8 Network Flows and Project Scheduling

Roads, pipelines, telephone circuits and supply chains are networks: nodes joined by arcs along which something flows. Many OR problems on networks are linear programmes whose constraint matrix is the node–arc incidence matrix of a directed graph, and like the transportation problem they have integral solutions and fast special algorithms. This section treats the three classical ones, shortest paths, maximum flows and minimum-cost flows, and then project scheduling by the critical path method and PERT, which is a longest-path problem on a network of activities.

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