Wrapping Up

Our last full day at Disney started early for some of us on Tuesday.  A group of seven went to Hollywood Studios for a final couple of rides on the Tower of Terror.  They had a fun time and bid farewell to one of the group’s favorite rides.

The entire class met after lunch in what has become our classroom away from Furman --- Room 440 (a.k.a. Dr. Harris and Dr. Hutson’s common room).  Groups of three each gave presentations on the projects on which they have been working.  Each group had prepared a poster (digital for now, but to be printed back at Furman) containing a description of the project and the findings.  The first two groups spoke about throughput and single rider lines (topics discussed in the previous two blog posts).  The final two groups discussed the third major project of the class.

Making the Rounds

As you may have read on the blog over the last few weeks, the students have been involved in a project that relates to the mathematically well-known Traveling Salesman Problem.  This problem concerns the discovery of shortest routes in a network of locations, and it is known to be very difficult to solve on a large scale.  The students developed networks that modeled the attractions at Epcot’s Future World and in the Magic Kingdom.  Using data collected by hand (and foot!) and from special distance-measuring iPad apps, the students determined all appropriate distances they needed to model these places.  A small group of students generated an algorithm that worked to find strategic routes through these parks.  The algorithm involved distances between attractions, average wait time for the attractions, and the ride times themselves.

Showing Your Work

The poster presentations were very well done.  Everyone was involved at some level with every project, and so each person was able to contribute to the content of the presentations.  The students will present these posters again as part of Furman Engaged (a day celebrating student research) in the spring of 2015.

After the poster portion of the meeting, the students spent some time discussing possible t-shirt ideas for our class.  They were excited about getting a t-shirt to commemorate what has been a great experience for them --- educationally, intellectually, personally, and socially.

The Final Evening

For dinner, the group went to Boma, a well-known restaurant in the Animal Kingdom Lodge.  This was a buffet style feast of food from Africa, and we enjoyed it so much we wished we could be carried out afterwards (some called this a Boma Coma).

After dinner, the group gathered by the pool and presented Dr. Bouzarth with a surprise “Golden Mickey” award --- recognizing the fact that the wonderful experience we all have had (students and faculty alike) would not have been possible without her foresight, inspiration, and dedication to making it all happen.

We finished off the evening by one last trip to the Magic Kingdom --- a fitting way to end the trip as this was where the trip began three weeks ago.  We stayed until the midnight closing and enjoyed being with one another as we experienced the magic that makes up Walt Disney World.

Signing Off

We hope you have enjoyed reading our blog posts over the past three weeks.  If you have read all of them or just one or two of them, we appreciate knowing that others have been interested in what we have been doing. 

There are many people and groups who have made this experience possible.  We appreciate the support of Furman, the Office of Study Away, and the Mathematics Department.  Most of all, we want to end our posts by thanking the families of all of the participants whose contributions of many types made this the wonderful experience that it was.

As they say around here, we’ll see ya real soon!

Heigh Ho, Heigh Ho...

Hello again! Hannah and Kelly here to tell you about the gems we experienced on Wednesday, May 28th.

It's Off to Work We Go

After a morning working away at various projects, we traveled over to meet with four different departments at Team Disney, where many major Disney offices are held.  While there, we met with representatives from the Workforce Management, Industrial Engineering, Design and Engineering, and Decision Sciences departments.

The Show Continues Even At Team Disney

Each of these departments use different mathematical models to accomplish their goals, from scheduling cast members in Workforce Management to designing attractions in Design and Engineering.  Every department plays a vital role in creating the Disney experience, and we throughly enjoyed getting a glimpse into that process.  The students on this trip have many varying backgrounds, but all got to see math at work in business world.

I, Hannah, as a recent Furman Mathematics graduate heading into a graduate program in Operations Research, thoroughly enjoyed getting to see and hear different applications of Operations Research outside of an academic setting.  It was a great experience to see how models and optimization play a big role in Disney's operations, and to see things that I love to do in a professional and industry setting.  In addition, it was intriguing to see how many different branches and types of mathematics and science weave together to make creative solutions.

