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Tight bounds for periodicity theorems on the unbounded Knapsack problem

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  • Huang, Ping H.
  • Lawley, Mark
  • Morin, Thomas

Abstract

Three new bounds for periodicity theorems on the unbounded Knapsack problem are developed. Periodicity theorems specify when it is optimal to pack one unit of the best item (the one with the highest profit-to-weight ratio). The successive applications of periodicity theorems can drastically reduce the size of the Knapsack problem under analysis, theoretical or empirical. We prove that each new bound is tight in the sense that no smaller bound exists under the given condition.

Suggested Citation

  • Huang, Ping H. & Lawley, Mark & Morin, Thomas, 2011. "Tight bounds for periodicity theorems on the unbounded Knapsack problem," European Journal of Operational Research, Elsevier, vol. 215(2), pages 319-324, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:2:p:319-324
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    References listed on IDEAS

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