Magical Keys, Brain Power Sprees, and Burnt Cookies

 DISCLAIMER: Due to the confidential nature of many of today’s events, this blog post has been censored, and confidential information has been redacted.

Day 11 of our Math and the Mouse trip started out bright and early as the group headed to Magic Kingdom for our Keys to the Kingdom Tour! We spent the morning walking around the park and backstage areas, led by our wonderful tour guide, Melissa. She was so enthusiastic in sharing the keys to the kingdom, which are *redacted* , *redacted* , *redacted* , *redacted*, and *redacted*. While backstage, she told us all about *redacted* things like *redacted* Disney *redacted* secrets! We loved learning about *redacted* how *redacted* Cast members *redacted* do *redacted* their *redacted* job and uphold the magic of Disney.

After the tour, our exhausted group made our way back to the hotel for a lunch break before getting back to work on our projects! Here, each group finished up the data-modeling grunt work of their projects and began transitioning into presentation and visualization mode. All of us were already burnt out from Excel, even in our short time using it, which made our next stage of the day particularly interesting.

We were then greeted by our second wave of guest speakers, Molly and Ross. Molly is a Furman and Math and the Mouse alum who is now working as a Merchandise Supply Chain Analyst for Disney! In this role, Molly focuses on reporting and analytics, inventory analysis, cost analysis, and labor and expansion. She shared with us about her team’s work in creating a tool to combine and organize past and present data, helping the Disney team determine how much new labor they will need for new shops and lands, and spearheading the initiative to add discrete digital signage to Disney merchandise scores. Additionally, Molly’s husband Ross works as a Shipboard Pricing Manager at Disney Cruise Line. In this role, he prices virtually everything on a Disney Cruise from specialty drinks to massages, excluding the initial room price and any merchandise on board.

After getting the chance to ask insightful questions and meet with our second guest speakers, we were able to brainstorm ideas for final projects. This was already done individually a couple of days ago, but we collaborated and put them all on the giant whiteboard within our classroom. These ideas ranged from the most optimal bench in epcot to minimize time in the sun throughout the day to whether the songs within Guardians of the Galaxy: Cosmic Rewind truly have the same probability, and whether the song played affects the overall ride enjoyment.

To finish out the day, our group headed in different directions. Della, Mara, and the professors headed to Hollywood Studios while the rest of the group enjoyed relaxing at the hotel, slow dinners, time at the pool, “family game night” featuring Brain Freeze, Mafia, and burnt stovetop cookies.

This blog post was written by Ashton Holt and Mara Johnson!

Trying to Decide: A Post from the Profs

A primary focus of the Math and the Mouse May Experience is the mathematics of decision-making.  Students learn how to mathematically model decision-making processes, and they learn about the ways people find optimal solutions to those models.  In three weeks, we can only scratch the surface of these models and methods, but we have future classes in the Mathematics Department for the students to explore these concepts in more depth.  Over the past week we have asked the students to model two decision problems.  The first was the Mickey Bar Problem in which our students decided where to move mobile concession stands around the Magic Kingdom throughout the day to achieve the most crowd exposure.  All of the student groups did a great job of solving this problem and presenting their work to the class. 

The second decision problem is something we call the Traveling Tourist Problem, which is a version of the better-known Traveling Salesman Problem (TSP).  In this problem a salesperson has some number of sites to visit during a day and wants to know the fastest route to visit all of the necessary locations and return home.  This is an easy problem to state but an extremely difficult problem to solve in practice.  Companies like UPS, FedEx, Amazon, and pretty much all other logistics companies try to solve this problem on a daily basis when routing their trucks to pick up and deliver packages.  The problem also shows up in a variety of other fields from crew scheduling in the airline industry to pattern cutting in the upholstery industry.  Touring Plans is a company that solves this problem for Disney patrons.  When planning a vacation to Walt Disney World, vacationers can visit touringplans.com, enter the attractions they want to see during the day (including breaks and meals), and Touring Plans will provide them with a tour for their visit.  

The Magic Kingdom Traveling Tourist Problem is a staple of our course, and it exemplifies the type of hands-on, engaged learning that May Experience courses are known for.  The problem asks our students to find the ordering of following 12 attractions/experiences that would minimize the total time it takes to complete the attractions when things like wait time, ride time, and walk time are taken into consideration.  

