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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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    2. Li, Linda & Firouz, Mohammad & Ahmed, Abdulaziz & Delen, Dursun, 2023. "On the Egalitarian–Utilitarian spectrum in stochastic capacitated resource allocation problems," International Journal of Production Economics, Elsevier, vol. 262(C).
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    13. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    14. DePaolo, Concetta A. & Rader, David Jr., 2007. "A heuristic algorithm for a chance constrained stochastic program," European Journal of Operational Research, Elsevier, vol. 176(1), pages 27-45, January.
    15. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    16. 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.
    17. Niederhoff, Julie A., 2007. "Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions," European Journal of Operational Research, Elsevier, vol. 176(2), pages 941-955, January.
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