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A Heuristic Ceiling Point Algorithm for General Integer Linear Programming

Listed author(s):
  • 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)

Registered author(s):

    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.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 38 (1992)
    Issue (Month): 2 (February)
    Pages: 263-283

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    Handle: RePEc:inm:ormnsc:v:38:y:1992:i:2:p:263-283
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