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The Knapsack Sharing Problem

Author

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  • J. Randall Brown

    (Kent State University, Kent, Ohio)

Abstract

The knapsack sharing problem has a utility or tradeoff function for each variable and seeks to maximize the value of the smallest tradeoff function (a maximin objective function). A single constraint places an upper bound on the sum of the non-negative variables. We develop efficient algorithms for piecewise linear, nonlinear, and piecewise nonlinear tradeoff functions and for any knapsack sharing problem with integer variables. These algorithms for the knapsack sharing problem extend the sharing problem algorithm in a companion paper to any piecewise linear, nonlinear, or piecewise nonlinear tradeoff functions.

Suggested Citation

  • J. Randall Brown, 1979. "The Knapsack Sharing Problem," Operations Research, INFORMS, vol. 27(2), pages 341-355, April.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:2:p:341-355
    DOI: 10.1287/opre.27.2.341
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    Cited by:

    1. Hervé Moulin & Jay Sethuraman, 2013. "The Bipartite Rationing Problem," Operations Research, INFORMS, vol. 61(5), pages 1087-1100, October.
    2. Yamada, Takeo & Futakawa, Mayumi & Kataoka, Seiji, 1998. "Some exact algorithms for the knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 177-183, April.
    3. Lisa M. Betts & J. Randall Brown & Hanan Luss, 1994. "Minimax resource allocation problems with ordering constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 719-738, October.
    4. Pursals, Salvador Casadesús & Garzón, Federico Garriga, 2009. "Optimal building evacuation time considering evacuation routes," European Journal of Operational Research, Elsevier, vol. 192(2), pages 692-699, January.
    5. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    6. Ahuja, Ravindra K., 1997. "The balanced linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 29-38, August.
    7. Mhand Hifi & Slim Sadfi, 2002. "The Knapsack Sharing Problem: An Exact Algorithm," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 35-54, March.
    8. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    9. Amirgaliyeva, Zhazira & Mladenović, Nenad & Todosijević, Raca & Urošević, Dragan, 2017. "Solving the maximum min-sum dispersion by alternating formulations of two different problems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 444-459.
    10. Florian Biermann & Victor Naroditskiy & Maria Polukarov & Alex Rogers & Nicholas Jennings, 2011. "Task Assignment with Autonomous and Controlled Agents," Working Papers 004-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.

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