1. General Information

The location of economic activities in generates a transport demand that is represented geographically by a set of origin-destination pairs. Gravity-type spatial interactions models offer a methodology to appraise the transport demand between a set of locations. For a transport company, knowing this information is very useful to the processes of scheduling vehicles along routes. This exercise involve the application of a gravity spatial interaction model for scheduling the activities of a fictive airline company.

A large airline company (Air Modal inc.) hired a consultant in order to help them reorganize their international links and to develop new service strategies. Indeed, the company wants to know the potential demand of air transport between and inside continents. Knowing this demand, it will be able to assign its flights more efficiently and see where growth perspectives are the most attractive. The following information is available to apply the spatial interaction model:

Both the lambda and alpha indexes have the same value, since it is assumed that on a yearly basis all the passengers are going back to their place of origin. The reality is more complex as some passengers may do multiple destination trips (e.g. North America to Europe to Asia and then back to North America), while others are doing a one-way flight only (immigration). The values of lambda and alpha are higher for Latin America than for Europe, which reflects better land based transport alternatives for Europe (mainly train) as well as a more compact location of the population.

The value of the k coefficient is 0.00001 (yearly value) and the friction of distance (beta) coefficient is 1.34 between all origins and destinations.

2. Results

Results must be presented as a report to the board of directors of Air Modal inc. This report must include the following:

• Calculation of spatial interactions. By using the available data (urban population, lambda, alpha and k indexes), appraise the origin-destination matrix of air transport passengers within and between continents.
• Model accuracy. If the actual air traffic was 1,400,000,000 people for this year, what is the accuracy of the model?
• Mapping. Put on a map the 10 most important origin-destination pairs of this matrix as proportional symbols. A basemap is available here.
• Market share. Knowing that Air Modal services 6% of the global market, what would be the value of k if one would want to know the transport demand that must fill Air Modal in one day?
• Allocation of flights. Knowing that a typical Air Modal flight contains 280 people, how many flights would be necessary (considering that Air Modal services 6% of the market) to fill the demand for one day between all the O-D pairs (matrix of required flights)?
• New conditions. If for Asia, lambda and alpha become 1.00, what would the resulting origin / destination matrix? If Air Modal wants to fill this supplementary demand while preserving its market share, how many new flights will it have to add per O-D pairs for one day?

The exercise can be extended to include more complex tasks:

• Different market shares. Two or more airline companies can be included, each having different market shares on each continent. The issue of competition and alliances (complementarity) can be brought forward.
• Higher market segmentation. Several regions can be sub-divided to provide a greater level of accuracy (and larger O-D matrices). For instance, Asia could be sub-divided into the Middle East, South Asia, Southeast Asia and East Asia.
• Different lambda and alpha values. By considering major global migration flows, it is possible to have different lambda and alpha values for a continent. For instance, there is a positive migratory balance between Latin America and North America. Since some of these movements take place by air transportation, the result would be an imbalanced yearly flow of air traffic.