MIT15_053S13_iprefguide

For any non empty subset 5 of cities with s n there

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Unformatted text preview: followed by city j on the tour ⎪ xij = ⎨ ⎪ 0 otherwise. ⎩ The formulation is as follows: n Minimize n ∑∑c x i =1 j =1 n subject to ∑x j =1 ij n ∑x i =1 ∑ ij i∈S , j ∈N \ S ij ij =1 for all i = 1 to n =1 for all j = 1 to n xij ≥ 1 for all S ⊂ {1,2,..., n} with 1 ≤ S ≤ n − 1 xij ∈{0,1}, for all i, j = 1 to n. The first set of constraints ensures that there is some city that follows city i in the solution. The second set of constraints ensures that there is some city that precedes city j in the solution. Unfortunately, there are not enough constraints to ensure that the solution is a tour. For example, a feasible solution to the first two sets of constraints for the six city problem consists of x12 = x23 = x31 = 1, and x45 = x56 = x64 = 1. This "solution" to the first two sets of constraints corresponds to the cycles 1-2-3-1 and 4-5-6-4. A tour should be one cycle only. The third set of constraints guarantees the following. For any non-empty subset...
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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.

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