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Minimum variance allocation among constrained intervals

Author

Listed:
  • Hsin-Min Sun

    (National University of Tainan)

  • Ruey-Lin Sheu

    (National Cheng Kung University)

Abstract

We propose a weighted minimum variance allocation model, denoted by WMVA, which distributes an amount of a divisible resource as fairly as possible while satisfying all demand intervals. We show that the problem WMVA has a unique optimal solution and it can be characterized by the uniform distribution property (UDP in short). Based on the UDP property, we develop an efficient algorithm. Theoretically, our algorithm has a worst-case $$O(n^2)$$ O ( n 2 ) complexity, but we prove that, subject to slight conditions, the worst case cannot happen on a 64-bit computer when the problem dimension is greater than 129. We provide extensive simulation results to support the argument and it explains why, in practice, our algorithm runs significantly faster than most existing algorithms, including many O(n) algorithms.

Suggested Citation

  • Hsin-Min Sun & Ruey-Lin Sheu, 2019. "Minimum variance allocation among constrained intervals," Journal of Global Optimization, Springer, vol. 74(1), pages 21-44, May.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:1:d:10.1007_s10898-019-00748-3
    DOI: 10.1007/s10898-019-00748-3
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    References listed on IDEAS

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    1. K. C. Kiwiel, 2008. "Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 445-458, March.
    2. 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.
    3. Patriksson, Michael & Strömberg, Christoffer, 2015. "Algorithms for the continuous nonlinear resource allocation problem—New implementations and numerical studies," European Journal of Operational Research, Elsevier, vol. 243(3), pages 703-722.
    4. K. C. Kiwiel, 2007. "On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 549-554, September.
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