Mathematical Programming

, Volume 13, Issue 1, pp 255–271 | Cite as

Fractional knapsack problems

  • Hiroaki Ishii
  • Toshihide Ibaraki
  • Hisashi Mine


The fractional knapsack problem to obtain an integer solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. A modification of the Dinkelbach's algorithm [3] is proposed to exploit the fact that good feasible solutions are easily obtained for both the fractional knapsack problem and the ordinary knapsack problem. An upper bound of the number of iterations is derived. In particular it is clarified how optimal solutions depend on the right hand side of the constraint; a fractional knapsack problem reduces to an ordinary knapsack problem if the right hand side exceeds a certain bound.

Key words

Fractional knapsack problem Knapsack problem Greedy solution Integer programming 


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Copyright information

© The Mathematical Programming Society 1977

Authors and Affiliations

  • Hiroaki Ishii
    • 1
  • Toshihide Ibaraki
    • 2
  • Hisashi Mine
    • 2
  1. 1.Osaka UniversitySuita-city, OsakaJapan
  2. 2.Kyoto UniversityKyoto-city, KyotoJapan

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