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Optimization: From Its Inception

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  • Thomas L. Magnanti

    (Department of Electrical Engineering and Computer Science and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

Optimization has been one of the most fundamental and extensive contributions of management science/operations research, with an enormous number of contributions and subfields developed by many researchers and practitioners. When the journal Management Science launched in 1954, little was known about optimization, including some results in nonlinear optimization and the simplex method and duality developed for linear programming. However, linear programming computations were limited to problems with at most 101 linear constraints. Then some early contributions by seminal researchers began to develop foundations for the field. I will review a few of these early contributions, focusing on the traveling sales problem and integer programming, decomposition, and column generation. I will summarize some research and applied contributions since then, including the enormous development of computations. I will focus on linear and integer programs with some material on combinatorial optimization.

Suggested Citation

  • Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:9:p:5349-5363
    DOI: 10.1287/mnsc.2021.3955
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    References listed on IDEAS

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    1. Egon Balas, 1971. "Intersection Cuts—A New Type of Cutting Planes for Integer Programming," Operations Research, INFORMS, vol. 19(1), pages 19-39, February.
    2. Ali Emrouznejad & Marianna Marra, 2017. "The state of the art development of AHP (1979–2017): a literature review with a social network analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6653-6675, November.
    3. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    4. Hugh Everett, 1963. "Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources," Operations Research, INFORMS, vol. 11(3), pages 399-417, June.
    5. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    6. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    7. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    8. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    9. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    10. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    11. William Orchard-Hays, 1990. "History of the Development of LP Solvers," Interfaces, INFORMS, vol. 20(4), pages 61-73, August.
    12. Egon Balas, 1965. "An Additive Algorithm for Solving Linear Programs with Zero-One Variables," Operations Research, INFORMS, vol. 13(4), pages 517-546, August.
    13. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    14. T. L. Magnanti & J. F. Shapiro & M. H. Wagner, 1976. "Generalized Linear Programming Solves the Dual," Management Science, INFORMS, vol. 22(11), pages 1195-1203, July.
    15. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    16. M. L. Balinski, 1965. "Integer Programming: Methods, Uses, Computations," Management Science, INFORMS, vol. 12(3), pages 253-313, November.
    17. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    18. A. Charnes & W. W. Cooper, 1954. "The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems," Management Science, INFORMS, vol. 1(1), pages 49-69, October.
    19. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    20. Wallace J. Hopp (Editor-in-Chief), 2004. "Ten Most Influential Papers of Management Science's First Fifty Years," Management Science, INFORMS, vol. 50(12_supple), pages 1763-1763, December.
    21. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    22. Richard M. Karp, 1977. "Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 209-224, August.
    23. Richard Bellman, 1954. "On some applications of the theory of dynamic programming to logistics," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(2), pages 141-153, June.
    24. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    25. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    26. C. E. Lemke, 1954. "The dual method of solving the linear programming problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 36-47, March.
    27. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    28. VAN ROY, Tony J. & WOLSEY, Laurence A., 1987. "Solving mixed integer programming problems using automatic reformulation," LIDAM Reprints CORE 782, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    29. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    30. Tony J. Van Roy & Laurence A. Wolsey, 1987. "Solving Mixed Integer Programming Problems Using Automatic Reformulation," Operations Research, INFORMS, vol. 35(1), pages 45-57, February.
    31. Kurt Spielberg & Monique Guignard-Spielberg, 2007. "Preface: History of integer programming: distinguished personal notes and reminiscences," Annals of Operations Research, Springer, vol. 149(1), pages 3-4, February.
    32. Gale, David, 1989. "The Theory of Linear Economic Models," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226278841, April.
    33. Harvey J. Greenberg & William P. Pierskalla, 1970. "Surrogate Mathematical Programming," Operations Research, INFORMS, vol. 18(5), pages 924-939, October.
    34. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    35. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
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