For me, Kelly, a rising junior Mathematics-Economics major, this trip has opened my eyes and raised my interest to opportunities for math majors that I didn’t really know existed. Being able to see applied mathematics in many areas around Disney Parks has made me both more excited for more upper level mathematics classes and made me realize there are a lot of opportunities for post-graduate life that I didn’t know were available.

Overall, we had a great experience and are grateful that we got a unique chance to see some of the behind the scenes work that goes on at Walt Disney World.

Whistle While You Work...Or Play

Even though none of us were grumpy after the long meeting at Team Disney, we were certainly not bashful in our excitement in getting to ride the Seven Dwarfs Mine Train on its opening day. We dragged the docs headlong across the park in order to utilize our coveted FastPasses for the attraction.

While on the Mine Train, guests are placed into swinging mine carts and whisked around and through the gem mine.  Riders can see all seven of the dwarfs busy at work mining gems and whistling.  It was a happy romp through a beloved classic, and quite possibly the smoothest ride in the Magic Kingdom.  Don't be dopey, it is worth the wait!

Before anyone could be sneezy, we split up for some more fun in the Magic Kingdom.  Groups rode classic attractions like Space Mountain and Jungle Cruise, while some enjoyed the Carousel of Progress and the Enchanted Tiki Room. We ended the night some delicious Dole Whip before everyone became sleepy.

We look forward to a great big beautiful tomorrow at the Animal Kingdom (though the birds don't sing words and the flowers don't croon).

Prices, Pirates, and Pooh

Annie and Jordan are back for one final time to convey the events of Tuesday, May 27, which happens to be our classmate, Jamey McDowell’s, birthday! Though we’re not at Furman, the university tradition of throwing a friend in the lake, or “laking” as we call it, at midnight on his birthday had to be upheld. Unfortunately, we don’t have a lake at our hotel (and the pool was locked) so we had to use our unlimited supply of brain power (thanks, Ellen…) and improvise. To make a long story short, Jamey ended up with three buckets of water oh-so-lovingly dumped on his head from a balcony a few stories higher. Happy birthday, Jamey!

Magic Kingdom

We spent the morning at Magic Kingdom working on two projects: our Magic Kingdom network project and our FastPass+ analysis side project. Regarding the big network project, the satellite images we found online were inadequate due to the new construction in Fantasyland. As a result, we each walked several “edges” today to and from certain waypoints and attractions to measure travel times in order to complete our data gathering. This will be entered into the algorithm that our Algorithm Team created to finish our outline of a complete tour of the Magic Kingdom with the shortest possible walking distances. Ideally, we’ll soon be able to take wait times into consideration to better optimize the tour! Our goal in the FastPass+ analysis is to determine how Disney’s implementation of their new FastPass+ system affected the standby wait times of two popular attractions: Winnie the Pooh and Pirates of the Caribbean. We collected this data throughout the morning by waiting in these two lines several times and measuring the amount of time we spent waiting for each. We’ll compare this data to wait time information from years past (before FastPass+ was implemented) to determine if there has been a statistically significant change in wait times.

Theme Parks and Resorts Pricing

This afternoon, we had the chance to meet with our first Disney representative. We left the familiar, highly decorated theme parks to travel to a large, much plainer office building, where a lot of “backstage” magic happens. There, we had the opportunity to meet with a cast member who works in Theme Parks and Resorts Pricing. During our meeting, we learned a lot about the extensive process of creating and adjusting prices for Disney’s products. Above all, we learned how much deep thought and consideration goes into a decision to adjust prices. Disney relies on an overwhelming amount of data including current economic trends, crowd levels, customer satisfaction, and overall demand. The pricing team carefully analyzes this data in consultation with numerous other entities within the Walt Disney Corporation to make an informed decision about pricing that benefits both the company and the customers. We really enjoyed our meeting with the representative from the Pricing Department and found all the factors that influence Disney prices very interesting!

'Ohana

To top off our busy day, the group ventured to Disney’s Polynesian Resort for dinner at the Hawaiian-themed ‘Ohana. We arrived early, so we had some time to explore the resort before dinner, including taking in the lake vistas during sunset.  Here's some of the group with the Grand Floridian Resort in the background.

