D. Ray Fulkerson

  • Robert G. Bland
  • James B. Orlin
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 147)


Ray Fulkerson’s seminal work in network flows, large-scale linear programming (LP), combinatorial optimization, and combinatorics has had an enormous influence on the practice of Operations Research (OR). His seminal book, Flows in Networks, co-written with Lester R. Ford, Jr., was instrumental in bringing network flow theory and algorithms to the domain of OR practice—in communications, transportation, supply systems—and in hastening the development of academic courses in networks, graph theory, and combinatorics. Much of his most influential work began with an application, a puzzle, or a specific computational obstacle. Pursuit of the underlying mathematical structures led Ray and his collaborators to broad and profound methodological innovations, such as cutting planes and column generation, and to the foundations of network flow theory and polyhedral combinatorics.


Travel Salesman Problem Column Generation Multicommodity Flow Linear Programming Duality Subtour Elimination Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We are extremely grateful to several of Ray’s family members, friends, and admirers who assisted in providing information for this chapter, including: Michel Balinski, Len Berkovitz, Louis Billera, Wendell Fleming, Les Ford, Dick Fulkerson, Lloyd Shapley, David Shmoys, Alan Tucker, David Weinberger, Allen Ziebur, and, especially, Merle Fulkerson Guthrie. The nice presentation of Ray’s personal story in Billera and Lucas (1978) and the source material they gathered provided background material for this chapter. Some of the content here is from Bland and Orlin (2005).


