Michael Cardiff, Gwyneth Hughes, and Bob Bosch
			Oberlin Students Develop Mathematics of Amusement By Robert Bosch
			SEPTEMBER 13, 2000--Michael Cardiff and Gwyneth Hughes spent last year's Fall Break at Walt Disney World, recuperating from strenuous but as-yet unsuccessful efforts to find an interesting final-project topic for my Optimization class (Math 331). Then they hit on it. Less than a year later, Cardiff and Hughes delivered a talk about their final project--"Maximizing Fun at a Theme Park"--to a standing-room-only audience at the 18th International Symposium on Mathematical Programming (ISMP), held in Atlanta. A large theme park like Walt Disney World presents guests with an interesting yet challenging problem: choosing which rides to visit and an order in which to visit them. For their Math 331 final project Cardiff and Hughes modeled the problem as a variation on the traditional Traveling Salesperson Problem (TSP). In the garden-variety TSP, a salesperson located in a base city must visit each of his or her client cities exactly once and then return home. The salesperson's goal is to minimize total distance traveled; the problem is to determine the best order in which to visit the client cities. In Cardiff and Hughes's model, the salesperson is the visitor to the theme park; the base city is the entrance; and the client cities are the rides. Each ride has three pieces of data associated with it: the number of stars the ride was awarded by a guidebook, the average amount of time a visitor must wait to get on the ride, and the amount of time the ride lasts. The visitor need not visit all of the rides. The visitor's goal is to select a subset of rides (and an order in which to visit them) that maximizes fun (measured in terms of total number of stars accumulated) and is subject to a constraint that limits the total amount of time the visitor has for visiting rides and traveling between them. This year's ISMP had more than 1000 attendees, most of them faculty or graduate students from large research universities or scientists from IBM, Lucent, AT&T, and other large companies. Cardiff and Hughes--both from Towson, Maryland, and due to graduate from Oberlin in 2001 with double majors in mathematics and geology--were the only undergraduates at the conference. In the audience for their talk--which was well received, judging from applause, follow-up questions, and subsequent e-mail--was the director of computer science research at IBM's Almaden lab, the winner of this year's Fulkerson Prize for Best Paper in Discrete Mathematics, and the optimization product manager for ILOG (the company that makes the software the Oberlin students used to solve their problem). Cardiff and Hughes will present their work at a Mathematics Department Student-Faculty Lunch tomorrow, September 14, in Wilder 211. The lunch will begin at 12:20; Cardiff and Hughes's presentation will begin at 12:40. The talk--free and open to the public--will be accessible to people who are taking or have taken calculus.
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