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A Finite Renewal Algorithm for the Knapsack and Turnpike Models

Author

Listed:
  • Jeremy F. Shapiro

    (Stanford University, Stanford, California)

  • Harvey M. Wagner

    (Stanford University, Stanford, California)

Abstract

The mathematical and algorithmic connections between the knapsack problem and a fundamental renewal-type problem are established. The renewal point of view leads to an efficient computational result and is based in part on an extension of a turnpike theorem shown by Gilmore and Gomory. The distribution of effort model is examined briefly by means of the renewal approach so as to add new insight to the mathematical structure of this problem.

Suggested Citation

  • Jeremy F. Shapiro & Harvey M. Wagner, 1967. "A Finite Renewal Algorithm for the Knapsack and Turnpike Models," Operations Research, INFORMS, vol. 15(2), pages 319-341, April.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:2:p:319-341
    DOI: 10.1287/opre.15.2.319
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    Cited by:

    1. Ryan, Sarah M., 1998. "Forecast frequency in rolling horizon hedging heuristics for capacity expansion," European Journal of Operational Research, Elsevier, vol. 109(3), pages 550-558, September.
    2. Becker, Henrique & Buriol, Luciana S., 2019. "An empirical analysis of exact algorithms for the unbounded knapsack problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 84-99.
    3. James C. Bean & Jack R. Lohmann & Robert L. Smith, 1994. "Equipment replacement under technological change," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 117-128, February.
    4. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.

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