rec3 - ORIE 321/521/522 RECITATION 3 Spring 2007 Consider...

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Unformatted text preview: ORIE 321/521/522 RECITATION 3 Spring 2007 Consider the following AMPL model file maxflow.mod for the maximum flow problem, which can be found in the MODELS folder within the amplcml folder. set nodes; param orig symbolic in nodes; param dest symbolic in nodes, <> orig; set arcs within (nodes diff {dest}) cross (nodes diff {orig}); param cap {arcs} >= 0; var Flow {(i,j) in arcs} >= 0, <= cap[i,j]; maximize Total_Flow: sum {(orig,j) in arcs} Flow[orig,j]; subject to Balance {k in nodes diff {orig,dest}}: sum {(i,k) in arcs} Flow[i,k] = sum {(k,j) in arcs} Flow[k,j]; Change this model so that the capacity constraints are explicit constraints of the model, rather than just upper bounds on the variable Flow . And also consider the corresponding data file, maxflow.dat : set nodes := s a b c d e t ; param orig := s ; param dest := t ; param: arcs: cap := s a 1 s b 4 s c 6 a b 3 a d 4 b a 2 b d 3 b e 1 c e 4 d t 9 e t 4 ; Draw the graph for this input. 1 Write out the linear programming formulation of the maximum flow problem for this input. There are 11 variables, 5 equality constraints, and 11 inequal- ity constraints. Write the flow conservation constraints in the form flow out - flow in equals 0. For each variable, try to be very careful to keep allout - flow in equals 0....
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rec3 - ORIE 321/521/522 RECITATION 3 Spring 2007 Consider...

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