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Minimum variance allocation among constrained intervals

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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 \(O(n^2)\) 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.

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Acknowledgements

The authors thank the reviewers for reading this article and for making suggestions. Thanks also to Professor Silva for providing the source codes for experiment.

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Authors and Affiliations

  1. Department of Applied Mathematics, National University of Tainan, Tainan, 70005, Taiwan

    Hsin-Min Sun

  2. Department of Mathematics, National Cheng Kung University, Tainan, 70101, Taiwan

    Ruey-Lin Sheu

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  1. Hsin-Min Sun
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  2. Ruey-Lin Sheu
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Correspondence to Hsin-Min Sun.

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Sun, HM., Sheu, RL. Minimum variance allocation among constrained intervals. J Glob Optim 74, 21–44 (2019). https://doi.org/10.1007/s10898-019-00748-3

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  • DOI: https://doi.org/10.1007/s10898-019-00748-3

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