1. Space Mountain
2. Buzz Lightyear's Space Ranger Spin
3. Seven Dwarfs Mine Train
4. Dumbo the Flying Elephant
5. Under the Sea – Journey of the Little Mermaid
6. Peter Pan’s Flight
7. “it’s a small world”
8. The Haunted Mansion
9. Big Thunder Mountain Railroad
10. Tiana’s Bayou Adventure
11. Pirates of the Caribbean
12. Jungle Cruise

Sunday night, before the Monday competition, we divided the students into four teams of size three and four.  We gave each group a park map, a list of ride durations, walking times between each pair of attractions, and projected wait times, all supplied by Touring Plans.  Each group was tasked to work together to design a tour of the 12 experiences and write down their thought process in creating the tour.  Then, on Monday, the four student groups and the group of professors raced to see which group could finish the attractions first.  Further, if a group deviated from their original plan during the Monday race, they were to describe their thought process in choosing to deviate.  As an added benefit, on Tuesday of this week, we met with Len Testa, founder and president of Touring Plans, who talked about how his company solves this problem for vacationers.

What makes this problem hard to solve is the combinatorial explosion of possible solutions.  In arranging/ordering the 12 experiences for their day, there are 12! = 479,001,600 possible orderings of these attractions.  So, the students have no hope of verifying how close their solutions are to being optimal, but that’s okay.  We want them to discover that the same thought processes that they come up with to produce and augment their solutions are similar to the thought processes that mathematicians have used for decades to produce good, but maybe not optimal, solutions to this problem.  (We should point out that the TTP is actually harder to solve than the historic TSP problem because the time that one waits at an attraction depends on the time one visits the attraction since many attraction wait times vary throughout the day.)  

These are some of the thought processes that students used in making their plans:

1. Minimize walking distance.  
2. Minimize time waiting in lines.
3. Take advantage of rides whose wait time is below the average wait time for that ride. This was the strategy of the first-place team.
4. Finish the highly popular rides (Seven Dwarfs, Space Mountain, Jungle Cruise, Peter Pan) first then ride the less popular rides.
5. Tackle rides that are in a geographically similar portion of the park together before moving to another geographic area.
6. Be opportunistic in changing their original plan by moving big rides up in their order if they see a wait time at that ride below a certain threshold.

The first two strategies employ an algorithmic approach to solving the problem known as the Nearest Neighbor Algorithm.  This approach attempts to create a tour by picking a starting ride and then going to the next ride based on some metric, such as the ride within the shortest walking distance or the ride that has the minimum wait time at that point in time.  The third approach, choosing a ride whose deviation from average is most advantageous, is the subject of a paper, “A Comparison of Algorithms for Finding an Efficient Theme Park Tour” appearing in the Journal of Applied Mathematics, that the professors wrote with Len Testa and two previous Math and the Mouse students in 2018.  So, it was really cool for us that our students recreated our published idea!  It turns out that the winning team, comprised of Cassie, The Ahn, Harrison, and Della, used this strategy in forming their initial tour.  

The first-place team (L to R): Della, Cassie, The Anh, and Harrison

Incidentally, after the race we entered the list of attractions into the Touring Plans Optimizer to see what they suggested was the optimal route to take on Monday.  It came back with

1. Jungle Cruise
2. Pirates of the Caribbean
3. Tiana’s Bayou Adventure
4. Big Thunder Mountain Railroad
5. Under the Sea - Journey of the Little Mermaid
6. Seven Dwarfs Mine Train
7. The Haunted Mansion
8. "it’s a small world"
9. Peter Pan’s Flight
10. Space Mountain
11. Buzz Lightyear’s Space Ranger Spin
12. Dumbo the Flying Elephant

This plan projected the finish time to be around 3:30pm.  Our group’s first place team finished at that time exactly (with a slightly modified tour).  Amazingly, each team, except the professors, actually started at Jungle Cruise.  In fact, one team’s plan was the same as the above plan from Touring Plans in the first three attractions to visit, and they came up with this without access to www.touringplans.com. 

