Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops

Chapter 9 · Networks, Dependence, and Resilience

D. Ray Fulkerson

1924 – 1976

The problem on the desk

How could several commodities share a capacitated network without explicitly enumerating an impractically large set of paths? Ford and Fulkerson’s 1958 paper proposed representing the necessary variables implicitly.1

A life in moments

  1. 1924

    Born on 14 August in southern Illinois.2

  2. 1947

    Southern Illinois University · Carbondale

    Completed his undergraduate degree.2

  3. 1951

    University of Wisconsin · Madison

    Completed his doctorate under Cyrus MacDuffee.2

  4. 1951

    RAND Corporation · Santa Monica

    Joined RAND’s mathematics group.2

  5. 1958

    RAND Corporation · Santa Monica

    Co-authored a computation for multicommodity network flows.1

  6. 1971

    Cornell University · Ithaca

    Joined Cornell.2

  7. 1976

    Died on 10 January.2

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

the number of variables in this formulation is too large

A Suggested Computation for Maximal Multi-Commodity Network Flows, 19584

A story

A practical flow problem

INFORMS traces Fulkerson’s out-of-kilter algorithm to work motivated by natural-gas transmission networks. Applied constraints helped shape the mathematical problem.3

Around Fulkerson

  • co-author Lester R. Ford Jr. Ford and Fulkerson studied multicommodity network flows together.1
  • co-author George B. Dantzig Fulkerson, Dantzig and Selmer Johnson jointly worked on the travelling-salesman problem.2

Advisor in the record Cyrus Colton MacDuffee Students in the record Robert Bland, Gary Harding, David Weinberger Mathematics Genealogy Project record

The genealogy lists only what the database records; a missing name is not a missing teacher.

The card in the book

Mathematician at the RAND Corporation from 1951 and, from 1971, at Cornell University. He worked on network flows, combinatorial optimisation and the theory of blocking and anti-blocking polyhedra; with George Dantzig and Selmer Johnson he solved a 49-city travelling-salesman problem by the cutting-plane method. A prize in discrete mathematics bears his name.

Main works “Solution of a large-scale traveling-salesman problem”, with G. B. Dantzig and S. M. Johnson (Operations Research 2, 1954); Flows in Networks, with L. R. Ford Jr. (1962); “Blocking and anti-blocking pairs of polyhedra” (Mathematical Programming 1, 1971).

To read further

Sources (4)
  1. A Suggested Computation for Maximal Multi-Commodity Network Flows, L. R. Ford Jr. and D. R. Fulkerson, 1958; Management Science 5(1), pp. 97–101; abstract
  2. D. Ray Fulkerson, INFORMS History and Traditions; Biography and selected publications
  3. D. Ray Fulkerson, INFORMS History and Traditions; Biography: network applications
  4. A Suggested Computation for Maximal Multi-Commodity Network Flows, L. R. Ford Jr. and D. R. Fulkerson, 1958; Abstract; co-authored with L. R. Ford Jr.; excerpt

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.