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The Sharing Problem

Author

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  • J. Randall Brown

    (Kent State University, Kent, Ohio)

Abstract

Many important problems are concerned with the equitable distribution of resources. A new approach to resource distribution problems is presented as a network flow problem with a maximum objective function. The value of the smallest linear tradeoff function at the terminal points in a capacitated network is maximized. We develop a polynomially bounded algorithm and give computational experience. We illustrate the importance and usefulness of the sharing-problem model by considering the equitable distribution of coal during a prolonged coal strike.

Suggested Citation

  • J. Randall Brown, 1979. "The Sharing Problem," Operations Research, INFORMS, vol. 27(2), pages 324-340, April.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:2:p:324-340
    DOI: 10.1287/opre.27.2.324
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    Citations

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    Cited by:

    1. 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.
    2. Rahmi İlkılıç & Çağatay Kayı, 2014. "Allocation rules on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 877-892, December.
    3. Csoka, Péter & Herings, P. Jean-Jacques, 2016. "Decentralized Clearing in Financial Networks (RM/16/005-revised-)," Research Memorandum 037, Maastricht University, Graduate School of Business and Economics (GSBE).
    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. Itoh, Takeshi & Ishii, Hiroaki, 1997. "Fuzzy sharing problem by possibility measure," European Journal of Operational Research, Elsevier, vol. 102(3), pages 648-656, November.
    6. Péter Csóka & P. Jean-Jacques Herings, 2018. "Decentralized Clearing in Financial Networks," Management Science, INFORMS, vol. 64(10), pages 4681-4699, October.
    7. Ahuja, Ravindra K., 1997. "The balanced linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 29-38, August.
    8. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    9. 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.
    10. David Hartvigsen, 1998. "A Submodular Optimization Problem with Side Constraints," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 661-679, August.
    11. Endre Bjørndal & Kurt Jörnsten, 2010. "Flow sharing and bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 11-28, March.
    12. 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.
    13. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    14. 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.
    15. Wang, Yang & Wu, Qinghua & Glover, Fred, 2017. "Effective metaheuristic algorithms for the minimum differential dispersion problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 829-843.

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