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We study the quadratic resource allocation problem and its variant with lowerand upper constraints on nested sums of variables. This problem occurs in manyapplications, in particular battery scheduling within decentralized energymanagement (DEM) for smart grids. We present an algorithm for this problem thatruns in $O(n \log n)$ time and, in contrast to existing algorithms for thisproblem, achieves this time complexity using relatively simple andeasy-to-implement subroutines and data structures. This makes our algorithmvery attractive for real-life adaptation and implementation. Numericalcomparisons of our algorithm with a subroutine for battery scheduling within anexisting tool for DEM research indicates that our algorithm significantlyreduces the overall execution time of the DEM system, especially when thebattery is expected to be completely full or empty multiple times in theoptimal schedule. Moreover, computational experiments with synthetic data showthat our algorithm outperforms the currently most efficient algorithm by morethan one order of magnitude. In particular, our algorithm is able to solves allconsidered instances with up to one million variables in less than 17 secondson a personal computer.

A fast algorithm for quadratic resource allocation problems with nested constraints