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An adaptive stochastic knapsack problem

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  • Chen, Kai
  • Ross, Sheldon M.

Abstract

We consider a stochastic knapsack problem in which the event of overflow results in the problem ending with zero return. We assume that there are n types of items available where each type has infinite supply. An item has an exponentially distributed random weight with a known mean depending on its type and the item’s value is proportional to its weight with a given factor depending on the item’s type. We have to make a decision on each stage whether to stop, or continue to put an item of a selected type in the knapsack. An item’s weight is learned when placed to the knapsack. The objective of this problem is to find a policy that maximizes the expected total values. Using the framework of dynamic programming, the optimal policy is found when n=2 and a heuristic policy is suggested for n>2.

Suggested Citation

  • Chen, Kai & Ross, Sheldon M., 2014. "An adaptive stochastic knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(3), pages 625-635.
    • Handle: RePEc:eee:ejores:v:239:y:2014:i:3:p:625-635
    DOI: 10.1016/j.ejor.2014.06.027
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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. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    3. Clifford Stein & Van-Anh Truong & Xinshang Wang, 2020. "Advance Service Reservations with Heterogeneous Customers," Management Science, INFORMS, vol. 66(7), pages 2929-2950, July.
    4. Kai Chen & Sheldon M. Ross, 2014. "The burglar problem with multiple options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 359-364, August.
    5. 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.

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