Network Flows

Network Flows is a graduate IE course built around a single idea: a huge range of optimization problems — routing, assignment, scheduling, matching, transportation — collapse into the same underlying structure of moving units through a graph, and that structure admits algorithms much faster than treating each as a generic LP. You'll spend the semester building shortest-path, max-flow, min-cost-flow, matching, and spanning-tree algorithms from first principles, proving their complexity bounds, and working through homework sets out of Ahuja that mix modeling exercises with algorithmic analysis. It sits downstream of linear programming and combinatorial optimization, and the machinery here — residual graphs, reduced costs, Lagrangean relaxation for multicommodity flows — is what later shows up in transportation, logistics, and large-scale integer programming work.