The ASSIGN.ltx Model

Assignment Problem

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Large airlines tend to base their route structure around the hub concept. An airline will try to have a large number of flights arrive at the hub airport during a certain short interval of time (e.g., 9 a.m. to 10 a.m.) and then have a large number of flights depart the hub shorly thereafter (e.g., 10 a.m. to 11 a.m.). This allows customers of that airline to travel between a large combination of origin/destination cities with one stop and at most one change of planes. For example, United Airlines uses one stop and at most one change of planes. For example, United Airlines uses Chicago as a hub, Delta Airlines uses Atlanta, TWA uses St. Louis, and American uses Dallas/Fort Worth.

A desirable goal in using a hub structure is to minimize the amount of changing of planes (and the resulting moving of baggage) at the hub. This model illustrates how to apply the assignment model.

A certain airline has siz flights arriving at O'Hare airport between 9 and 9:30 a.m. The same six airplanes depart on different flights between 9:40 and 10:20 a.m. You know the average number of people transferring between incoming and leaving flights.

All the planes are identical. A decision problem is which incoming flight should be assigned to which outgoing flight. This model helps determine how incoming flights should be assigned to leaving flights so that a minimum number of people need to change planes at the O'Hare stop.


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