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It indeed excludes subtours, as (1) the arc-constraint for (i, j) forces uj a?? ui +1,
when xij = 1; (2) if a feasible solution of (2.1)a?"(2.2) contained more than one subtour,
then at least one of these would not contain node 1, and along this subtour the ui
values would have to increase to infinity. This argument, with the bounds on the ui
variables, also implies that the only feasible value of ui is the position of node i in the
tour. The advantages of the MTZ formulation are
a?? its small size (we need only n extra variables and roughly n2/2 extra constraints),
a?? if it is preferable to visit, say, city i early in the tour, one can easily model
this by adding a term a?'I±ui with some I± > 0 to the objective...
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Common topics in this essay:
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