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TECHNICAL NOTE---The Adaptive Knapsack Problem with Stochastic Rewards

Author

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  • Taylan İlhan

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Seyed M. R. Iravani

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Mark S. Daskin

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

Given a set of items with associated deterministic weights and random rewards, the adaptive stochastic knapsack problem (adaptive SKP) maximizes the probability of reaching a predetermined target reward level when items are inserted sequentially into a capacitated knapsack before the reward of each item is realized. This model arises in resource allocation problems that permit or require sequential allocation decisions in a probabilistic setting. One particular application is in obsolescence inventory management. In this paper, the adaptive SKP is formulated as a dynamic programming (DP) problem for discrete random rewards. The paper also presents a heuristic that mixes adaptive and static policies to overcome the “curse of dimensionality” in the DP. The proposed heuristic is extended to problems with normally distributed random rewards. The heuristic can solve large problems quickly, and its solution always outperforms a static policy. The numerical study indicates that a near-optimal solution can be obtained by using an algorithm with limited look-ahead capabilities.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:1:p:242-248
    DOI: 10.1287/opre.1100.0857
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    References listed on IDEAS

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    Cited by:

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    3. 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.
    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.

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