In the graph below we outline the path that the first-place team took.  The dots are color-coded by time of day.  The lighter dots are earlier in the day, and the darker dots are later in the day.  The team completed the tour in the following order: 

1. Jungle Cruise
2. Big Thunder Mountain Railroad
3. Tiana’s Bayou Adventure
4. Seven Dwarfs Mine Train
5. Peter Pan's Flight
6. The Haunted Mansion
7. Under the Sea - Journey of the Little Mermaid
8. Dumbo the Flying Elephant
9. Space Mountain
10. Buzz Lightyear's Space Ranger Spin
11. "it’s a small world"
12. Pirates of the Caribbean 

Their tour is only a couple of small permutations away from the Touring Plans tour, showing that with the proper data, analysis, and sparks of inspiration, our students can do hard things! 

Winning team's tour

Since the strategy of the winning team was to try and visit a ride when it offered a bargain compared to the average wait time, the following chart shows the wait time comparison between teams for each ride.  The horizontal line for each ride is the average wait time that our teams waited for that ride throughout the day.  The star represents how long the winning team waited for each ride.  For the winning team, they waited less than average for eight of the twelve rides, slightly above average for two rides, and more above average for two rides.  This shows that everyone is going to have to wait for some ride during the day, but minimizing the number of times that happens is important if you don’t want to spend your entire day waiting in line.  Unfortunately for them, their longest wait was for Dumbo, a ride that they probably wouldn’t have even ridden if we hadn’t made them.  In contrast, the second-place team only had six rides where they had a below average wait time.  That group was on the lower end of walking distances of all groups which allowed them to “catch up.”

Wait times for each team by attraction. Horizontal lines indicate average wait time of the five groups for each attraction and the stars indicate the first-place team's wait times.

For the fourth-place finishers, the professors, we will try again next time to win our first TTP, but it is rewarding for us to see our students discover mathematics for themselves in a fun way.  What the students discovered in all of this will be important for them to remember as they carry on in school and in their future careers.  First, sometimes data is unreliable, such as the posted wait time on the attraction, and you have to be able to adapt to variation (such as encountering an unforeseen wait or an attraction because it was running at half capacity).  Making decisions under uncertainty is difficult but is something that every manager has to do, and the students are learning that the deterministic problems that they see in textbooks only partially reflect what happens in the real world.  Lastly, working collaboratively in teams, they produced their own algorithms to solve this problem, but at the same time, they reproduced some of the great ideas that great mathematicians have had before them.  We hope they recognize the significance of that and that they build confidence in their own abilities!   

Day 10: Project Craze and Ride Delays

This morning  the group was able to make a choice. You could either wake up early and rope drop the new Millenium Falcon ride at Hollywood Studios or you could choose to sleep in and have the morning to yourself at the hotel. 8 of us made the choice to head over to Star Wars land and see the new ride. Lots of other Disney fans had the same idea as us so the line was already long before the park even opened. Luckily we were able to hustle in when the rope dropped and head over to the ride. While we were waiting in line we were able to see a cast member, The Mandalorian, and his cute but powerful friend, Grogu.

The new movie Star Wars: The Mandalorian and Grogu came out last night so this ride was rethemed to match that movie. We had two groups fly the ship and I think it’s safe to say, we made it out successfully (with only a few life threatening crashes). After that ride we chose to ride the other Star Wars ride, Rise of the Resistance. This line however was very long so we chose to all enter the line as single riders and we were able to get on the ride in half the time. After a fun morning at Hollywood Studios, we headed back to the hotel for some project work.

For project two in this class, we were split into 4 groups. 2 groups were assigned project 2A and two groups were assigned project 2B. In project 2A the students are tasked to figure out Work Scheduling for a restaurant in Disney. In the first part the workers work 8 hour shifts and will have a one hour break either early or later in the day. Based on how busy this restaurant is at different times there is a required amount of people that have to be working, so our goal is to minimize the amount of total people working throughout the day. This task was much more complicated and complex compared to the examples that we had done previously in class. Then to make the problem even harder we are allowed to give the workers an hour break any time throughout the day, meaning that we can be more efficient in minimizing the total amount of workers for the day, but makes the problem much more complex. Project 2B focuses on the queueing data we collected at Magic Kingdom earlier this week. The groups with this project were tasked with creating a simulation for what the first 2 hours of Magic Kingdom would look like for Big Thunder Mountain's and Tron’s waiting queue. We had to use our data taken over 30 minutes, to simulate the next 90 minutes for the following data points: Number of people entering the line per minute, number of people exiting the line per minute, number of people on each ride, and the time that occurs in between each ride. After using the randomization feature on excel to find data points for each of these categories for the first 2 hours of the day, we then have to see what the wait time would be throughout those two hours. After each group worked on their project for several hours, we called it a night and stopped working for the day.

