It’s a Wrap

The professors have had a couple of days to sit back and reflect on Math and the Mouse 2026.  In the blog, the students have highlighted all of the fun experiences they’ve had exploring the parks and exploring the math.  In this final blog, the professors want to highlight the academic content of the course to recap what these students have learned and why it is important.

This class is set up to show students how mathematics is used to model real-world decisions.  Our students have the opportunity to apply math to solve problems that Disney professionals face.  In fact, students met with industrial engineers at Disney who talked about working on similar problems to the queuing and scheduling problems that our students were doing.  This connection between class content and job experience is our attempt to show students what they can pursue as careers with the skills they are acquiring at Furman.  In each of the three weeks of the course, we have a project.  The first two projects model three classical problems in Industrial Engineering: the facility location problem, the workforce scheduling problem, and the queuing problem.  Our Mickey Bar problem of having to find where to place a mobile Mickey Bar concession stand is the same problem companies and governments face when trying to find where to locate a new fire station, plant, corporate office, etc.  For the second project, the class was divided to pursue two different projects.  The first was a workforce scheduling problem trying to assign workers to jobs to cover forecasted demand.  Disney solves this problem for thousands of workers each day trying to assign workers to roles in the park throughout the day.  The second is a queuing project which tries to model how a queue in front of an attraction builds throughout the day.  Although we phrase this in terms of attraction lines, it is the same problem that companies face when trying to plan production schedules and forecast the build up of inventory storage in plants and warehouses as production build-up in front of a machine in a manufacturing plant is modeled the same way as people in front of Big Thunder Mountain Railroad. 

The third project in the course is of the students' design.  Here, we seek to foster a sense of (mathematical) wonder about their surroundings.  In each of the four final projects, the students decided the focus of the project, how to collect the data for the project, and with a little help from us, how to analyze the data.  We will describe the projects below.

The first group studied the sequence of ups and downs on the ride Tower of Terror to determine how many unique drop sequences there are, whether those sequences are uniformly-distributed across the four different loading bays, and whether there are differences between the sequences in the two drop shafts that the elevators lead into.  The group consisting of Mara, Della, and Julia determined there were four unique sequences differentiated by the first two moves that the car undertakes (Up/Up, Up/Down, Down/Up, and Down/Down).  They used chi-squared tests to determine that they believed that the sequences indeed uniformly distributed (equally-likely) and that there was not a discernible difference between sequence distributions within each shaft.  They gave a wonderful presentation complete with a dramatic recreation of Tower of Terror ride narration.  

The second group, consisting of Annmarie, Dylan, Cassie, and Tram, studied the loading procedures Disney employs to load parties onto ride vehicles.  In particular, for some rides, Disney separates the line into even-sized parties and odd-sized parties.  They will then fill an entire vehicle with all even-sized parties and the next vehicle with all odd-sized parties.  The students first determined party-size distributions for different rides, that is, the percentage of parties of size one, two, three, etc.  They then used simulation to determine how effective this “even-odd” strategy is as opposed to not separating the parties on the rides Expedition Everest and Seven Dwarfs Mine Train.  On each of these rides, they noticed a reduction of average number of empty seats on the two rides by employing the “even-odd” strategy, from 1.596 to 1.389 on Everest and from 1.633 to 1.536 on Seven Dwarfs.

The third group, consisting of Harrison, Connor, and The Ahn, studied a traditional problem in Operations Research called the Knapsack Problem.  As classically stated, this problem seeks to determine which items to load into a knapsack/suitcase by maximizing the total utility of the items chosen without exceeding the weight/volume constraint of the knapsack.  In our implementation, the group assigned a utility score to each attraction in the Magic Kingdom and sought to determine the optimal number of attractions to experience within four hours in the Magic Kingdom.  They used customer ratings from touringplans.com and average weight times to determine each ride’s utility score.  They then used estimated wait times for the Magic Kingdom to determine the time-to-complete for each attraction.  They used an optimization solver to determine the best set of rides.  They then separated our class into teams of size two or three, and we all tried to solve the problem on paper and then in the park the next day.  Since their problem is complicated by variations in wait time during the day, one team actually found a better solution than the solver solution generated with average wait times.

