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Essay

Mtz Formulation

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Issue:

Science

 

Written by:

Grace W

 

Date added:

February 18, 2016

 

Level:

College

 

Grade:

A

 

No of pages / words:

2 / 302

 

Was viewed:

9366 times

 

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Essay content:

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...
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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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General issues of this essay:
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