D5 Annex report WP 3: ETIS Database methodology ... - ETIS plus

D5 Annex WP 3: DATABASE METHODOLOGY AND DATABASE USER MANUAL –
FREIGHT TRANSPORT DEMAND
Building Region­Region Matrices: A Solution
The solution employed by MDS­Transmodal has been to build a Gravity model for seeding the
unknown cells in the matrix, and to optimise this for each commodity, using an optimisation
algorithm known as an "amoeba". The optimisation was conducted on a country­country matrix
where all the genuine values for the cells were known in advance. The parameters were stored,
and then re­used when the national data was broken down into regions.
Thus, the problem was explored at a national level, and then an optimum solution was
transplanted to a regional level. Naturally, the regional results produced could not be tested, but
at least the matrix could be seeded with values known to produce vastly improved results at a
more aggregated level. Furthermore, the pattern of parameter values for the gravity model used
to implement the seeding, could be used to categorize specific commodities in terms of their
propensity to be widely or narrowly distributed.
Step 1: Selecting the Seeding Model
The selection process was driven mainly by practicality. It was decided that for simplicity, just 3
parameters would be considered:
1. A measure of the cost in terms of distance between the 2 regions
2. The total exports of the exporting region
3. The total imports of the importing region
Volume indicators such as population and GDP tended to be highly correlated with the total
exports/imports.
A simple formula based on physical common sense could be:
T = d
e
n - md
EI
where T= trade, d= measure of cost in terms of distance, E= total exports of exporting region, I=
total imports of importing region. The n and m are variables.
Step 2: Optimising the Parameters
After running this formula, a furnessing algorithm is run to ‘massage’ these ‘seed’ values to the
known totals. The furnessing algorithm finds the existing total of one column and compares this
to the required column total. All values in this column are then scaled up accordingly such that
the new column total equals the required column total. This is done separately for all columns.
This process is then repeated for the rows. If this combined column and row process is repeated
several times, gradually the cell values become stable and converge.
It was noted that the column totals (E) are redundant because the furness scaling cancels them
out immediately but for the formula to have a sensible physical representation, they were still
included.
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Document2
27 May 2004