Converting conditional subtour elimination of CVRP into normal ones
I am trying to eliminate the if condition constraints from the following CVRP formulation.
I tried some big M methods on paper but failed to come up with a proper reformulation. Can you please help me to find a solution?
Thanks!
Solution
You can split the equation into two inequalities and the apply the big-M method:
ui + qj <= uj + M(1-xij)
ui + qj >= uj - M(1-xij)
Models with big-M constants tend to be weak and numerically instable, so I suggest to select the constant as small as possible (i.e. make M depend on ij, if possible). To learn more about that have a look at the Perils of "Big M".
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