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A unified method for a class of convex separable nonlinear knapsack problems

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  • Zhang, Bin
  • Hua, Zhongsheng

Abstract

In this paper, a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems, which are characterized by positive marginal cost (PMC) and increasing marginal loss-cost ratio (IMLCR). By taking advantage of these two characteristics, the proposed algorithm is applicable to the problem with equality or inequality constraints. In contrast to the methods based on Karush-Kuhn-Tucker (KKT) conditions, our approach has linear computation complexity. Numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems.

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  • Zhang, Bin & Hua, Zhongsheng, 2008. "A unified method for a class of convex separable nonlinear knapsack problems," European Journal of Operational Research, Elsevier, vol. 191(1), pages 1-6, November.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:1:p:1-6
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    Cited by:

    1. Zhang, Bin, 2012. "Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 426-434.
    2. Zhang, Bin & Du, Shaofu, 2010. "Multi-product newsboy problem with limited capacity and outsourcing," European Journal of Operational Research, Elsevier, vol. 202(1), pages 107-113, April.
    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.
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    5. Yang, Cheng-Hu & Wang, Hai-Tang & Ma, Xin & Talluri, Srinivas, 2023. "A data-driven newsvendor problem: A high-dimensional and mixed-frequency method," International Journal of Production Economics, Elsevier, vol. 266(C).
    6. Zhang, Bin & Xu, Xiaoyan & Hua, Zhongsheng, 2009. "A binary solution method for the multi-product newsboy problem with budget constraint," International Journal of Production Economics, Elsevier, vol. 117(1), pages 136-141, January.

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