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Topic: Graph theory - train problem
Replies: 1   Last Post: Jan 25, 2010 11:44 PM

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Posts: 1
From: US
Registered: 1/25/10
Graph theory - train problem
Posted: Jan 25, 2010 3:27 PM
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I have theoretical problem about trains. I think it can be solved with graph theory, but I am not really good at math. Can you help me figure this out?

Train must go from A to B. There are many rail routes it can take. It must pay a pass fare to use the a route. They all differently charged. Each route leads to station. Each station pays train to visit station, but payments are also different. Goal is to arrive at B via route that makes most money.

For example, if A to B had 2 routes:

Route one
A to A1 train must pay $100, A1 pays $1000 for train to visit
A1 to A2 train must pay $800, A2 pays $2000 for train to visit
A2 to B tain must pay $200

Train makes $1900.

Route two
A to C1 train must pay $10, C1 pays $100 for train to visit
C1 to C2 train must pay $5, C2 pays $200 for train to visit
C2 to B train must pay $100

Train makes $185

We should pick route two because it train makes most money.

We have many routes to chose from in our actual problem.

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