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### Costs in a network

Posted: Fri Feb 27, 2015 10:35 am
Hi all,

I am trying to find the best model to solve the following problem:

I have various players in a network. I have to visit all these players in the network. The players are visited in an optimal route, and to visit all the players I have costs (km and hours). Some of these players have time restrictions: that means I can only visit these players within specific time windows, for example between 16:00 and 17:00. The route to visit all the players is influenced by this player.

I want to know: what are the extra costs I have to make because of this restriction?

An option is to calculate the costs of the whole network with these players and the costs of the network without these players. But it could be that in the same region (or street) there is another player with the same time window. So in this case they would split the extra costs of this restriction.

So If I have 3 players with time restrictions, I would have the following costs:

costs(the 3 players with their time restricitions are present) =

costs(only player 1 and 2 have the time restriction, player 3 not) =

costs(only player 2 and 3 have the time restriction, player 1 not) =

costs(only player 1 and 3 have the time restriction, player 2 not) =

costs(only player 1 has the time restriction) =

costs(only player 2 has the time restriction) =

costs(only player 3 has the time restriction) =

costs(none of the players have the time restriction) =

These costs can be calculated. But the question is: what is now the costs of a specific time restriction of a player?