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<br />Network Flow Optimi7.3tion Problem <br /> <br />Within the confmes of mass balance throughout the network, <br />MODSIM sequentially solves the following linear <br />optimization problem via Lagrangian Relaxation over each <br />successive time period in the simulation: <br /> <br />N N <br />minimize ~ ~ c..q.. <br />L L IJ IJ <br />i=l j=l <br /> <br />(1) <br /> <br />subject to: <br /> <br />N N <br />L qij - L qjk - 0; j=l,...,N (2) <br />i = 1 k= 1 <br /> <br />~ij (qi) ~ qij ~ uij (qi) i,j';" 1,...,N <br /> <br />(3) <br /> <br />~.. ~ 0 <br />IJ <br /> <br />12 <br />