Lecture19 - Advanced Operations Research Techniques IE316...

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Unformatted text preview: Advanced Operations Research Techniques IE316 Lecture 19 Dr. Ted Ralphs IE316 Lecture 19 1 Reading for This Lecture • Bertsimas 7.4-7.5 IE316 Lecture 19 2 Negative Cost Cycle Algorithm • Recall the negative cost cycle algorithm from last lecture. • The basic algorithm consisted of iteratively saturating unsaturated negative cost cycles. • Questions to be Answered • How do we start the algorithm (find a feasible flow)? • How do we find unsaturated, negative cost cycles? • If there are no unsaturated negative cost cycles, is the current solution optimal? • Is the algorithm guaranteed to terminate? IE316 Lecture 19 3 The Residual Network • We are only interested in arcs on which flow can be pushed (forwards or backwards). • Corresponding to a given flow f , we build a residual network . • For each arc ( i,j ) in the original network, we introduce two arcs into the residual network: – an arc ( i,j ) with capacity u ij- f ij and cost c ij , and – an arc ( j,i ) with capacity f ij and cost- c ij . • We delete arcs that have zero capacity from the network. • Flow on the arc ( j,i ) in the residual network can be interpreted as a reduction in the flow on arc ( i,j ) in the original network. IE316 Lecture 19 4 Interpreting the Residual Network • Consider a feasible flow f and another feasible flow f + ¯ f ....
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This note was uploaded on 08/06/2008 for the course IE 316 taught by Professor Ralphs during the Fall '08 term at Lehigh University .

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Lecture19 - Advanced Operations Research Techniques IE316...

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