The final project group of Aidan, Isabella, Ashton, and Luke looked at the song distribution on the class’s favorite ride, Guardians of the Galaxy: Cosmic Rewind.  On this ride, a ride vehicle will play one of six possible songs during the ride experience.  They used a Chi Square test to determine that the song distribution is indeed equally-distributed.  They also determined the expected number of rides that a person would need to take to hear all songs.  On average, a person would need to ride the roller coaster 14.7 times in order to get all songs.  They figured this out empirically using simulation and verified their results theoretically using conditional probability.  This problem is traditionally known as the Coupon Collector’s Problem, and it is the problem collectors face when trying to achieve a set of collectible items where items are achieved at random.   The whole group enjoyed this project as it give us all the opportunity to collect data on a great ride.  

We were very impressed with how each student was able to grasp mathematical concepts in a quick fashion in order to perform the analysis for these projects.  This is actually true for every project during the course.  Given that the course has material from eleven different mathematics courses in our curriculum, there was no student who had seen every concept in the course before coming on the trip.  Most students had only had material out of only one or two of those courses.  So, the ability of our students to be able to perform these types of analyses quickly and present on it within a week speaks to their ability to be adaptive.  It is also a skill that will serve them will in the workforce.

To finish the blog for this Math and the Mouse course, we asked the students to reflect on their experiences by submitting phrases that they thought exemplified the trip.  We’ve compiled these into a Top Ten List.

Top 10 Math and the Mouse Experiences

10. The Food: We had three big meals at the Disney restaurants Roundup Rodeo BBQ, Biergarten, and ‘Ohana.  At Roundup Rodeo BBQ, we got to play as toys in Andy's backyard., even riding in on play horses. At Biergarten, we enjoyed a German buffet complete with red cabbage, potato salad, sauerkraut, sausages, etc.  We even got to see one of the final performances of the lead singer of the German band before he retired (he's been at Biergarten since its opening in the early 1980s)! We ended the trip with ‘Ohana where we enjoyed a Polynesian-style dinner, complete with POG (Passion Fruit, Orange, and Guava juices, a personal favorite of Dr. Hutson).  To add to these delicious meals, we enjoyed daily breakfast tacos and Mickey waffles at the hotel, frequent meals from Firehouse Subs and Pita, and sweet treats such as Mickey Bars, Gideon’s cookies and ice cream from Twistee Treat.  We had a tasty time!

9. Exhaustion: To combat all of the food, we walked a lot, averaging over 14,000 steps per day.  Dr. Hutson walks through the parks quickly, and some students had a hard time keeping up, except on the Traveling Tourist Problem and Knapsack Problem days.  On these days, they had no trouble moving as fast as they needed to win.  The Traveling Tourist problem in the Magic Kingdom was really fun, and the students thought it was a good way to integrate solving a TSP-style problem, but it was exhausting.  Repeating the hustle for the Knapsack Problem added to the struggle, unless you are one of the winners.  Getting in all of the math and all of the mouse is pretty much a 16-hour day every day.  We will all sleep well now that we are back.    

8. The Van Rides: One van had frequent sing-alongs to Disney songs while the other van listened to fantastic music from artists like the Barenaked Ladies, U2, and Aerosmith.  Special shout out to Annmarie for playing music that the old guys would like!  During these rides we always have great conversations about all kinds of things.  These van rides are priceless.  

7. The Hotel Lobby: The hotel lobby/breakfast area served as the location for the professors’ office hours.  All of the groups would work there to have easy access to the professors to ask questions about modeling, probability, Excel, Solver, and Tableau.  With every question we could see the confidence of the students grow.  It was a plus that the lobby had an upbeat playlist and free hot cocoa and coffee, which was needed because it was often cold in the hotel.

