We’ve had a couple of days to sit back and reflect on Math and the Mouse 2016. We, the professors, agree that this class was fantastic, and we are so appreciative of the efforts of these students. The class is designed to help students explore the ways mathematics is used to not only model real-world problems but also ways in which it is used to produce solutions. Further, we want to foster in the students an inquisitive nature and sense of wonder associated with how they view the world. This was on display in their final projects. In each of the 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. Every group decided to take on a question related to the length of time spent waiting in queues, and we will describe these projects below.
The group consisting of Alex, Courtney, McKenna, and Johanna particularly enjoyed visiting characters during the May X. Alex alone visited at least 17 characters over the three-week time period. This group decided to investigate queues for characters for their project. In particular, they wanted to investigate the lines for characters who had visible queues, such as Peter Pan and Tigger, to determine how long a guest would expect to wait. Their analysis showed that there is a statistically significant difference in times characters spend with patrons who want 0, 1, and 2 or more autographs. They found that on average characters spend 45 seconds with groups who want no autographs, 60 seconds with groups that want one autograph, and 80 seconds with groups that want two or more autographs. Further, they estimated the percentage of patrons who want 0, 1, and 2 or more autographs and came up with an equation that would estimate the wait time in line based on the number of family groups waiting in front of you.
The group consisting of Alyssa, Jamie, Zack, and Caroline were some of our most ardent fans of roller coasters, and they decided to investigate how long they would expect to wait in a special queue, called a single rider line, given a fixed number of guests in front of them. In order to help with efficiency, Disney offers passengers who are willing to ride solo and fill in empty seats on rollercoaster trains the opportunity to wait in a single rider line instead of the regular standby queue. The only three rides that have single rider lines available at Disney are on Rock ’n’ Roller Coaster, Expedition Everest, and Test Track. The group decided that Test Track offered some particular challenges that precluded it from examination given the limited amount of time that they had. So, they analyzed the single rider queues on the other two rides. The time it takes to make it on to the ride depends on the distribution of even and odd party sizes that come through the standby line. Their analysis showed that patrons should expect to wait 19 seconds per person in front of them on Rock ’n’ Roller Coaster and 14.5 seconds per person on Expedition Everest. They also determined that the distribution of even and odd party sizes was not different on the two rides so that the difference in wait time can be attributed solely to increased throughput capacity on Expedition Everest, whose trains have 10 more seats than those on Rock 'n' Rollercoaster.
The group consisting of Maria, Lindsay, Molly, and Mary Lib were curious about the benefit of getting a FastPass for certain rides. Disney offers guests a limited number of special queue privileges during a park visit. These privileges allow a patron to enter a special FastPass queue that bypasses most of the standby line and merges with the standby queue very near the front of the line. The FastPass dictates an hour-long time window for the patron to return to the ride to obtain the privilege. Further, a Disney operator controls the merge of the standby and Fast Pass lines so that preference is given to the FastPass line. This group quickly determined, based on the speed at which FastPass guests exit the ride as compared to the standby line, that FastPasses always gave the patron an advantage and are worth obtaining. They then changed their focus to determine when patrons show up to redeem their FastPasses so as to determine when might be the optimal time to redeem the opportunity to enter the FastPass queue. They broke hours down into ten minute intervals and looked at how many people show up when the time ends in a 0, 1, 2, 3, …, 9. They found that FastPasses are mostly redeemed at times when the last minute digits are 0, 4, and 9. They concluded that since FastPass time windows start on the ‘0’ or the ‘5’ and Disney often allows patrons into the line slightly before that time window starts, that people show up and enter the Fast Pass line right before their Fast Pass time. So, to avoid waiting in longer FastPass lines, one would want to be slightly ahead of the groups showing up when the minute digits were 0, 4, and 9.
The growth that each of these groups showed during the course of gathering data and analyzing the data was amazing. We were impressed with all of their progress. To celebrate the successful final projects, we went to Boma at the Animal Kingdom Lodge for one last delicious group dinner before heading to the Magic Kingdom to end the trip where it began.
|After our last group dinner at Boma|
Top 10 Math and the Mouse ExperiencesTo finish the blog for this Math and the Mouse course, we asked the students to submit their top experiences from the course. We’ve compiled these into a Math and the Mouse Top Ten List.
