TRANSIENT FLOWS IN NETWORKS (REVISED EDITION)
RAND CORP SANTA MONICA CA
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The paper is concerned with flows in two-terminal dynamic networks as defined by Ford and Fulkerson. These authors have shown how to construct for each positive integer k a flow phi sub k that maximizes the amount u sub k shipped from source to sink in k time periods. Their method leads to different functions phi sub k for different values of k. It is here shown that the problem can be solved by means of a single flow phi that at each time 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 paper are applicable, for instance, to the analysis of logistics problems involving railway networks.
- Operations Research