# Optimal capacity expansion in a flow network

by Alan W. McMasters

Publisher: Naval Postgraduate School in Monterey, California

Written in English

## Subjects:

• Mathematical optimization,
• Network analysis (Planning),
• Graph theory

The capacity expansion problem for flow networks, first studied by D. R. Fulkerson, is reexamined. In the case where no free initial capacity is available, it is shown that the optimal expansion takes place on the arcs of the cheapest chain in the sense of unit expansion costs through the network. The proof makes use of Dantzig"s decomposition principle of linear programming. In the case where some free initial capacity is available, an algorithm based on the topological dual is presented. This algorithm does not require that the flow network be planar and can be easily extended to problems having positive lower bound restrictions on arc flows, problems having bounds on individual arc expansion or nonlinear convex expansion costs, and capacity reduction problems.

## Edition Notes

The Physical Object ID Numbers Statement by Alan W. McMasters Contributions Naval Postgraduate School (U.S.) Pagination 35 p. : Number of Pages 35 Open Library OL25481294M OCLC/WorldCa 438072068

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## Optimal capacity expansion in a flow network by Alan W. McMasters Download PDF EPUB FB2

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