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Risk Criteria in a Stochastic Knapsack Problem

Author

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  • Mordechai I. Henig

    (Tel-Aviv University, Tel-Aviv, Israel)

Abstract

We consider an investor who wants to allocate funds among several projects. Each project is expected to yield a certain reward, and the objective is that a total reward will achieve a certain given amount, called the target. This problem is relatively easy to solve when rewards are deterministic, but may be hard in a more realistic setting when the rewards are stochastic and the investor wants to maximize the probability of attaining the target. We show that, by combining dynamic programming with a search procedure, the stochastic version of the problem can be solved relatively fast when rewards are normally distributed. The procedure is also useful for other risk criteria, which involve both the mean and the variance of the total reward.

Suggested Citation

  • Mordechai I. Henig, 1990. "Risk Criteria in a Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 38(5), pages 820-825, October.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:5:p:820-825
    DOI: 10.1287/opre.38.5.820
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    Citations

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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. S Das & D Ghosh, 2003. "Binary knapsack problems with random budgets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 970-983, September.
    3. Perboli, Guido & Tadei, Roberto & Gobbato, Luca, 2014. "The Multi-Handler Knapsack Problem under Uncertainty," European Journal of Operational Research, Elsevier, vol. 236(3), pages 1000-1007.
    4. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    5. Sam Ransbotham & Ishwar Murthy & Sabyasachi Mitra & Sridhar Narasimhan, 2011. "Sequential Grid Computing: Models and Computational Experiments," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 174-188, May.
    6. João Claro & Jorge Sousa, 2010. "A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 427-450, July.
    7. Chernonog, Tatyana & Avinadav, Tal, 2014. "Profit criteria involving risk in price setting of virtual products," European Journal of Operational Research, Elsevier, vol. 236(1), pages 351-360.
    8. Asaf Levin & Aleksander Vainer, 2018. "Lower bounds on the adaptivity gaps in variants of the stochastic knapsack problem," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 794-813, April.
    9. Range, Troels Martin & Kozlowski, Dawid & Petersen, Niels Chr., 2017. "A shortest-path-based approach for the stochastic knapsack problem with non-decreasing expected overfilling costs," Discussion Papers on Economics 9/2017, University of Southern Denmark, Department of Economics.
    10. 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.
    11. Nicholas G. Hall & Daniel Zhuoyu Long & Jin Qi & Melvyn Sim, 2015. "Managing Underperformance Risk in Project Portfolio Selection," Operations Research, INFORMS, vol. 63(3), pages 660-675, June.
    12. Wang, Xin & Kuo, Yong-Hong & Shen, Houcai & Zhang, Lianmin, 2021. "Target-oriented robust location–transportation problem with service-level measure," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 1-20.
    13. 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.
    14. Murthy, Ishwar & Sarkar, Sumit, 1997. "Exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function," European Journal of Operational Research, Elsevier, vol. 103(1), pages 209-229, November.
    15. 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.
    16. 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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