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Dynamic Programming Algorithms for the Integer Programming Problem—I: The Integer Programming Problem Viewed as a Knapsack Type Problem

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  • Jeremy F. Shapiro

    (Massachusetts Institute of Technology)

Abstract

Gomory has transformed the integer programming problem into a related group optimization problem which can be more easily solved. An optimal solution to the group problem is optimal for the integer programming problem from which it is derived if the solution is feasible. An algorithm (IP Algorithm I) for solving the group optimization problem is developed, and sufficient conditions on its use are given. The usefulness of IP Algorithm I is extended by amending it to find alternative optima. In a subsequent paper, this algorithm is extended to an algorithm that can solve any integer programming problem.

Suggested Citation

  • Jeremy F. Shapiro, 1968. "Dynamic Programming Algorithms for the Integer Programming Problem—I: The Integer Programming Problem Viewed as a Knapsack Type Problem," Operations Research, INFORMS, vol. 16(1), pages 103-121, February.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:1:p:103-121
    DOI: 10.1287/opre.16.1.103
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    Cited by:

    1. Hansen, Paul & Ryan, Jennifer, 1996. "Testing integer knapsacks for feasibility," European Journal of Operational Research, Elsevier, vol. 88(3), pages 578-582, February.
    2. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    3. Maxence Delorme & Manuel Iori, 2020. "Enhanced Pseudo-polynomial Formulations for Bin Packing and Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 101-119, January.

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