I have the following scenario:
I want to find a flight between two cities: A and B. There is no direct flight from A to B; so, I need to find a connecting flight with the lowest cost.
In addition, the air ticket is not fixed. It depends on the time that I buy it; for example, the price will be cheaper if I buy it early.
Moreover, the time affects the flight too; for example, there is only one flight from C to D on May 31 at 7 AM. If the plane flies from A to C on May 31 at 8 AM, I miss the flight. For this reason, I represent the cities as vertices of a graph. The path AB exists if there is a valid flight from A to B. The weight will be the ticket fee.
Is there any idea or suggestion for my problem?
Thanks