6. Presentations: One of the things we try to highlight on Math and the Mouse is the ability to communicate technical results to an audience, and we ask that the students give presentations at the end of each project.  The first project presentation day took over three hours to get through four 15-minute presentations due to many critiques of slides and storytelling issues.  Dr. Bouzarth is a hawk about noticing errors on slides and students quickly became adept at picking out those as well.  Throughout the course, students dramatically improved, and the need to give feedback significantly reduced.  The students gave four fantastic presentations to Disney professionals and many incorporated cumulative feedback into their final presentations.  Every student on this trip has worked hard to improve their presentation skills and it shows!

5. Lots of Work, Lots of Reward: Each project started at a level that was beyond the students’ abilities, but after struggling with it for days, they got each one.  They learned techniques in Excel and Tableau to visualize and analyze the problems we gave them.  Mostly, the students found that they can learn new material quickly and apply mathematics to solve real-world problems.  It was fun to see the smiles on their faces at overcoming those challenges.  For us, hearing Disney professionals comment on the strength of our students’ presentations was a huge reward for us.

4. Data Collection: Data collection is challenging every year, mostly because our students don’t have access to the same data collection devices that Disney professionals do.  Many times our students have to sneakily gather data while waiting in line or riding attractions.  It took seven students deployed to each of Tron and Big Thunder Mountain to gather data for our queuing project.  For final projects, the students had to “suffer” through riding Guardians of the Galaxy: Cosmic Rewind and Tower of Terror multiple times.  For the Tower of Terror rides especially, students “ruined some of the magic” by talking into voice memo recorders during the ride.  This sometimes drew strange looks from other passengers.  On Cosmic Rewind, cast members let us congregate at the unloading zone to gather song data, which was very enlightening.  To get party size distributions, our students often had to get data while listening in line to the stated party sizes gathered by cast members.  The students learned that data collection is not always a glamorous job, but if done well, has huge payoffs.

3. Making new friends and building community: Not many of the students knew each other before the trip, and not many of the students really knew each of the professors.  However, this group came together quickly.  The professors intentionally try to choose activity and project groups to give each student the opportunity to meet and work with every other student.  However, special bonds formed quickly without our need to intervene.  From singalong groups to groups creating new demographics,  students found ways to bond in line playing games, through competition, through shared work responsibilities, or through late night viewing parties of terrible movies.  We love to see this happen every time we run this course! 

2. The Guest Speakers: We had 16 different guest speakers this year, which is a record for us.  Team Disney offered insights into what goes in to making Disney World such a magical place. They also opened the students’ eyes to the mathematics that inform their jobs every day and the possible career paths in their divisions.  The students even discovered that they came up with a project for their final project that Disney Industrial Engineers are also working on.  They even asked for our data.  Getting to talk with three Furman alumni was a huge plus.  Each offered interesting insights into their jobs.  Len Testa, founder and president of Touring Plans, drew rave reviews from our students for being a down-to-earth, knowledgeable, and awesome person.  The fact that he shared so much about how he and his company uses math and computer science to solve problems related to the travel and medical industries was impressive.

1. The Payoff: This one is from the professors’ perspective.  The payoff for the decision to teach decision modeling and data analytics is that the students can complete a difficult workforce scheduling project, control the movement of a Mickey Bar cart to maximize exposure, and model the build up of a queue.  These are projects that industrial engineers at Disney work on in their jobs, and the students can relate more to these careers.  The payoff for critiquing the students’ presentations and getting them to understand how to tell a story with data is that they can deliver fantastic presentation and answer questions from professionals working at Disney about the types of issues that arise in modeling such problems.  The payoff for having them try to design their own time-dependent traveling tourist tours is that they understand the difficulty that Len Testa faces in his company, and they can ask informed questions of him.  Len even remarked about the sophistication of the questions that they asked.  The payoff for teaching statistics and probability is that the students understand how to incorporate uncertainty in their models and understand that best laid plans never work out the way they think they should.  The payoff for making them generate their own project is that they gain confidence that they can perform a park study, analyze their results, and increase their confidence in their own abilities.  

These payoffs are the entire experience for us, and we feel honored to be able to share this experience with the students.  We noted that many of them are looking forward to future Furman math experiences and we are too!  Thanks for a great course!