The restaurant's motto is "'Ohana means family and we're all cousins here, so sit back, relax, eat, and enjoy time with family" (or something to that effect).  Our waiters told us to simply sit back and eat the mountains of food they brought us (it's family style, so you can ask for second helpings of anything you'd like), but what’s a Hawaiian dinner without some hula dancing? With that mindset, a group of us students took a break during the meal to take a mini hula lesson in the middle of the restaurant. Finally, after an overwhelmingly filling dinner, we watched the Magic Kingdom Wishes fireworks show from a new perspective, a dock at the Polynesian (across the lake from Magic Kingdom). We’re looking forward to a marathon day tomorrow of progressing on our projects as well as meeting with four more Disney representatives!

Sing-a-Long in the Mathmobile

We had a pretty relaxing day today here at Disney.  We had free time in the morning and early afternoon, and several of us spent time working on the big class project of creating an optimal tour of attractions in the Magic Kingdom.  We are working in three teams to complete the project.  

Beginning to create our  network of the Magic Kingdom

Team Waypoint is tasked with determining which nodes (attractions) and edges (walking paths) will be present in the network model of the Magic Kingdom.  They are also determining ‘waypoints,’ which are locations in the park that link attractions.  The use of waypoints allows us to measure the distance from an attraction to the nearest waypoint, and then use the distance between waypoints to determine the distance between attractions.  In this map of our network, you can see the nodes in yellow and the waypoints in pink.  This method prevents us from having to measure the distance from each attraction to every other attraction.

Team Map My Run is working on measuring the distances between attractions and waypoints.  They are using the iPhone app Map My Run to measure distances along sidewalks between attractions and waypoints.  The app’s website has satellite images that allow us the team to calculate distances without having to walk them.

Team Algorithm is working on writing a computer program to calculate an optimal tour through the Magic Kingdom.  The program will take the list of attractions and distances created by Team Waypoint and Team Map My Run as input.  The program will use a genetic algorithm to create an optimal a tour through the Magic Kingdom than minimizes walking distance.  Genetic algorithms are modeled after evolutionary processes, and involve mutating tours and replacing longer tours with ‘more fit’ shorter tours.  We hope to later extend the algorithm to minimize the time spent waiting in line.  However this complicates the problem significantly, since these wait times change throughout the day.

This afternoon we collectively voted to visit Hollywood Studios to experience Disney's "Star Wars Weekend" and to grab another ride what many would argue are the best two rides in all of Walt Disney World. (Tower of Terror and Rock 'n Roller Coaster of course!) It has been very hot here in Orlando, so a later start and a few showers this afternoon and evening greatly helped with the heat. We split up, hitting some highlights including the delicious ice cream shop outside of Tower of Terror and the Toy Story Pizza Palace Arcade. 

The whole group reconvened to watch Fantasmic, a dazzling light show featuring our favorite Disney characters adventuring through the world of Mickey's dreams. Although we got a little wet from the showers, it was a fun conclusion to our day. On the drive back we mustered up enough energy for a dance party and sing-a-long in the mathmobile. Moving from pop to classics to Italian opera to Disney ("Let it Go" of course), Dr. Bouzarth was a trooper to drive the van which was quite literally rocking and maybe even sing along!

Stella and Kate

Furman Engaged!

Today was a very unique experience for us all.  Disney had a 24 Hour party where Magic Kingdom was open from 6AM Friday to 5:59AM Saturday.  A few of us decided to be brave and get there right as the park opened.  We departed from the hotel at approximately 4:15 AM! Those of us who ventured to the park at opening had a very clear goal in mind -- meet Anna and Elsa from Disney's Frozen.  You're probably wondering why a bunch of college students had the urge to meet Disney Princesses at the crack of dawn.  Turns out, the average wait time to meet these two characters is 300 minutes (that's 5 hours)! In fact, there are so many people trying to get to this meet-and-greet when the park opens that all cast members have to line up with a rope every morning and walk people into the park.  Lucky for us, we were at the front of the Furman Frozen Family Fun Five K.

