Hi,
I'm working on a method to find a path in a network from two different
nodes with the total distance being as closest as possible to a certain
number.
I started from the idea explained by Andrew Makhorin in examples/tsp.mod
in the GLPK distribution, then I consider n as a variable (the number of
traversed nodes) instead of a parameter.
n is computed as the sum over (i,j) of x[i,j] plus 1.
Then, quoting from example/tsp.mod we have:
s.t. cap{(i,j) in E}: y[i,j] <= (n-1) * x[i,j];
/* if arc (i,j) does not belong to the salesman's tour, its capacity
must be zero; it is obvious that on leaving a node, it is sufficient
to have not more than n-1 cars */
The problem is that the constraint becomes nonlinear because of the
product between n and x[i,j].
Is this a bad approach or the problem cannot be solved by LP?
Many thanks
Gianmarco Bruno
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