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Journal of Optimization Theory and Applications

, Volume 80, Issue 2, pp 289–297 | Cite as

Solving the 0–1 proportional knapsack problem by sampling

  • M. Penn
  • D. Hasson
  • M. Avriel
Contributed Papers

Abstract

In this paper, we deal with the proportional knapsack problem that is a variation on the ordinary knapsack problem. In the proportional knapsack problem, we look at filling an urn with objects having two characteristics: color and weight. The colors of the objects in the urn should be proportional to the distribution of the colors in the object universe, and the total weight of the objects in the urn should be as close as possible to the capacity of the urn. The formulation of the problem was motivated by a real-life application from the area of finance, called a dollar roll. We show that the proportional knapsack problem is NP-hard, and then, using sampling, develop a heuristic procedure for solving the problem.

Key Words

Knapsack problems heuristic algorithms sampling 

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References

  1. 1.
    Martello, S., andToth, P.,Knapsack Problems: Algorithms and Computer Implementations, John Wiley and Sons, Chichester, England, 1990.Google Scholar
  2. 2.
    Garey, M. R., andJohnson, D. S.,Computer and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, California, 1979.Google Scholar
  3. 3.
    Karp, R. M.,Reducibility among Combinatorial Problems, Complexity of Computer computations, Edited by R. E. Miller and J. W. Thatcher, Plenum Press, New York, pp. 85–103, 1972.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • M. Penn
    • 1
  • D. Hasson
    • 1
  • M. Avriel
    • 1
  1. 1.Faculty of Industrial Engineering and ManagementTechnionHaifaIsrael

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