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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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    1. 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.
    2. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    3. Richard Van Slyke & Yi Young, 2000. "Finite Horizon Stochastic Knapsacks with Applications to Yield Management," Operations Research, INFORMS, vol. 48(1), pages 155-172, February.
    4. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
    5. Mordechai I. Henig, 1990. "Risk Criteria in a Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 38(5), pages 820-825, October.
    6. 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.
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    Cited by:

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    2. Keskin, Burcu B. & Griffin, Emily C. & Prell, Jonathan O. & Dilkina, Bistra & Ferber, Aaron & MacDonald, John & Hilend, Rowan & Griffis, Stanley & Gore, Meredith L., 2023. "Quantitative Investigation of Wildlife Trafficking Supply Chains: A Review," Omega, Elsevier, vol. 115(C).
    3. 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.
    4. 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.

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