In a recent paper Gutirrez et al. [1] show that the lot-sizing problem with inventory bounds can be solved in O(TlogT) time. In this note we show that their algorithm does not lead to an optimal solution in general.

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van den Heuvel, M. G. W., Gutiérrez, J. M., & Hwang, H.-C. (2011). Note on "an efficient approach for solving the lot-sizing problem with time-varying storage capacities". European Journal of Operational Research, 213(2), 455–457. doi:10.1016/j.ejor.2011.04.002