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Discrete Programming by the Filter Method

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  • Egon Balas

    (Stanford University, Stanford, California)

Abstract

In this paper (section 1) a two-phase procedure, the filter method or accelerated additive algorithm, is proposed for solving linear programs with zero-one variables. In Phase I an auxiliary problem is constructed that, in Phase II, is used to “filter” the solutions to which the tests of the additive algorithm are to be applied. The filter method is then extended (section 2) by J. F. Benders’ partitioning procedure to the mixed-integer zero-one case, as well as to general integer and mixed-integer programs. Finally, a specialized version of this method is used (section 3) to tackle a general machine-sequencing model, formulated as the problem of finding a minimaximal path in a disjunctive graph.

Suggested Citation

  • Egon Balas, 1967. "Discrete Programming by the Filter Method," Operations Research, INFORMS, vol. 15(5), pages 915-957, October.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:5:p:915-957
    DOI: 10.1287/opre.15.5.915
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    Cited by:

    1. 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.
    2. Jouglet, Antoine & Carlier, Jacques, 2011. "Dominance rules in combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 212(3), pages 433-444, August.
    3. Balev, Stefan & Yanev, Nicola & Freville, Arnaud & Andonov, Rumen, 2008. "A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 63-76, April.
    4. Jiang, Bo & Tzavellas, Hector, 2023. "Optimal liquidity allocation in an equity network," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 286-294.
    5. Mohammadi Bidhandi, Hadi & Mohd. Yusuff, Rosnah & Megat Ahmad, Megat Mohamad Hamdan & Abu Bakar, Mohd Rizam, 2009. "Development of a new approach for deterministic supply chain network design," European Journal of Operational Research, Elsevier, vol. 198(1), pages 121-128, October.
    6. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    7. Nikolaos Argyris & José Figueira & Alec Morton, 2011. "Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem," Journal of Global Optimization, Springer, vol. 49(2), pages 213-235, February.
    8. van Dam, Wim & Telgen, Jan, 1978. "Some Computational Experiments With A Primal-Dual Surrogate Simplex Algorithm," Econometric Institute Archives 272174, Erasmus University Rotterdam.

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