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The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options

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  • Tianke Feng
  • Joseph C. Hartman

Abstract

This article generalizes the dynamic and stochastic knapsack problem by allowing the decision‐maker to postpone the accept/reject decision for an item and maintain a queue of waiting items to be considered later. Postponed decisions are penalized with delay costs, while idle capacity incurs a holding cost. This generalization addresses applications where requests of scarce resources can be delayed, for example, dispatching in logistics and allocation of funding to investments. We model the problem as a Markov decision process and analyze it through dynamic programming. We show that the optimal policy with homogeneous‐sized items possesses a bithreshold structure, despite the high dimensionality of the decision space. Finally, the value (or price) of postponement is illustrated through numerical examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 267–292, 2015

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  • Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:4:p:267-292
    DOI: 10.1002/nav.21627
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