Notes on Linear Programming

Part XLIV Transient Flows in Networks

by David Gale

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A study concerned with flows in two-terminal dynamic networks as defined by Ford and Fulkerson (RM-1981). These authors have shown how to construct for each positive integer k a flow <> that maximizes the amount <> shipped from source to sink in k time periods. Their method leads to different functions <> for different values of k. The present research memorandum shows that the problem can be solved by a single flow <> when k maximizes the cumulative amount shipped from source to sink. The conclusion holds even when the capacities and transit times in the network are allowed to vary with time. The results of this study may be applied in analyzing logistics problems involving railway networks.

This report is part of the RAND Corporation research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

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