DOCUMENTA MATHEMATICA, Vol. Extra Volume: Optimization Stories (2012), 169-180

Alexander Schrijver

On the History of the Transportation and Maximum Flow Problems

We review two papers that are of historical interest for combinatorial optimization: an article of A.N. Tolsto\u{\i} from 1930, in which the transportation problem is studied, and a negative cycle criterion is developed and applied to solve a (for that time) large-scale ($10\times 68$) transportation problem to optimality; and an, until recently secret, RAND report of T.E. Harris and F.S. Ross from 1955, that Ford and Fulkerson mention as motivation to study the maximum flow problem. The papers have in common that they both apply their methods to the Soviet railway network.

2010 Mathematics Subject Classification: 01A60, 05-03, 05C21, 05C85, 90C27

Keywords and Phrases: Maximum flow, minimum cut, transportation, algorithm, cycle cancelling, history

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