Mathematical Contest in Modeling 2007: A Judge’s Perspective
June 12, 20075 r6 Q5 R5 I' d7 i# S3 W6 @
Longtime SIAM MCM judge James Case, after a weekend in
Between February 8 and February 12, 2007, 949 teams from 12 countries participated in the 23rd annual Mathematical Contest in Modeling. Three hundred fifty-one of the three-person teams elected to work on the "continuous" problem A, and 598 chose the "discrete" problem B. A total of 14 papers were judged "outstanding": five for problem A (two from the University of Washington, and one each from Harvard, MIT, and Duke) and nine for problem B (two from Duke, and one each from Truman State University, Kirksville, Missouri; Stellenbosch University, South Africa; Singapore National University; Peking University; the University of Puget Sound; the National University of Defense Technology, China; and Slippery Rock University, Slippery Rock, Pennsylvania).
The authors of two of the outstanding papers were named the SIAM winners: the team from MIT for problem A (see "MIT's 'Dream Team' Wins SIAM Award for MCM 2007" for highlights of the team's four-year MCM run) and the team from Stellenbosch---Louise Viljoen, Chris Rohwer, and Andreas Hafver, with faculty adviser Jan van Vuuren---as described here. With no SIAM Annual Meeting scheduled for this year, the
The students who worked on the continuous problem were asked to devise a method for dividing a state into the constitutionally mandated number of congressional districts having the "simplest" possible geometric shapes, after which they were to apply their method to the state of
The discrete problem concerned protocols for boarding and deboarding passenger aircraft. With the advent of ever-larger planes---the new Airbus model A380 is expected to hold as many as 800 seats in some configurations---the time spent on the ground (the bulk of which is devoted to on- and offloading of passengers) can represent a significant fraction of the time an aircraft and/or crew is in service, as well as a significant drain on airline revenues. Contestants were asked to devise and compare procedures for boarding and deboarding aircraft of different sizes: small (85–210 seats), midsize (211–330), and large (450–800).
The simplest way to board an aircraft is simply to open the doors and let the passengers enter at random. Experience suggests, however, that there are better ways to proceed. Almost all airlines currently allow first-class passengers and passengers with special needs---including the elderly, the infirm, and families traveling with small children---to board before others. But in filling the rest of their seats, individual airlines follow markedly different protocols, with little consensus as to which ones perform best. The New York Times (November 14, 2006) ran an article describing airlines' concern with the problem, along with their methods for dealing with it.
To reduce congestion in the aisles, Southwest Airlines has long issued boarding passes labeled group A, B, or C, on a first-come, first-served basis. Most other airlines assign seats, often allowing passengers with seats near the back of the plane to enter the cabin as soon as the preboarding process is complete, followed by passengers with seats amidships, and finally those seated near the front. Call it the "back to front" (B
Combining the considerable virtues of B
Many of the MCM teams merely tested---via simulation---the variants of the foregoing protocols obtained by varying the numbers and sizes of the boarding groups. Others invented alternative protocols to test against those in current use, or used genetic algorithms to do the inventing for them. Most observed that enplaning was a more serious problem than deplaning, and advised that cabin crews refrain from interfering with the latter. It was also widely noted that baggage is the enemy of boarding efficiency, and advised that carry-on luggage be strictly limited.
The team from
Readers can find detailed information about the Mathematical Contest in Modeling, including complete results for MCM 2007, at& W$ x" S' O& D! [- Z www.comap.com.
( C' ]8 Y, f6 |& g
顶
| 欢迎光临 数学建模社区-数学中国 (http://www.madio.net/) | Powered by Discuz! X2.5 |