7 Transportation and Assignment Problems

Some linear programmes have so much structure that the simplex method can be carried out on a table of numbers by hand, and their optimal solutions are automatically whole numbers. The transportation problem, shipping a commodity from sources to destinations at least cost, was posed by Hitchcock in 1941 and by Kantorovich, and the assignment problem, matching workers to jobs, is its special case. This section develops the special methods and explains the integrality through total unimodularity, which will reappear for network flows and is the link between linear and integer programming.

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