Optimal Capacity Expansion in a Flow Network

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 12, 1972
Accession Number
AD0754376

Entities

People

  • Alan W. Mcmasters

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • California
  • Computer Programming
  • Construction
  • Evolutionary Algorithms
  • Flow Network
  • Graph Theory
  • Graphs
  • Heuristic Methods
  • Interdiction
  • Linear Programming
  • Mathematical Programming
  • Nonplanar
  • Operations Research
  • Procedures (Computers)
  • Two Dimensional
  • United States

Readers

  • Calculus or Mathematical Analysis
  • Operations Research