[This is one of a series of posts that explore real world examples of mathematical modeling to help educators better understand its applications. This is not intended to be a context for a student lesson. To learn about Spies and Analysts, I recommend watching this webinar (with elementary, middle, and high school versions) or reading this blog post.]

We now live in a world where ride sharing services like Uber and Lyft are considered commonplace. You just open the app on your mobile device, request a vehicle to pick you up, get in, and you’re on your way. If you’ve used such a service a few times, you’ve also probably noticed that the same trip might cost significantly different prices, depending on when you use it. So, how does a ride sharing service like Uber know how much to charge you? This really matters because if they charge too much, you might use a competitor, a taxi, or public transportation. If they charge too little, they may not make enough money to stay in business.

So, what if you worked for Uber and they asked you to create a formula to competitively price their trips? Where would you begin? What information would you want to know? What would you do with that data once you had access to it? These are the topics I’m exploring in my spies and analysts post. I want to walk you through the process so that you can better appreciate the complexities of mathematical modeling.

The first part of the process requires the spies. So, I want you to stop and take thirty seconds to think about what information you would use to competitively price customers’ trips. Would you look at how far the driver has to go? Does traffic matter? Does the driver’s experience level matter? Should fancier cars cost more? Should it cost more if you have more passengers? Should it cost less when demand is low and more when demand is high? Does the city you’re in matter? As I hope you realize, the list of questions could go on and on. So, think about what information you’d pick if this was your job. Once you’ve determined what information you’d want, keep reading.

Spies
Uber considers a variety of factors when determining your fare including:

• Time the trip takes
• Distance the trip takes
• Tolls and fees
• Whether there are enough drivers in the area to meet demand
• Whether you are sharing a ride with other passengers you don’t know
• The vehicle’s luxury level

So, much of what I imagined them using was included, but the reality is that we are still far from a dollar amount to charge. How do you take all those factors and turn them into a formula that pumps out a competitive price?
This is where the analysts come in. Their job is to take the data, figure out what parts are more or less important, and break it down in such a way that it becomes useful. Take 30 more seconds to think about how you might even begin to work with the data.

Analysts
Turning this into a formula is not easy. If it is was, then everyone would be on their way to having a company valued at over \$72 billion, like Uber is. So, here’s what Uber does to calculate their fares:

Your Uber fare is first calculated on 4 main criteria:

• Base fare – A flat fee charged at the beginning of every ride
• Cost per minute – How much you are charged for each minute you are inside the ride
• Cost per mile – How much you are charged for each mile of the ride
• Booking Fee – A flat fee to cover Uber’s operating costs

Here’s how Uber uses the 4 main criteria above to calculate your fare:

Base Fare + (Cost per minute * time in ride) + (Cost per mile * ride distance) + Booking Fee = Your Fare

From there it gets a little more complicated. First, comes the issue of driver supply and demand. If there are more people requesting rides than there are drivers to supply them, Uber uses something called “Surge Pricing” which will multiply the cost of your trip by a multiplier. For example, when a sporting event ends and everyone wants a ride at the same time, your fare might be multiplied by 2 or 3. While this might seem like price gouging, it is also a huge incentive for drivers from distant areas to come to your area and pick you up.

Then come many other factors that get added in like tolls and fees, how luxurious the vehicle you request is, whether you’re sharing a ride with strangers, and the city you’re traveling in.

Conclusion
I’m hoping that at this point, you have a better appreciation for the complexities of mathematical modeling. Once the spies and analysts are done acquiring the information and putting it together, they still have to determine whether the formula (or mathematical model) they come up with is any good. For example, if people open your app to check for the price but don’t actually take a ride, it could be sign that your mathematical model is not doing its job. Can you imagine the never-ending refinement that a model like this must require?

At this point, there are no computers or calculators that can figure this out on their own. This is where the jobs are at. If we truly want to focus our time and energy in a skill that will really help our students become college and career ready, mathematical modeling is where we need to be.

1. Melissa says:

I love these.

• Robert Kaplinsky says:

Thanks Melissa.

2. Leslie Salinas says:

I think this would be a great task for a Pre-Algebra, Algebra or even an Advanced 7th grade math class. Having small groups work together and then try to “sell” their model to the teacher or a groups of “consumers” in the class. 🙂 Thanks for the launch!

3. Michelle C says:

I’m going to use this for order of operations with my 5th graders as a three act task. Thanks for the great idea!