After finishing working on the projects for the day, we were told that we would be going to Animal Kingdom in the evening, though it was already 4:30pm and the park closed at 6:00pm. The professors then changed their plans to go to Epcot, and to get back at the hotel at 9:30pm. Though because of the very early morning the next day, almost everyone decided to stay at the hotel. Though the students decided that if they could go to Epcot to just ride Guardian of the Galaxy, they would be willing to go do that. A group of 7 decided to go on the quick trip to Epcot, while the others stayed to get dinner at 5 guys and relax.

While waiting in the long line for Disney the group of 7 played fun games with each other while the professors went to get food. The estimated wait time was around an hour, though tragedy would strike when the group was inches from the preshow room. The ride shut down. Though we didn’t notice the announcement at first we found the lack of movement strange until we realized what was happening. We stuck it out for 2 hours, before giving up. This was extremely disappointing for us and we were all very sad.

After meeting up with the professors under the Epcot ball we expressed our disappointment, but not all hope was lost. Dr. Harris used his sweet-talking skills with the Disney Visitor Experience people to get all 7 of us fast passes for the next time that we ride Guardians of the Galaxy. This helped to raise the mood and we went back to the hotel to get enough sleep before for our Keys to the Kingdom tour tomorrow. 

Today's blog was written by Connor Lockett and Dylan Daniels!

Day 9: From Markov Chains to Roller Coaster Screams

Time flies so fast that we are already on the first day of week two for this Math and the Mouse trip! On the math side of things, we learned about Markov chains, Monte Carlo simulations and began our work on project two. As for the mouse, we got early annual pass access to a newly themed ride. So, fasten your seatbelts and follow us as we transition back and forth between class and Hollywood Studios! 

Rock with us!

When we walked into class at 9:00 this morning, we were surprised with green MatM pins from the professors! Once everyone got one, we began class with a lesson from Dr. Harris about Markov chains. With a realistic example using playing cards, it is really interesting to see the difference between deterministic and stochastic problems in math. He then created a decision tree showing the probabilities of certain outcomes with playing cards. Using this information, we discovered that if we ran the same simulation with playing cards over and over again, the probability of ending in a certain state converged to a certain probability. Following up with that, Dr. Hutson showed us a real-world application of Markov chains, which are queues at Disney! Imagine you are at Disney World; have you ever wondered how the cast members estimate the posted waiting time? Behind that number is a complex mathematical model using Markov chains with several different variables that affect the wait time.

After nearly two hours of learning new material, we got on the vans and headed to Hollywood Studios. After being closed for two years, today was the very first day that annual passholders got early access to ride the newly-branded Rock n Rollercoaster starring the Muppets! It is the only roller coaster that goes upside-down at Disney World, which was really thrilling and well worth the trip to Hollywood Studios.

Rock 'n' Roller Coaster, starring Math and the Mouse

Shifting gears back to the classroom, we all got on the vans, drove back to the hotel, and got a 30-minute break before having the second class of the day. At 1:15, Dr. Bouzarth introduced us to the Monte Carlo simulation, revisiting our first project, the Mickey Bar mobile stand, as an example. To forecast the profit from the Mickey Bar stands, we had to take several variables into account, such as labor costs, material costs, demand, and the fixed cost, which changes with every Mickey Bar produced and sold. It would be much easier to predict the cart’s total profit if these variables were constant with every Mickey Bar sold. However, in the real world (including at Disney), this is not the case, as these variables change greatly with every Mickey Bar sold from the stands. From there, Dr. Bouzarth showed us how to construct a mathematical model in Excel, demonstrating the relationship between the input variables (material cost, labor cost, etc.) and the output profit. These are the kinds of models that some of the class will create in Project 2B. Then, we got to visualize the data by creating bar graphs in Tableau. To get more accustomed to what we have been learning for the past two days, we split into our Project 2A and 2B groups to brainstorm how we are going to apply our new knowledge to build several models for our upcoming presentation.

