! Ravinia Max Flow problem;
! One of the problems associated with the Ravinia festival
in Highland Park in the summer is the management of the
associated traffic. Electric signs are sometimes used to
suggest routes to incoming motorists so as to evenly
utilize all available routes. Below is a model for
finding the maximum possible flow per minute of cars
into the main parking area for Ravinia. Each decision
variable represents the traffic per minute on a one way street;
!Keywords: Max flow, Min cut, Traffic, Network;
MODEL:
MAX = FE; ! Max flow/minute entering parking lot;
[CLAVEY] F0 -F1 -F2 = 0;
[LKCOOK] +F2 +F4 -F5 +F9 = 0;
[DUNDEE] +F3 -F7 +F8 = 0;
[BRODST] F1 -F3 -F4 -F6 = 0;
[MAINST] +F5 +F6 +F7 -FE= 0;
! Link capacities;
[UB0] F0 <= 70;
[UB1] F1 <= 45;
[UB2] F2 <= 27;
[UB3] F3 <= 22;
[UB4] F4 <= 10;
[UB5] F5 <= 40;
[UB6] F6 <= 20;
[UB7] F7 <= 30;
[UB8] F8 <= 10;
[UB9] F9 <= 20;
END
! The UB constraints with nonzero dual prices in the solution
constitute a minimum cut or bottleneck, i.e., a set of arcs
that partition the nodes into two sets, pre-bottleneck and
post bottleneck, for which the
sum of the arc capacities is minimum;
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