American Airlines Next Top Model 455 plane configurations and sizes along with different boarding algorithms. We then compare which algorithms yielded the most efficient boarding process Assumptions The environment within a plane during the boarding process is far too unpredictable to be modeled accurately. To make our model more tractable we make the following simplifying assumptions There is no first-class or special-needs seating. Because the standard in make up a small portion of the overall plane capacity, any chan &esen the All passengers board when their boarding group is called. No passengers rrive late or try to board the plane early Passengers do not pass each other in the aisles; the aisles are too narrow There are no gaps between boarding groups. Airline staff call a new board ing group before the previous boarding group has finished boarding the Passengers do not travel in groups. Often, airlines allow passengers board- ng with groups, especially with younger children, to board in a manner onvenient for them rather than in accordance with the boarding plan. These events are too unpredictable to model precisely The plane is full. A full plane would typically cause the most passenger interferences, allowing us to view the worst-case scenario in our model Every row contains the same number of seats. In reality, the number of seats n a row varies due to engineering reasons or to accommodate luxury-class asse Implementation We formulate the boarding process as follows The layout of a plane is represented by a matrix, with the rows representing s of seats, and each column describing whether a row is next to the win- dow,aisle, etc. The specific dimensions vary with each plane type. Integer parameters track which columns are aisles. The line of passengers waiting to board is represented by an ordered array of integers that shrinks appropriately as they board the planAmerican Airlines' Next Top Model 455 plane configurations and sizes along with different boarding algorithms. We then compare which algorithms yielded the most efficient boarding process. Assumptions The environment within a plane during the boarding process is far too unpredictable to be modeled accurately. To make our model more tractable, we make the following simplifying assumptions: "* There is no first-class or special-needs seating. Because the standard in￾dustry practice is to board these passengers first, and because they generally make up a small portion of the overall plane capacity, any changes in the overall boarding technique will not apply to these passengers. "* All passengers board when their boarding group is called. No passengers arrive late or try to board the plane early. "* Passengers do not pass each other in the aisles; the aisles are too narrow. "* There are no gaps between boarding groups. Airline staff call a new board￾ing group before the previous boarding group has finished boarding the plane. "* Passengers do not travel in groups. Often, airlines allow passengers board￾ing with groups, especially with younger children, to board in a manner convenient for them rather than in accordance with the boarding plan. These events are too unpredictable to model precisely. "* The plane is full. A full plane would typically cause the most passenger interferences, allowing us to view the worst-case scenario in our model. "* Every row contains the same number of seats. In reality, the number of seats in a row varies due to engineering reasons or to accommodate luxury-class passengers. Implementation We formulate the boarding process as follows: "* The layout of a plane is represented by a matrix, with the rows representing rows of seats, and each column describing whether a row is next to the win￾dow, aisle, etc. The specific dimensions vary with each plane type. Integer parameters track which columns are aisles. "* The line of passengers waiting to board is represented by an ordered array of integers that shrinks appropriately as they board the plane