From the first edition of the Unofficial Guide, minimizing our readers' wait in lines has been a top priority. We know from our research and that of others that theme-park patrons measure overall satisfaction based on the number of attractions they're able to experience during a visit: the more attractions, the better. Thus, we developed and offered our readers field-tested touring plans that allow them to experience as many attractions as possible with the least amount of waiting in line.
Our touring plans have always been based on theme-park traffic flow, attraction capacity, the maximum time a guest is willing to wait (called a "balking constraint"), walking distance between attractions, and waiting-time data collected at specific intervals throughout the day and at various times of year. The plans derived from a combinatorial model (for anyone who cares) that married the well-known assignment problem of linear programming with queuing (waiting-line) theory. The model approximated the most time-efficient sequence in which to visit the attractions of a specific park. After we created a preliminary touring plan from the model, we field-tested it in the park, using a test group (who followed our plan) and a control group (who didn't have our plan and who toured according to their own best judgment).
The two groups were compared, and the results were amazing. On days of heavy attendance, the groups touring without our plans spent an average of three and a half hours more in line and experienced 37% fewer attractions than did those who used our touring plans. Over the years, this research has been recognized by both the travel industry and academe, having been cited by such diverse sources as the New York Times, USA Today, Travel Weekly, Bottom Line, Money, Operations Research Forum, CBS News, Fox News, the BBC, the Travel Channel, and The Dallas Morning News, among others.
John Henry and the Nail-driving Machine
As sophisticated as our model may sound, we recognized that it was cumbersome and slow, and that it didn't approximate the "perfect" touring plan as closely as we desired. Moreover, advances in computer technology and science, specifically in the field of genetic algorithms, demonstrated that it wouldn't be long before a model, or program, was created that would leave ours in the dust.
Do you remember the story of John Henry, the fastest nail driver on the railroad? One day a man appeared with a machine he claimed could drive spikes faster than any man. John Henry challenged the machine to a race, which he won, but which killed him in the process. We felt a bit like John Henry. We were still very good at what we did but knew with absolute certainty that sooner or later we'd have to confront the touring-plan version of a nail-driving machine.
Our response was to build our own nail-driving machine. We teamed up during the mid-1990s with Len Testa, a scientist and programmer who was working in the field of evolutionary algorithms and who, coincidentally, was a theme-park junkie. Marrying our many years of collecting Walt Disney World observations and data to Len's vision and programming expertise, we developed a state-of-the-art program for creating nearly perfect touring plans.
Several university professors, many of them leaders in their fields, have contributed research or ideas to the new software program. Findings from early versions of the software have been published in peer reviewed academic journals. The most recent versions of the program are protected through pending patent applications. Special thanks go to Albert C. Esterline, PhD, of North Carolina A&T State University and Gerry V. Dozier, PhD, of Auburn University. Credit is also due to Nikolaos Sahinidis, PhD, as well as his graduate students at the University of Illinois at Urbana-Champaign, who have contributed a number of exceptionally helpful studies. Chryssi Malandraki, PhD, of United Parcel Service and Robert Dial, PhD, of the Volpe National Transportation System Center have likewise provided assistance and encouragement over the years.
It has been a process of evolution and refinement, but in each year of its development, the new program came closer to beating the results of our long-lived model. In 2002 at field trials during the busy spring-break period, the new program beat the best touring plan generated by the traditional Unofficial model by 90 minutes at the Magic Kingdom. This was in addition to the three hours saved by the earlier model. Getting there, however, wasn't easy.
The Challenge
One factor that makes creating effective touring plans difficult is that there are many ways to see the same attractions. For example, if we want to visit Space Mountain, Pirates of the Caribbean, and Splash Mountain as soon as the Magic Kingdom opens, there are six ways to do so:
- First ride Space Mountain, then Pirates of the Caribbean, then Splash Mountain.
- First ride Space Mountain, then Splash Mountain, then Pirates of the Caribbean.
- First ride Splash Mountain, then Space Mountain, then Pirates of the Caribbean.
- First ride Splash Mountain, then Pirates of the Caribbean, then Space Mountain.
