# AMPL model for the Minimum Cost Network Flow Problem # # By default, this model assumes that b[i] = 0, c[i,j] = 0, # l[i,j] = 0 and u[i,j] = Infinity. # # Parameters not specified in the data file will get their default values. set NODES; # nodes in the network set ARCS within {NODES, NODES}; # arcs in the network param b {NODES} default 0; # supply/demand for node i param c {ARCS} default 0; # cost of one of flow on arc(i,j) param l {ARCS} default 0; # lower bound on flow on arc(i,j) param u {ARCS} default Infinity; # upper bound on flow on arc(i,j) var x {ARCS}; # flow on arc (i,j) minimize cost: sum{(i,j) in ARCS} c[i,j] * x[i,j]; # Flow Out(i) - Flow In(i) = b(i) subject to flow_balance {i in NODES}: sum{j in NODES: (i,j) in ARCS} x[i,j] - sum{j in NODES: (j,i) in ARCS} x[j,i] = b[i]; subject to capacity {(i,j) in ARCS}: l[i,j] <= x[i,j] <= u[i,j];