After our adventure to meet the two most popular princesses, we wanted to take advantage of the sunrise over the castle and found a Disney photographer to capture this moment for us.  Well, the photographer saw the Happy Birthday button Jamey was wearing in anticipation of his birthday and decided to have a little fun.  He had Jamey close his eyes and Annie kneel down and... well, I think this picture will explain the rest (and the title of this post):

The day was going so well and we were having a blast!  But it was only 6:50 and we, for the first time ever, didn't know what to go do.  As I'm sure you can guess, that didn't take long to change as we saw the Seven Dwarfs Train was open.  This is a brand new ride that wasn't supposed to open until May 28th.  Today was the first time they were letting people (besides cast members) ride this, and we got to ride it! 

As we were walking to the renovated Carousel of Progress, we happened upon the kugel ball. It was cool to play with this because we just talked about how this works in our physics lessons.  Basically, even though the stone ball weighs a lot, we are able to easily push it around because of the film of water underneath it which reduces the friction.  Without this water, it's practically impossible for even eight full grown adults to budge the kugel.

Around this time, half of the group decided not to brave the huge crowds and heat and needed to recover while others were just venturing out to Hollywood Studios.  It just so happens that this weekend was part of Star Wars weekend and some of us had the opportunity to meet Luke Skywalker!

After all of the excitement during the day, the unique adventure began as we entered Magic Kingdom after hours.  

There were many parades going on throughout the night including the Villains parade to introduce the new Disney Movie Maleficent. One of the favorite parades was the Electric Parade. Here we are waiting for the 12:45am parade.  

We conquered the three Mountains (Splash, Space, and Big Thunder) all after 1am and danced away to Dance Parties with Chip and Dale and Minnie Mouse.

Today was certainly a unique experience as we beat the crowds and partied away at the 24 Hour Party; class tomorrow is gonna be a struggle.

The Keys to a Mathemagical Adventure

Selfie by our tour guide with another cast member

Hayden and Rahul are back to give you the most recent updates from our mathemagical adventures. 

The Mouse

 

This morning we got to go “backstage” in Magic Kingdom on the Keys to the Kingdom tour given to us by our hilarious tour guide Megan. This signature Disney tour goes behind the magic of Disney World, explaining some of the little known history and secrets of the happiest place on earth. And lucky you, we’re going to share some of these “secrets” with you. One of the coolest parts of the tour was getting to explore part of the Utilidor; that’s right, the Magic Kingdom really does have secret underground tunnels! The Utilidor is the real ground level to the Magic Kingdom that is used by staff and cast members to help maintain the four keys to the Kingdom- safety, courtesy, show, and efficiency. Cast members and characters can use the Utilidor to travel across the park without being seen out of costume or in the wrong “land.” Maintenance use the corridors to quickly transport any require tools or equipment, and Reedy Creek Emergency Services (Disney has to provide their own emergency services due to its size and spread across two counties) can use the tunnels to quickly access guests in need without dealing with crowds above. Part of the Utilidor is also used to vacuum trash collected above into a tunnel that sucks the over 80,000 pounds of trash produced each day to backstage trash compactors.

Students take picture on tour

We also learned interesting new facts about some of the more visible “upstairs” Disney secrets. As you walk down Main Street, you may have noticed some of the writing on the stores’ upstairs windows; this is what Disney World considers its “credits.” When you first walk in and look above the Confectionery, you see Roy Disney’s name. Roy, Walt’s brother and partner, helped start Disney World, taking care of most of the business’s finances. Walt in on the other end of Main Street, above the Ice Cream Parlor since he had a nightly bowl of ice cream. We also learned about the cues they use to transition between the different lands, such as changes in the sidewalk color and texture, different music, changes in decorations, and some less obvious and more symbolic details. For example in Liberty Square, the light-colored stone path throughout this section of the park, symbolizes towns before plumbing where waste was thrown into the street. Each branch of the stone path leads to a bathroom, all of which are technically outside of Liberty Square and in the next land. This is just one of the many details that helps to make the “show” by bringing guests back to pre-twentieth century United States. Overall the tour was an incredible experience, that exposed the hard work and detailed ingenuity needed to create such a magical destination.