- First ride Pirates of the Caribbean, then Splash Mountain, then Space Mountain.
- First ride Pirates of the Caribbean, then Space Mountain, then Splash Mountain.
Some of these combinations make better touring plans than others. Because the queue for Space Mountain increases rapidly, it's best to ride this particular attraction first thing in the morning. For similar reasons, it would be better to ride Splash Mountain before Pirates. In this example, touring plan number 2 would probably save us the most time standing in line. Touring plan 5 would probably result in the most waiting in line.
As we add attractions to our list, the number of possible touring plans grows rapidly. Adding a fourth attraction would result in 24 possible touring plans, since there are four possible variations for each of the 6 plans listed previously. In general, the number of possible touring plans for n attractions is n * (n - 1) * (n - 2) ... * 1. (Don't let the mathematical notation throw you. If we plug real numbers in, it's quite simple.) For five attractions, as an example, there are 5x4x3x2x1 possible touring plans. If you don't have a calculator handy, that adds up to 120 potential plans. For six attractions, there are 6x5x4x3x2x1, or 720 possible plans. A list of ten attractions has more than 3 million possible plans. The 21 attractions in the Magic Kingdom One-day Touring Plan for Adults have a staggering 51,090,942,171,709,440,000 possible touring plans. That's over 51 billion billion combinations, or roughly six times as many as the estimated number of grains of sand on Earth. Adding in complexities such as FASTPASS, parades, meals, and breaks further increases the combinations.
Scientists have been working on similar problems for years. Companies that deliver packages, for example, plan each driver's route to minimize the distance driven, saving time and fuel. In fact, finding ways to visit many places with minimal effort is such a common problem that it has its own nickname: the traveling-salesman problem.
For more than a small number of attractions, the number of possible touring plans is so large it would take a very long time for even a powerful computer to find the single best plan. A number of proposed techniques give very good, but not necessarily exact, solutions to the traveling-salesman problem in a reasonable amount of time.
The Unofficial Guide Touring Plan program contains two algorithms that allow it to quickly analyze tens of millions of possible plans in a very short time. (An algorithm is to a computer what a recipe is to a chef. Just as a chef takes specific steps to make a cake, a computer takes specific steps to process information. Those steps, when grouped, form an algorithm.) The program can analyze FASTPASS distribution patterns at all attractions, for example, and suggest the best times and attractions to use FASTPASS. The software can also schedule rest breaks throughout the day. If you're going to eat lunch in the park, the software can suggest restaurants near where you'll be at lunchtime that will minimize the time you spend looking for food.
The program, however, is only part of what's needed to create a good touring plan. Good data is also important. For more than six years, we've been collecting data in the theme parks at every conceivable time of year. At each park, researchers recorded the estimated wait at every attraction, show, FASTPASS booth, and restaurant, every 30 minutes, from park opening to closing. On a typical day at the Magic Kingdom, for example, each researcher walked about 18 miles and collected around 500 pieces of data. One of several research routes would start researchers at the Swiss Family Treehouse in Adventureland. After collecting data on all of Adventureland, they would continue to the attractions and restaurants in Frontierland. After that came Liberty Square, then finally half of Fantasyland, before they returned to Swiss Family Treehouse for an eight-minute break before starting the next round of data collection. A platoon of additional volunteers collected data in the other half of the park.
So how good are the new touring plans in the Unofficial Guide? Our computer program typically gets within about 2% of the optimal touring plan and finds an optimal plan for most straightforward situations around 70% of the time. To put this in perspective, if the hypothetical "perfect" Adult One-day Touring Plan took about 10 hours to complete, the Unofficial touring plan would take about 10 hours and 12 minutes. Since it would take about 30 years for a really powerful computer to find that "perfect" plan, the extra 12 minutes is a reasonable trade-off.
In the 2003 edition of this guidebook, we noted the possibility of using our touring-plan software to see all of the 40-plus attractions in the Magic Kingdom in one day. We dubbed this the Ultimate Magic Kingdom Touring Plan and offered it free to anyone up for the challenge. Several people have completed this plan since that time, and many others have come close. The current record-holders are listed in our Ultimate Touring Plan Hall of Fame.
