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An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns

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  • Robert L. Carraway
  • Robert L. Schmidt
  • Lawrence R. Weatherford

Abstract

We consider the stochastic linear knapsack problem in which costs are known with certainty but returns are independent, normally distributed random variables. The objective is to maximize the probability that the overall return equals or exceeds a specified target value. A previously proposed preference order dynamic programming‐based algorithm has been shown to be potentially suboptimal. We offer an alternative hybrid DP/branch‐and‐bound algorithm that both guarantees optimality and significantly outperforms generating the set of Pareto optimal returns.© 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Robert L. Carraway & Robert L. Schmidt & Lawrence R. Weatherford, 1993. "An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 161-173, March.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:2:p:161-173
    DOI: 10.1002/nav.3220400203
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    References listed on IDEAS

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    Cited by:

    1. Yasemin Merzifonluoglu & Joseph Geunes, 2021. "The Risk-Averse Static Stochastic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 931-948, July.
    2. Will Ma, 2018. "Improvements and Generalizations of Stochastic Knapsack and Markovian Bandits Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 789-812, August.
    3. Brian C. Dean & Michel X. Goemans & Jan Vondrák, 2008. "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 945-964, November.
    4. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    5. Taylan İlhan & Seyed M. R. Iravani & Mark S. Daskin, 2011. "TECHNICAL NOTE---The Adaptive Knapsack Problem with Stochastic Rewards," Operations Research, INFORMS, vol. 59(1), pages 242-248, February.
    6. Jian Li & Amol Deshpande, 2019. "Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 354-375, February.
    7. Stefanie Kosuch & Abdel Lisser, 2010. "Upper bounds for the 0-1 stochastic knapsack problem and a B&B algorithm," Annals of Operations Research, Springer, vol. 176(1), pages 77-93, April.

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