The Math
 

The tour was far from the end of our day. We had lunch at the park and then returned to our hotel. After a quick 20 minute break, we were back at work. We had previously been split up into groups and assigned to read mathematical papers and present on the mathematical models they described. These papers related to various problems faced at amusement parks like Disney: optimizing hotel reservations, golf tours and crowd flow.  These were peer reviewed papers published in respected journals, not aimed at undergraduate students. Mirroring last week, we, Hayden and Rahul, had contrasting yet similar experiences here. I, Hayden, am a rising sophomore Chemistry major, so before this I’ve had almost no experience reading mathematics journals. However, each of our groups included students with a wide range of experience with this type of work. Students like Rahul were able to explain some of the math notation and terminology that was new to me, so ultimately, I was able to fully understand the paper I had read. I, Rahul, am a rising senior Mathematics major, and have done Mathematical research both of my previous summers at Furman and have as a result have read a number of mathematical papers. However, reading a mathematics paper on an unfamiliar topic is always challenging, no matter your background, it took time and effort before I had any idea how the model worked. At the presentations today, it was clear that all three groups had put in a good deal of work and displayed a full understanding of the situations being modeled as well as the mathematics behind it: objective function being optimized, the variables and the constraints.

Planning locations of Waypoints

Now that we had shown that we had a solid grasp of how mathematical modeling worked, we finally began what we hope will be our primary project for the remainder of the course. We are going to create our own model for optimizing tours of Disney World. Like with any other project, the key is to start small. The first step is to gather data about a small segment of the park. We will use our data gathered from the Epcot Challenge last Friday as a starting point. We plan to gather more information tomorrow while visiting the park and will combine this with data scraped from the internet. Rather than trying to calculate travel time between every single attraction at the park, we created a set of “waypoints” on the map of Epcot which will form the nodes of our graph. We will only need to know the travel times to the central node. Other travel times can be computed with this data using, for example, Dijkstra's Algorithm. Another advantage of using such a system with waypoints is that it is easily expandable, thus making for a robust model.

The Fun
 

About half the group chose to stay at the hotel this evening, but the rest of us decided to venture back into Disney, this time to Hollywood Studios. This was mostly just for fun, although we did try to test out a few theories we had developed about wait times, with some success. We finished up the night watching the fantastic Fantasmic! show, featuring everything from fireworks and lights to costumed actors and animations projected onto sheets of water. As we left the park, we noticed cast members closing the gates to Tower of Terror and Rock ‘n’ Roller Coaster. Just this morning, Megan had described Disney’s closing process of checking one attraction at a time and moving toward the main exit from there, and she assured us there was no way to hide out over night with this thorough shutdown plan. Dr. Harris, however, seemed to have taken this as a challenge and was working on an algorithm or two to solve this particular problem as we walked out.

Be Our Guest: A Day with TouringPlans

TouringPlans is a company that specializes in providing information to Walt Disney World visitors.  Their website touringplans.com is the number one online Disney community in the world.  Their guidebook, The Unofficial Guide to Walt Disney World, is one of the bestselling travel books in the world, with over four million copies sold.  TouringPlans also produces an app called Disney World Lines from TouringPlans.com.  This app provides both posted attraction wait times and actual attraction wait times.  The app also allows users to create an optimal tour through any of the four parks, choosing which attractions to visit.  The app will order the attractions to minimize the time spent walking and waiting in line.  It allows users to further customize their plan with breaks, pace and other preference settings.  Walt Disney World Lines is the highest rated Disney World app including My Disney Experience, the official Walt Disney World app.

Our "classroom" for the day.

Today we had the incredible opportunity to meet with three scientists from TouringPlans.  Len Testa is the president of TouringPlans and the co-author of several guidebooks, including The Unofficial Guide to Walt Disney World.  Len Testa was also accompanied by two statisticians from TouringPlans, Fred Hazelton and Steve Bloom.  They led us through the Magic Kingdom to the upstairs of Liberty Tree Tavern, where they talked to us about using math and science to optimize visits to Disney.  While we were sitting in the Tavern, a man eating nearby with his family noticed the company T-Shirts the TouringPlans representatives were wearing and said “Are you guys with TouringPlans?  You guys do a great job!”  At this point the group realized what an incredible opportunity we had indeed!

