An Optimization Model to Estimate the Air Travel Demand
for the United States (2014)

Worldwide, air travel demand has greatly increased and historical travel
demand data is essential for air transportation planning, policy-making and
market evaluation. However, historical air travel demand is not always
available or complete and oftentimes must be estimated. To address this
problem, we present a non-linear optimization model to estimate the historical
air travel demand between origin and destination (OD) airports in the
United States (US). In contrast to existing models, our model estimates
itinerary-level OD demand served by air carriers while considering travelers'
choice behaviors. The model formulation is based on a logit model along with
observed data. To consider travelers' choice behaviors, an observed utility
is assigned to each itinerary. The utility is a function of factors such as
fare, flight time, number of connections, and departure and arrival times.
Travelers between an OD pair are assumed to choose itineraries that have
maximum utility. In the optimal solution, the demand between an OD pair
distributes among the itineraries connecting the OD pair by a logit model.
An evolutionary strategy is used to calibrate the model parameters such that
the model estimates match sample results from the Airline Origin and
Destination Survey as close as possible. This method solves a least square
parameter estimation model and our model iteratively until the parameter
estimation is stabilized. To make the demand estimation consistent with
observed data, the statistics from the Airline Origin and Destination Survey,
T100 Domestic Market data, and Official Airline Guide are used to create the
constraints in the model. An efficient iterative balancing algorithm is used
to solve the optimization model. The algorithm iteratively maximizes the dual
of the model along directions defined by unit vectors and keeps some first
order optimality conditions satisfied. We applied the model to estimate the
travel demand served by seven major US carriers in a la- ge-size US network.
The network contains 457 airports and about 200,000 itineraries. We compared
with our estimation results with the statistics from the American Travel
Survey. The comparisons are done at national level and state level
respectively. Our comparisons suggest that the demand estimation produced by
our model is generally consistent with those statistics.