Hello Everybody
Thanks For Reading My Question
Im writing a model for a flight network and there is one constraint that Ive added for flow conservation. In fact Im trying to say the number of aircraft entering a city must equal the number of aircraft exiting it. Ive written this Constraint:
for each j : sum(i,y(i,j))=sum(i,y(j,i))
In which y(i,j) is the number of aircraft going from city i to city j.
By this constraint I mean: the number of aircrafts from cities i which enter a specific city j must be equal to the number of aircraft departing from this city j to other cities i.
Now there is the problem. There are SUBTOURS in this solution.
In fact this somehow resembles the TSP(traveling salesman problem) but the difference here is that I do not care weather a specific city is passed through for many times(in TSP each city should be passed through just once). How can I eliminate these subtours. I really appreciate if someone can help me with adding a constraint or modifying the above constraint. The constraint that is ideal for me is something that says the aircraft rotates between different cities (AND DOESNT JUMP FROM ONE CITY TO ANOTHER) and returns to the the originating city.
Thanks For Reading My Question
Im writing a model for a flight network and there is one constraint that Ive added for flow conservation. In fact Im trying to say the number of aircraft entering a city must equal the number of aircraft exiting it. Ive written this Constraint:
for each j : sum(i,y(i,j))=sum(i,y(j,i))
In which y(i,j) is the number of aircraft going from city i to city j.
By this constraint I mean: the number of aircrafts from cities i which enter a specific city j must be equal to the number of aircraft departing from this city j to other cities i.
Now there is the problem. There are SUBTOURS in this solution.
In fact this somehow resembles the TSP(traveling salesman problem) but the difference here is that I do not care weather a specific city is passed through for many times(in TSP each city should be passed through just once). How can I eliminate these subtours. I really appreciate if someone can help me with adding a constraint or modifying the above constraint. The constraint that is ideal for me is something that says the aircraft rotates between different cities (AND DOESNT JUMP FROM ONE CITY TO ANOTHER) and returns to the the originating city.
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