) against two others (time and flexibility). While I didn’t sit down to quantify these factors, I know that time and flexibility were our biggest priorities, and once we’d identified this it was easy to make the change.

The same ideas can be applied to a variety of decisions that our students have to make. From big questions like the colleges they should apply to, to smaller questions like what they should do with their free time, these decisions can be broken down, quantified, and analyzed. So that’s my big what if question for the day: what if the mathematics of decision making was a part of our new integrated mathematics curriculum?

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