Mara, Tram, Aidan, and Annmarie's group

Della, Luke, and Cassie's group

Harrison, Julia, Ashton, and Dylan's group

Connor, The Anh, and Isabella's group

Transitioning one more time between the math and the mouse, we departed the hotel at 3:45 for Hollywood Studios after several hard-working hours. We had Lightning Lane passes to the first ride of the afternoon, Toy Story Mania, which we all rode a few days prior. It was much more competitive between our group since most people knew about the tricks and secrets to score higher. After Toy Story Mania, we rode Slinky Dog Dash and Tower of Terror (again). Since we had all ridden it several times at this point, we decided to all make straight, emotionless faces for the picture on the Tower of Terror. We think it came out great!

1..2..3 Drop time!!

Next, we made our way to Mickey and Minnie’s Runaway Railway, which was our last ride as a group before we broke off into smaller groups. Every group had dinner right after the Runaway Railway; then, one big group went off to explore Galaxy’s Edge while the other group went back to Toy Story Land to ride the Alien Swirling Saucers ride. After a couple of hours of exploring the park on our own, the groups met back up at the entrance of the park at closing time. From there, most of us made a run to Target to get some groceries while the rest of the group went straight back to the hotel to catch up on some much-needed sleep.

We are super excited for yet another action-packed day tomorrow! A group of us will be rope-dropping Hollywood Studios to check out the newly-themed Smuggler’s Run ride, temporarily themed for the new Mandalorian movie releasing tomorrow! Additionally, we will have some more time to work on our projects, as well as an outing to Animal Kingdom in the afternoon. Stay tuned for tomorrow’s blog to see how our day goes!

For those who made it to the end, thanks so much for following along on our journey today!

Today's blog is brought to you by Tram Le and Aidan Barnard!

Day 8: Disney Springs and Getting Ready for New Things

It has officially been one week since we arrived in Orlando, time really has flown by! We hope you have been enjoying following our journey thus far! After wrapping up the first project of the trip yesterday, we were rewarded by being able to sleep in after 3 consecutive days of rope dropping, with class starting at 9:30 am. 

Today in class we learned more about resource allocation modeling and assignment/ transshipment modeling. In the section on resource allocation, we learned that when there is a supply of raw materials that are needed in order to manufacture a product, mathematicians use a model to accurately maximize the potential profit. And the section on assignment and transshipment basically uses a similar model except that the raw materials and products are not a physical item, but instead are assignments to imaginary things, like pairing groups together. 

Afterwards, we were able to do practice problems in small groups to gain experience for our next upcoming project. While working diligently in our separate groups, Dr. Harris accidentally stepped on Annmarie's claw clip during class and, despite her reassurance that it did not matter nor did she care, he insisted on buying her a replacement at some point on this trip so she plans to keep her eyes peeled!

At around noon we got a break for lunch before the majority of the group headed to an optional trip to Disney Springs!

For those who chose to go to Disney Springs, we had around 2 hours to look and shop around. Out of all the cool stores, restaurants, and attractions, our favorite places include the World of Disney store, the Lego store, and Gideons(a delicious cookie place). Additionally, those who stayed at the hotel got to take naps, do laundry, and relax by the pool after a long week of hard work! 

When we arrived at Epcot, the professors told us to head towards Morocco in the World Showcase and go all the way down the Moroccan street for a surprise. As we walked down the empty street we were met with a secret passage exclusively for Disney Annual Passholders! As we made our way through the passage, we discovered a lounge room filled with comfortable cushioned seating and yummy snacks. Here we were introduced to Project 2. For this project we will be divided into 2 sections, those who will work in Project 2A and those who will work in Project 2B. Those in 2A will solve the problem of scheduling Disney Cast Members with the most efficient schedule and breaks, and those working in Project 2B will be modeling a queue simulation for either Big Thunder Mountain and TRON. 

After our brief break and talk about Project 2, the professors let us run free in Epcot for the rest of the night! Everyone went to explore the World Showcase, which features eleven different countries, each with their own attractions, restaurants, cultural shops, and more. While we all split up into groups, rode different rides, and ate dinner at separate places, we all ended our night at Epcot on a crowd favorite ride, Guardians of the Galaxy. 

