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A stochastic linear knapsack problem

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  • Shōgo Shiode
  • Hiroaki Ishi
  • Toshio Nishida

Abstract

In this article we consider a stochastic version of the continuous linear knapsack problem, i.e., a model with a random linear constraint, and provide an efficient algorithm for solving it. An original problem Po is first transformed into a deterministic equivalent problem Po. Furthermore, by a change of variables, Po is transformed into P. Then, in order to solve P, a subproblem P(μ.) with positive parameter μ is introduced, and a close relation between P and P(μ) is clarified. Furthermore, an auxiliary problem PR(μ) of P(μ) with positive parameter R is introduced, and a relation between PR(μ) and P(μ) is also clarified. From these relations, a direct relation connecting PR(μ) with P is derived. An efficient algorithm based on this relation for solving P is proposed. It is shown that time complexity of the algorithm is O(n log n), where n is the number of items. Finally, some further research problems are discussed.

Suggested Citation

  • Shōgo Shiode & Hiroaki Ishi & Toshio Nishida, 1987. "A stochastic linear knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 753-759, October.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:5:p:753-759
    DOI: 10.1002/1520-6750(198710)34:53.0.CO;2-0
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    1. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
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