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A Heuristic Ceiling Point Algorithm for General Integer Linear Programming

Author

Listed:
  • Robert M. Saltzman

    (School of Business, San Francisco State University, San Francisco, California 94132)

  • Frederick S. Hillier

    (Department of Operations Research, Stanford University, Stanford, California 94305)

Abstract

This paper first examines the role of ceiling points in solving a pure, general integer linear programming problem (P). Several kinds of ceiling points are defined and analyzed and one kind called "feasible 1-ceiling points" proves to be of special interest. We demonstrate that all optimal solutions for a problem (P) whose feasible region is nonempty and bounded are feasible 1-ceiling points. Consequently, such a problem may be solved by enumerating just its feasible 1-ceiling points. The paper then describes an algorithm called the Heuristic Ceiling Point Algorithm (HCPA) which approximately solves (P) by searching only for feasible 1-ceiling points relatively near the optimal solution for the LP-relaxation; such solutions are apt to have a high (possibly even optimal) objective function value. The results of applying the HCPA to 48 test problems taken from the literature indicate that this approach usually yields a very good solution with a moderate amount of computational effort.

Suggested Citation

  • Robert M. Saltzman & Frederick S. Hillier, 1992. "A Heuristic Ceiling Point Algorithm for General Integer Linear Programming," Management Science, INFORMS, vol. 38(2), pages 263-283, February.
  • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:2:p:263-283
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    File URL: http://dx.doi.org/10.1287/mnsc.38.2.263
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    References listed on IDEAS

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    1. Leech, Dennis, 1985. "Ownership Concentration and the Theory of the Firm : A Simple-Game-Theoretic Approach to Applied US Corporations in the 1930's," The Warwick Economics Research Paper Series (TWERPS) 262, University of Warwick, Department of Economics.
    2. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    Citations

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    Cited by:

    1. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2013. "A new class of functions for measuring solution integrality in the Feasibility Pump approach: Complete Results," DIAG Technical Reports 2013-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Joseph, Anito & Gass, Saul I. & Bryson, Noel, 1998. "An objective hyperplane search procedure for solving the general all-integer linear programming (ILP) problem," European Journal of Operational Research, Elsevier, vol. 104(3), pages 601-614, February.
    3. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "New concave penalty functions for improving the Feasibility Pump," DIS Technical Reports 2010-10, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "Feasibility Pump-Like Heuristics for Mixed Integer Problems," DIS Technical Reports 2010-15, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    5. Joseph, A. & Gass, S. I., 2002. "A framework for constructing general integer problems with well-determined duality gaps," European Journal of Operational Research, Elsevier, vol. 136(1), pages 81-94, January.
    6. repec:spr:joheur:v:23:y:2017:i:4:d:10.1007_s10732-017-9336-y is not listed on IDEAS
    7. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2011. "A new class of functions for measuring solution integrality in the Feasibility Pump approach," DIS Technical Reports 2011-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    8. Mansini, Renata & Savelsbergh, Martin W.P. & Tocchella, Barbara, 2012. "The supplier selection problem with quantity discounts and truckload shipping," Omega, Elsevier, vol. 40(4), pages 445-455.

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