This preview shows page 1. Sign up to view the full content.
Unformatted text preview: e. ⎧ x
⎪
x1 = ⎨ ⎪0
⎩ ⎧1
⎪
w2 = ⎨
⎪0
⎩ if 4 ≤ x ≤ 7
otherwise. ⎧
⎪1
w3 = ⎨
⎪0
⎩ if 8 ≤ x ≤ 9
otherwise. ⎧
⎪ x if 4 ≤ x ≤ 7
x2 = ⎨ ⎪ 0 otherwise. ⎩
⎧
⎪ x if 8 ≤ x ≤ 9
x3 = ⎨ ⎪ 0 otherwise. ⎩ if 0 ≤ x ≤ 3
otherwise. We complete the model as follows. IP formulation y = 2 x 1 + 9 w 2  x 2 5 w 3 + x 3
0 : x1 : 3w 1 4w 2 : x2 : 7w 2 8w3 : x3 : 9w3 w 1 + w 2 + w 3 = 1 x = x1 + x2 + x3 wi E {0, 1} for i = 1 to 3. For any choice of w1, w2, and w3, the variables x and y are correctly defined. Section 7. The traveling salesman problem
In this section, we give the standard model for the traveling salesman problem. It has an exponential
number of constraints, which may seem quite unusual for an integer programming model. We
explain how it can be implemented so as to be practical.
We assume that there are n cities, and that Cij denotes the distance from city i to city j.
In this model, the following are the variables: ⎧ 1 if city i is immediately...
View
Full
Document
This note was uploaded on 03/18/2014 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.
 Spring '07
 JamesOrli
 Management

Click to edit the document details