10. The FoodDisney offers a variety of tasty alternatives, and so many of them stand out. Most impressively was the fact that many of the students trained for and actually finished enormous ice cream cookie sandwiches from Hollywood Scoops.
|Training for Hollywood Scoops ice cream sandwiches|
Further, Jamie’s one submission for top experiences was the following picture from Biergarten.
|The highlight of Jamie's trip|
This was a night full of delicious German food, chicken dances, and a reminder that we’re all kids at heart as we (professors included) happily splashed our way through gigantic puddles and pouring rain when heading to the van after dinner.
|Disney World (and rain storms with big puddles) bring out the kid in all of us!|
9. The Magic Kingdom “Traveling Tourist Problem” RaceThe Magic Kingdom race was really fun, and the students thought it was a good way to integrate solving a Traveling Salesman Problem while still having a fun day in the parks. Even though we didn’t win, we agree.
|The professors take a twirl in the Mad Tea Party tea cups during the Traveling Tourist activity|
8. The Keys to the Kingdom TourThis tour explores the behind-the-scenes activities at the Magic Kingdom and integrates the history of Disney into the narrative. Most students love to go into the “tunnels” underground. Further, the biggest takeaway from the tour was that the students won’t ever forget who Walt Disney’s brother is or what he did. Who was that man? Roy Disney.
|Keys to the Kingdom tour|
7. Overcoming FearsMany rides at Disney can be daunting, but one ride stood out as being particularly ferocious in the eyes of many students. That ride was Dinosaur (pronounced Dino-SAAAAARRR). It actually took several rides before some students would open their eyes on the ride. On one particular ride on this attraction, the professors thought it would be a good idea for the students to ride in one, 12-person car in order to get a group picture. As luck with have it, the ride broke down right as the group was entering a particularly scary part of the ride. We’ll let you judge for yourself what the reaction was based on the picture below.
|Students together on Dinosaur|
6. The ShowsFrom Fantasmic to the Festival of the Lion King, Disney offers first-rate show experiences. We all marvel at the technical choreography that goes into these performances. Many students attended the same show multiple times to take it all in (and probably to sing along). There is even a rumor that some students learned the choreography to Fantasmic and put on a “Mathmasmic” show. Fireworks shows were also a group favorite; Wishes in the Magic Kingdom (both viewed in traditional viewing spots as well as while riding Big Thunder Mountain Railroad), Illuminations in Epcot, and Symphony of the Stars fireworks set to music from Star Wars were regularly enjoyed by all!
5. Finishing the Workforce Scheduling ProjectThe students were able to successfully model the scheduling of employees to cover the workload for the Pecos Bill Inn & Café using data that was crafted by a Disney professional to resemble the type of data that Disney deals with each day. The task required groups to create over 250 constraints each in order to successfully model the scenario, and some students dubbed the problem ‘The Beast.’ It was beyond their abilities, but after struggling with it for four days, they got it. It was fun to see the smiles on their faces at overcoming that challenge (taming the beast). This project also gave a glimpse into the creativity required to develop mathematical models; all three groups were solving variations on the same theme, but the strategies employed when building constraints were all fairly different.
|The students stop by to say good by to Pecos Bill on their last night in the Magic Kingdom|
4. Animal Kingdom at NightOur course happened to overlap with the very first time that Animal Kingdom would be open at night. It was a totally different experience at night and some of the rides took on a different dimension, particularly Expedition Everest, which seems much faster at night and gives better views of the yeti at the end. Students (and professors) were averaging 7-10 rides on Everest during the nighttime hours.
|The Tree of Life at night|
|Everest peering behind the show area for the Jungle Book nighttime show|
3. The Genetic Algorithm Project
This project seems to have been the class favorite. Some students indicated that they were doubtful of the accuracy of the method at first because it relied heavily on randomness to generate solutions, but after trying out the mutations and crossovers the created, they found it cool to see how their population of solutions was actually getting better and better. It is fun to see how a simple idea borrowed from nature can be so effective at solving hard problems.
2. The Guest SpeakersTeam 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. Len Testa, founder and president of Touring Plans, drew rave reviews from our students for being a down-to-earth, knowledgeable, and all-other-positive-adjective 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 industry was impressive. Students appreciated the Furman connections to Disney as well!
1. The PayoffThis one is from the professors’ perspective. The payoff for the decision to teach modeling is that the students can complete a difficult workforce scheduling project and talk intelligently with professionals working in Disney Workforce Management about the types of issues that arise in modeling such problems.
|Alex explains part of her group's workforce scheduling project|
|Courtney demonstrates a network solution|