Fun fact: Guardians of the Galaxy has 6 different song options that are randomly chosen for each ride. So there are 6 different variations of the ride. For the many times Dr. Hutson has ridden this ride, he has listened to every song that is played on this ride except for Everybody Wants to Rule the World by Tears for Fears, five out of six of the songs played on this ride. However, today, against all odds, he rode Guardians and the song started playing! But that’s not even the best part, not only did he get to hear the song the first time he rode Guardians of the Galaxy today, but also the second time when we all rode together! He was 2/2 for the day! Feeling on top of the world, he can now finally say he has heard all six songs that are played on this ride.

 

Today's blog was written by Julia Torres and Annmarie Henderson!

Day 7: No Rollercoaster Quite Like Group Presentations (But We Rode Those Too!)

We started the day strong and early by rope dropping Epcot to meet Len Testa, the owner of TouringPlans.com, for our first guest speaker. During the talk, we learned a lot about his background, his company, and the story behind its creation. I was especially surprised by how Len transformed a common vacation problem -long wait times at Disney parks - into the topic of his master’s thesis and eventually an entire company built around solving it. By collecting large amounts of data and applying computer science and mathematics, his team is able to predict ride and restaurant wait times, estimate crowd levels, and create personalized touring plans for different demographics and guest needs. It was really interesting to see how math and technology can be used in such a practical way to improve the guest experience at Disney parks.

The 2026 Cohort with Len Testa!

When the talk was over, smaller groups split up to get lunch, ride attractions, and walk around the world showcase. This month at Epcot is the Flower and Garden Festival; all around the park, there are different kiosks and food stations with yummy, unique spring foods from all over the world. Right before we left, we realized that Soarin’ across America was open for previews for annual passholders, which is us! Soarin’ across America is a special program replacing the normal Soarin’ across the World for a limited time, celebrating America’s 250th birthday. It was such an amazing experience to walk onto Soarin’ and be among the first to see the new program. Patrick Warburton of The Emperor’s New Groove fame, who filmed the original pre-show safety announcement for Soarin’ across the World, filmed a new segment to be included in the program. 

The Anh's group in Japan (Epcot's version!)

Della's group on Guardians of the Galaxy: Cosmic Rewind

The group on Soarin' across America

After a short break in the hotel to freshen up, we got right to class! Continuing with topics we were introduced to during our first day in Orlando about states and decisions, we learned how to turn decision-making into a linear mathematical model to achieve a goal. The example we used in class was determining how Disney decided how many Buzz Lightyear and Woody toys to make. This technique is also really useful in solving larger optimization problems where companies, like Disney, want to maximize their profits with resource constraints. 

After our class period, we got started on our FIRST round of presentations! As the professors have told us, one of the biggest improvements students see from this experience is in their presentation skills: good becomes great. So, after about twenty minutes to run through everything one last time, each team presented their work to the rest of the group. Although we all know the premise of the project, we presented our work as if we were standing in front of Disney executives (no pressure, right?), and the rest of the group gave feedback so that whenever someone outside of our group does get to see our work, they can understand everything. Everyone was a little nervous, but all of the presentations went well! Everyone got valuable feedback, ranging from small structural changes to the color of the data points on graphs. Each group had unique strengths and insights, so it was interesting, even after having worked on basically the same project, to see everyone’s different perspectives. 

Dylan, Cassie, and Aidan

Luke, Mara, Harrison, and Isabella

The Anh, Ashton, and Annmarie

Tram, Della, Connor, and Julia

With our first project presentation came our first big group dinner! After some time to recharge, we headed over to Hollywood Studios and ate dinner together at Roundup Rodeo BBQ. This restaurant is in Toy Story Land, so when we walked in, we were all toys! Every now and then, someone yelled “Andy’s Coming!” so we all had to freeze! The food was amazing and the company was better. A group of us even rode in on stick horses. Everyone was laughing by the end of dinner!

Aidan, Ashton, and The Anh riding stick horses

Since the park didn’t close until 10pm, we had time to ride Rise of the Resistance (it was our first time, and such an immersive experience) and Tower of Terror (again), but we had to RUN across the park in 5 minutes to make it before closing! We managed today to have an elevator full of just Furman! Once we got off the ride, we realized that Fantasia still had one more showing at 10:30pm, so a little over half of us stayed to see the performance. Overall, our day was packed, but it was such a magical day!

Signing off, 

The Anh and Della! :)