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In Modeling a Traveling Salesman Problem, Let XijkX_{\mathrm{ijk}} Be a 0-1 Decision Variable, Which Takes a Value of 0-1

Question 30

Multiple Choice

In modeling a traveling salesman problem, let XijkX_{\mathrm{ijk}} be a 0-1 decision variable, which takes a value of 0 if in the kth leg the tour corresponding to the solution does not go from node i\mathrm{i} to node j\mathrm{j} . Xijk\mathrm{X}_{\mathrm{ijk}} is set to be equal to 1 if the tour goes from node i\mathrm{i} to node j\mathrm{j} in the kth leg. In a problem with just 4 nodes and without loss of generality, assume that the tour starts and ends in node 1. Mark the correct constraint to make sure that the tour starts in node 1


A) X121+X131+X1411\mathrm{X}_{121}+\mathrm{X}_{131}+\mathrm{X}_{141} \leq 1
B) X121+X131+X1411X_{121}+X_{131}+X_{141} \geq 1
C) X121+X131+X141=1X_{121}+X_{131}+X_{141}=1
D) X214+X314+X414=1X_{214}+X_{314}+X_{414}=1

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