  1. Ahuja R, Magnanti T, Orlin J (1993) Network flows: theory and applications. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  2. Applegate D, Bixby R, Chvátal V, Cook W (2006) The Traveling salesman problem: a computational study. Princeton University Press, Princeton, NJGoogle Scholar
  3. Billera L, Lucas W (1978) Delbert Ray Fulkerson. Math Oper Res 1(4):298–310Google Scholar
  4. Bland R (1974) Complementary orthogonal subspaces of Rn and orientability of Matroids. Unpublished doctoral dissertation, Cornell University, Ithaca, NYGoogle Scholar
  5. Bland R (1977) New finite pivoting rules for the simplex method. Math Oper Res 12(3):103–107CrossRefGoogle Scholar
  6. Bland R, Orlin J (2005) IFORS’ operational research hall of fame: Delbert Ray Fulkerson. Int Trans Oper Res 12(3):367–372CrossRefGoogle Scholar
  7. Bruck R, Ryser H (1949) The nonexistence of certain finite projective planes. Can J Math 1:88–93CrossRefGoogle Scholar
  8. Camion P (1968) Modules unimodulaires. J Comb Theory 4:301–362CrossRefGoogle Scholar
  9. Chvátal V (1976) D. Ray Fulkerson’s contributions to operations research. Math Oper Res 1(4):311–320CrossRefGoogle Scholar
  10. Dantzig G (1951) Application of the simplex method to a transportation problem. In: Koopmans TC (ed) Activity analysis of production and allocation: proceedings of a conference. Wiley, New York, NY, pp 359–373Google Scholar
  11. Dantzig G (1959) Optimum gas balance (unpublished report)Google Scholar
  12. Dantzig G, Ford L Jr, Fulkerson DR (1956) A primal-dual algorithm for linear programs. In: Kuhn H, Tucker AW (eds) Annals of mathematics study, vol 38. Princeton University Press, Princeton, NJ, pp 171–181Google Scholar
  13. Dantzig G, Fulkerson DR (1954) Minimizing the number of tankers to meet a fixed schedule. Nav Res Log Q 1(3):217–222CrossRefGoogle Scholar
  14. Dantzig G, Fulkerson DR, Johnson S (1954) Solution of a large-scale traveling salesman problem. Oper Res 2(4):393–410CrossRefGoogle Scholar
  15. Dantzig G, Fulkerson DR, Johnson S (1959) On a linear-programming, combinatorial approach to the travelling salesman problem. Oper Res 7(1):58–66CrossRefGoogle Scholar
  16. Dantzig G, Wolfe P (1961) The decomposition algorithm for linear programming. Econometrica 29(3):767–778CrossRefGoogle Scholar
  17. Dilworth R (1950) A decomposition theorem for partially ordered sets. Ann Math 51:161–166CrossRefGoogle Scholar
  18. Edmonds J, Fulkerson DR (1970) Bottleneck extrema. J Comb Theory 8:299–306CrossRefGoogle Scholar
  19. Fleming W (2009) Personal communicationGoogle Scholar
  20. Folkman J, Fulkerson DR (1970) Flows in infinite graphs. J Comb Theory 8:30–44CrossRefGoogle Scholar
  21. Ford L Jr, Fulkerson DR (1954) Maximal flow through a network. Research Memorandum RM-1400. The RAND Corporation, Santa Monica, CAGoogle Scholar
  22. Ford L Jr, Fulkerson DR (1956a) Maximal flow through a network. Can J Math 8:399–404CrossRefGoogle Scholar
  23. Ford L Jr, Fulkerson DR (1956b) Solving the transportation problem. Manage Sci 3(1):24–32CrossRefGoogle Scholar
  24. Ford L Jr, Fulkerson DR (1957) A simple algorithm for finding maximal network flows and an application to the Hitchcock problem. Can J Math 9:210–218CrossRefGoogle Scholar
  25. Ford L Jr, Fulkerson DR (1958) A suggested computation for maximal multicommodity network flows. Manage Sci 5(1):97–101CrossRefGoogle Scholar
  26. Ford L Jr, Fulkerson DR (1962) Flows in networks. Princeton University Press, Princeton, NJ. Reissued 2010, Princeton University PressGoogle Scholar
  27. Fulkerson DR (1959) Letter to Lester FordGoogle Scholar
  28. Fulkerson DR (1961a) An out-of-kilter method for minimum cost flow problems. J Soc Ind Appl Math 9:18–27CrossRefGoogle Scholar
  29. Fulkerson DR (1961b) A network flow computation for project cost curves. Manage Sci 7(2):167–178CrossRefGoogle Scholar
  30. Fulkerson DR (1966) Flow networks and combinatorial operations research. Am Math Mon 73(2):115–138CrossRefGoogle Scholar
  31. Fulkerson DR (1968) Networks, frames, blocking systems. In: Dantzig GB, Veinott AF Jr (eds) Mathematics of the decision sciences. American Mathematical Society, Providence, RI, pp 303–335Google Scholar
  32. Fulkerson DR (1971) Blocking and anti-blocking pairs of polyhedra. Math Progr 1(2):168–194CrossRefGoogle Scholar
  33. Fulkerson DR (1972) In memoriam: Elbert Fulkerson, April 5, 1972. UnpublishedGoogle Scholar
  34. Fulkerson DR, Harding G (1976) On edge-disjoint branchings. Networks 6(2):97–104CrossRefGoogle Scholar
  35. Fulkerson DR, Harding G (1977) Maximizing the minimum source-sink path subject to a budget constraint. Math Program 13(1):116–118CrossRefGoogle Scholar
  36. Fulkerson DR, Weinberger D (1975) Blocking pairs of polyhedra arising from network flows. J Comb Theory Ser B 18:265–283CrossRefGoogle Scholar
  37. Gilmore P, Gomory R (1961) A linear programming approach to the cutting stock problem: part I. Oper Res 9(6):849–859CrossRefGoogle Scholar
  38. Gilmore P, Gomory R (1963) A linear programming approach to the cutting stock problem: part I. Oper Res 11(6):863–887CrossRefGoogle Scholar
  39. Harding G (1977) Some budgeted optimization problems and the edge-disjoint branchings problem. Unpublished doctoral dissertation, Cornell University, Ithaca, NYGoogle Scholar
  40. Harris T, Ross F (1955) Fundamentals of a method for evaluating rail net capacities. Research Memorandum RM-1573. The RAND Corporation, Santa Monica, CAGoogle Scholar
  41. Heller I (1953) On the problem of the shortest path between points. I. Abstract 664t, Bull Am Math Soc 59:551–551Google Scholar
  42. Hoffman A (1978) D. R. Fulkerson’s contributions to polyhedral combinatorics. Math Program Stud 8(1):17–23Google Scholar
  43. Hoffman A, Wolfe P (1985) History. In: Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (eds) The traveling salesman problem: a guided tour of combinatorial optimization. Wiley, New York, NY, pp 1–15Google Scholar
  44. Kelley J Jr (1961) The critical path planning and scheduling: mathematical basis. Oper Res 9(3):296–320CrossRefGoogle Scholar
  45. Kuhn H (1955) On certain convex polyhedra. Abstract 779t, Bull Am Math Soc 61:557–558Google Scholar
  46. Kuhn H (1991) On the origin of the Hungarian method. In: Lenstra JK, Rinnooy Kan AHG, Schrijver A (eds) History of mathematical programming: a collection of personal reminiscences. CWI and North Holland, Amsterdam, pp 77–81Google Scholar
  47. Menger K (1927) Zur allgemeinen Kurventhoerie. Fundam Math 10:96–115Google Scholar
  48. Minty G (1966) On the axiomatic foundations of the theories of directed linear graphs, electrical networks, and network programming. J Math Mechan 15(3):485–520Google Scholar
  49. Nering E, Tucker A (1993) Linear programming and related problems. Academic, Boston, MAGoogle Scholar
  50. RAND Corporation (1948) Accessed 10 Apr 2008
  51. Robacker J (1955) On network theory. Research Memorandum RM-1498. The RAND Corporation, Santa Monica, CAGoogle Scholar
  52. Robinson J (1949) On the Hamiltonian game (a traveling salesman problem). Research Memorandum RM-303. The RAND Corporation, Santa Monica, CAGoogle Scholar
  53. Rockafellar R (1969) The elementary vectors of a subspace of Rn. In: Bose RC, Dowling TA (eds) Combinatorial mathematics and its applications. University of North Carolina Press, New York, NY, pp 104–127Google Scholar
  54. Ryser H (1977) In memoriam. D. Ray Fulkerson, 1924–1976. J Comb Theory Ser B 23:1–2CrossRefGoogle Scholar
  55. Tucker A (1976) Personal letter to L.J. Billera and W.H. LucasGoogle Scholar
  56. Veinott A (ed) (1976) Math Oper Res 1(4)Google Scholar
  57. Weinberger D (1973) Investigations in the theory of blocking pairs of polyhedra. Unpublished doctoral dissertation, Cornell University, Ithaca, NYGoogle Scholar
  58. Williamson D (2002) The primal-dual method for approximation algorithms. Math Program B 91(3):447–478CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Robert G. Bland
    • 1
  • James B. Orlin
    • 2
  1. 1.Cornell UniversityIthacaUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations