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Algorithms for Separable Nonlinear Resource Allocation Problems

Author

Listed:
  • Muralidharan S. Kodialam

    (Bell Labs, Lucent Technologies, Holmdel, New Jersey)

  • Hanan Luss

    (AT&T Labs, Holmdel, New Jersey)

Abstract

We consider a simple resource allocation problem with a single resource constraint. The objective function is composed of separable, convex performance functions, one for each activity. Likewise, the constraint has separable, convex resource-usage functions, one for each activity. The objective is to minimize the sum of the performance functions, subject to satisfying the resource constraint and nonnegativity constraints. This problem extends the well-studied problem in which the resource constraint is linear. We present several algorithms to solve the problem. These algorithms extend approaches developed for the linearly constrained problem. They can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables. We provide several examples for illustration purposes, present computational results, and highlight the similarities and differences among the algorithms.

Suggested Citation

  • Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:2:p:272-284
    DOI: 10.1287/opre.46.2.272
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    References listed on IDEAS

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    1. Christopher S. Tang, 1988. "A Max-Min Allocation Problem: Its Solutions and Applications," Operations Research, INFORMS, vol. 36(2), pages 359-367, April.
    2. Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    3. Czuchra, Waldemar, 1986. "A graphical method to solve a maximin allocation problem," European Journal of Operational Research, Elsevier, vol. 26(2), pages 259-261, August.
    4. John M. Einbu, 1981. "Technical Note—Extension of the Luss-Gupta Resource Allocation Algorithm by Means of First Order Approximation Techniques," Operations Research, INFORMS, vol. 29(3), pages 621-626, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

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    2. De Waegenaere, A.M.B. & Wielhouwer, J.L., 2001. "A Partial Ranking Algorithm for Resource Allocation Problems," Other publications TiSEM 8b2e0185-36f9-43df-8a3d-d, Tilburg University, School of Economics and Management.
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    6. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    7. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    8. De Waegenaere, A.M.B. & Wielhouwer, J.L., 2001. "A Partial Ranking Algorithm for Resource Allocation Problems," Discussion Paper 2001-40, Tilburg University, Center for Economic Research.
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    14. Zhang, Jianzhong & Xu, Chengxian, 2010. "Inverse optimization for linearly constrained convex separable programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 671-679, February.
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    16. AgralI, Semra & Geunes, Joseph, 2009. "Solving knapsack problems with S-curve return functions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 605-615, March.
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    20. Selcuk Karabati & Panagiotis Kouvelis & Gang Yu, 2001. "A Min-Max-Sum Resource Allocation Problem and Its Applications," Operations Research, INFORMS, vol. 49(6), pages 913-922, December.

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