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.
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| After our last group dinner at Boma |
Top 10 Math and the Mouse Experiences
To 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 Food
Disney 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.
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| Training for Hollywood Scoops ice cream sandwiches |
Further, Jamie’s one submission for top
experiences was the following picture from Biergarten.
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| 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.
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| Disney World (and rain storms with big puddles) bring out the kid in all of us! |
9. The Magic Kingdom “Traveling Tourist Problem” Race
The 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.
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| The professors take a twirl in the Mad Tea Party tea cups during the Traveling Tourist activity |
8. The Keys to the Kingdom Tour
This 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.
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| Keys to the Kingdom tour |
7. Overcoming Fears
Many 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.
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| Students together on Dinosaur |
6. The Shows
From 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!
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| Wishes fireworks |
5. Finishing the Workforce Scheduling
Project
The 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.
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| The students stop by to say good by to Pecos Bill on their last night in the Magic Kingdom |
4. Animal Kingdom at Night
Our 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.
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| The Tree of Life at night |
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| 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 Speakers
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.
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 Payoff
This 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.
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| Alex explains part of her group's workforce scheduling project |
The payoff for teaching
network modeling and search procedures (including genetic algorithms) is that
they can design their own search algorithms and have a peer-to-peer discussion
with Len Testa.
Len even remarked about
the sophistication of the questions that they asked.
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| Courtney demonstrates a network solution |
The payoff for teaching queuing theory is
that the students can perform a park study, analyze their results, and increase
their confidence in their own abilities.
The payoff for writing a daily blog is to watch the students work together to articulate a day’s events, whether academic, technical,
challenging, unexpected, or proprietary, to a broader audience.
The payoff in meeting with a variety of guest
speakers is watching the lightbulbs go off when students realize that they
discovered a job they didn’t know existed and would love to do.
These payoffs are the entire experience for
us, and we feel honored to be able to give this experience to the
students.
Thanks for a great course!