Len Testa is a computer scientist and talked to us about the algorithms used to created optimal touring plans.  Creating a touring plan is a version of the Time Dependent Traveling Salesman Problem (TDTSP), which we had previously studied in our learning modules.  TouringPlans’ version of the TDTSP seeks to find the shortest path connecting a group of attractions in which each is visited only once.  The time necessary to visit each attraction changes throughout the day.  The TDTSP is in a class of problems which take an exponentially long time to solve with a guarantee of optimality.  Len Testa explained some of the heuristics his algorithm uses to produce near optimal solutions in the short period of time permitted by the computer and mobile apps (generally about 15 seconds). Fred Hazelton explained how Touring Plans uses statistics to produce accurate estimations of wait times. We were surprised to learn that Disney often posts higher wait times than are actually expected in order to dissuade guests from different rides at different times of day.  TouringPlans uses data and regression analysis to provide more realistic wait time predictions.  TouringPlans also provides its users with an estimation of how crowded each park will be on each day of the year.  Steve Bloom explained how TouringPlans uses statistics to determine how many different variables influence crowd levels.

After the presentations, Len Testa and his friends surprised us by treating us to lunch with Beauty and the Beast at the new Be Our Guest restaurant.  The restaurant is inside the Beauty and the Beast Castle.  With the delicious food and the interesting company, a great time was had by all. 

Our "Grey Stuff" cupcake:
"Try the grey stuff; it's delicious!
Don't believe us? Ask the dishes!"

We concluded our afternoon with free time in the Magic Kingdom, with a new found suspicion of Disney’s posted wait times.  Learning more about Disney today got us all even more excited for our Keys to the Kingdom Tour tomorrow, but we have a feeling our new friends from TouringPlans were able to tell us more than any cast member could reveal.

Kate and Stella

First Day - Mathemagical

Daily Posts

As we begin our adventures, different students will be giving daily updates on our activities. We, Hayden and Rahul, will be kicking off this with a report from our first day!

Departure

We met bright and early in the morning at 5:45 AM, and after packing our suitcases into the back of the vans left around 6 AM. After some much needed naps by most of the students, the professors kept us entertained as we traveled down 95. Our conversations ranged from high school sweethearts to guessing television shows from their theme songs. With a few pit stops, including lunch at Subway, we arrived in about 10 hours at our hotel. Once we checked in, we did some grocery shopping at a nearby Publix and ate a quick dinner in our rooms, eager to get to the park!

Magic Kingdom

We started with the oldest and most iconic park at Disney World, Magic Kingdom. In true Disney fashion, we made sure to get our first group photo in front of Cinderella's Castle.

We made it to several different rides before the park closed, visiting Pirates of the Caribbean, Splash Mountain, Space Mountain, and Buzz Lightyear Space Ranger. Along the way we even spotted our first Hidden Mickey. A Hidden Mickey, for those unfamiliar with the term, is a silhouette of Mickey Mouse's head hidden within a Disney attraction. One point of interest was comparing our experiences to each other, based on our history with Disney.

I, Hayden, have been to Disney three times before, so I already had a few favorite rides. One of my favorite attractions is Space Mountain; it's one of the first rides I want to do when I get to Disney. I was really excited when I learned we had FastPasses for Space Mountain on our first day! Even though I knew what to expect, by riding with a couple of students who had never been to Disney before I was reminded of the incomparable excitement that comes from your first time on the ride.

I, Rahul, had never been to Disney before, so I spent most of my time following around more experienced Disney visitors like Hayden. The only reason I rode on Space Mountain was because we had a FastPass for it and because Hayden was so excited about it she nearly walked my legs off getting there in time. However, when the lights went out and we were hurtling around at high speeds in the dark, I was having as much fun as any Disney pro!

We ended the night with the Wishes Firework Show. The show incorporated many of Disney's classic movies, but also included more recent ones such as Frozen and Wreck-It Ralph. While today's visit to the park was only for entertainment, learning starts tomorrow. We already feel like the trip if flying by and we wish that we could stay here all summer.