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An Algorithm for the Solution of Mixed Integer Programming Problems

Author

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  • Norman J. Driebeek

    (Arthur D. Little, Inc., Cambridge, Massachusetts)

Abstract

An algorithm is presented for the solution of mixed integer programming problems. The method was developed to solve primarily those programming problems which contain a large number of continuous variables in addition to a few variables that are restricted to discrete values. The algorithm solves a continuous, non-integer constrained problem first. Subsequently, a search for the optimum integer solution is made on the basis of those changes in the value of the objective function that are produced by activating integer constraints.

Suggested Citation

  • Norman J. Driebeek, 1966. "An Algorithm for the Solution of Mixed Integer Programming Problems," Management Science, INFORMS, vol. 12(7), pages 576-587, March.
    • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:7:p:576-587
    DOI: 10.1287/mnsc.12.7.576
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    Cited by:

    1. Bożena Staruch & Bogdan Staruch, 2021. "Competence-based assignment of tasks to workers in factories with demand-driven manufacturing," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 553-565, June.
    2. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    3. Renata Mansini & Roberto Zanotti, 2020. "A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1061-1079, October.
    4. Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    5. Jawahar, N. & Balaji, A.N., 2009. "A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge," European Journal of Operational Research, Elsevier, vol. 194(2), pages 496-537, April.
    6. Sun, Minghe, 2002. "The transportation problem with exclusionary side constraints and two branch-and-bound algorithms," European Journal of Operational Research, Elsevier, vol. 140(3), pages 629-647, August.
    7. Hajra Khan & Imran Fareed Nizami & Saeed Mian Qaisar & Asad Waqar & Moez Krichen & Abdulaziz Turki Almaktoom, 2022. "Analyzing Optimal Battery Sizing in Microgrids Based on the Feature Selection and Machine Learning Approaches," Energies, MDPI, vol. 15(21), pages 1-22, October.
    8. Kurt M. Bretthauer & A. Victor Cabot & M. A. Venkataramanan, 1994. "An algorithm and new penalties for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 435-454, April.
    9. J. T. Linderoth & M. W. P. Savelsbergh, 1999. "A Computational Study of Search Strategies for Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 173-187, May.
    10. Alejandro Marcos Alvarez & Quentin Louveaux & Louis Wehenkel, 2017. "A Machine Learning-Based Approximation of Strong Branching," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 185-195, February.
    11. 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.
    12. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.

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