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== Bonus approach ==
 
== Bonus approach ==
The eco-score approach intends to give a bonus to locally produced (and purchased) products. This bonus is +15, which is equal to a transport score of 100. This bonus is however now given to any product produced/purchased in France. No account has been taken of the very large size of France and impact of transport within the country.
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The eco-score approach intends to give a bonus to locally produced (and purchased) products. This bonus is +15, which is equal to a transport score of 100. This bonus is however now given to any product produced/purchased in France. No account has been taken of the very large size of France and impact of transport within the country.
    
Can this approach be adapted, so that the size of a country is taken into account?
 
Can this approach be adapted, so that the size of a country is taken into account?
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== Maximum bonus ==
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It would be more logic to give the maximum bonus (transport score of 100) only to very local production and purchase. Ideally this will imply an area as small as possible, i.e. a city or very small country. Production and purchase that occurs in a country such as Andorra, Monaco, Liechtenstein or San Marino could be viewed as having a transportation score of 100.
It would be logic to give the maximum bonus (transport score if 100) only to very locally production and purchase. Ideally this will imply an area as small as possible, i.e. a city or very small country. Production and purchase that occurs in a country such as Andorra, Monaco, Liechtenstein or San Marino could be viewed as having a transportation score of 100.
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== No bonus ==
   
In the current calculation the no bonus (transportation score 0) is (arbitrarily) set at a distance of 2000 km. This distance covers roughly the size of Europe.
 
In the current calculation the no bonus (transportation score 0) is (arbitrarily) set at a distance of 2000 km. This distance covers roughly the size of Europe.
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== Centroids to the rescue ==
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== Centroids to the rescue? ==
 
Is it possible to use the centroid calculations in determining the (transportation) size of a country?
 
Is it possible to use the centroid calculations in determining the (transportation) size of a country?
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The weighted sum for a country that consists of single city will be zero. This can then correspond to a transportation (bonus) score of 100. This means it is preferred to have no transportation.
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The weighted sum for a country that consists of single city will be zero. This means there is no transportation required. The country size is then zero.  
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The weighted sum of the major cities in the European Union (or larger area) could be used to define the transportation score of 0. This means a maximum transportation impact.
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The centroid approach can be used to calculate the country transportation size. We just have to add all cities, so that the entire population is covered. The resulting weighted distance is the size we are looking for. This size is the average distance to the entire population.
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From Any weighted sum in between it is now possible to calculate a country transportation score. The larger the country, the lower the country transportation score. This country transportation score can be used to determine the maximum bonus for a country.
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How can the centroid data be used and does it need to be extended?
 
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The centroid approach can also be used to calculate the country transportation size. We just have to add all cities, so that the entire population is covered. The resulting weighted distance is the size we are looking for.
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In practice this approach is not feasible. It is just to much work to (to do by hand a least). So we need a way to get a reasonable approximation. For the calculation of the centroids a limited number of cities are used. We could try to extrapolate this data to get the transportation country size.
      
== Approach ==
 
== Approach ==
In the figure the results for the french departments are shown.
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In the figure the weighted distances for France using the departments are shown.
 
[[File:France transportation size.png|thumb|The population road-distance weighted size of France based on the departments]]
 
[[File:France transportation size.png|thumb|The population road-distance weighted size of France based on the departments]]
 
The cumulative population road-distance weighted distances are plotted against the cumulative population ratios. Each added city adds a point, increasing the cumulative population ratio and the cumulative distance. If the cumulative population ratio is 1, we have covered the entire population. And the corresponding cumulative distance is the value we are looking for.
 
The cumulative population road-distance weighted distances are plotted against the cumulative population ratios. Each added city adds a point, increasing the cumulative population ratio and the cumulative distance. If the cumulative population ratio is 1, we have covered the entire population. And the corresponding cumulative distance is the value we are looking for.
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