A salesman will visit all the cities in the table below from Cincinnati and returned to Cincinnati. Your help is needed to determine the route to be taken this salesman for a minimum total mileage.

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A salesman will visit all the cities in the table below from Cincinnati and returned to Cincinnati. Your help is needed to determine the route to be taken this salesman for a minimum total mileage.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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travelling salesman problem... is this from graph theory ?
yes this is travelling salesman problem, but i just need the linear programming, not the solution

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the decision variable, objective function and constraints
okay.. . this is heavy for me. i hope someone else would answer this,.. @TuringTest @experimentX @Outkast3r09 @zzr0ck3r
n = 12 c_ij= distance from city i to city j x_ij = 1, if a tour includes travelling from city i to city j 0, otherwise from here i don't know
the objective function would be the sum of all the miles for route \[O = \sum_{i=1}^{12}\sum_{j=1}^{12} x_{ij} *c_{ij}\] as far as the programming, not sure, it seems there are 11! possible routes so the goal is to use a bunch of loops to assign all 11! combinations to x_ij then evaluate each sum and determine the route that yields the minimum value
i read the final model for TSP, but in the decision variable there is y_ij=flow from node i to node j, should i use this too?
yes probably, the decision variable y_ij will tell the program what to assign to x_ij sorry i haven't done too much with linear programming or graph theory
do you have any references, e-book or ever find the similarly question?
http://www.tsp.gatech.edu/index.html
thank you
I'm sorry but this would take a bit too much detail for me to investigate right now. I am also quite tired (it's almost 3am here) so I afraid I'll have to pass you off @Zarkon @myininaya @Callisto @KingGeorge most of them are online right now, hopefully one comes and helps Good luck!
thank you turing

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