SCLP-Simplex Algorithm for Robust Fluid Processing Networks

Evgeny Shindin; Roi Ben Gigi; Odellia Boni

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arXiv · 2412.00901

SCLP-Simplex Algorithm for Robust Fluid Processing Networks

Evgeny Shindin·Roi Ben Gigi·Odellia Boni

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Abstract

Fluid models provide a tractable approach to approximate multiclass processing networks. This tractability is a due to the fact that optimal control for such models is a solution of a Separated Continuous Linear Programming (SCLP) problem. Recently developed revised SCLP-simplex algorithm allows to exactly solve very large instances of SCLPs in a reasonable time. Furthermore, to deal with the inherent stochasticity in arrival and service rates in processing networks, robust optimization approach is applied to SCLP models. However, a robust counterpart of SCLP problem has two important drawbacks limiting its tractability. First, the robust counterpart of SCLP problem is a huge SCLP problem itself, that can be in several orders of magnitude bigger then the nominal SCLP problem. Second, robust counterpart of SCLP is a degenerate optimization problem, that is not suitable for revised SCLP-simplex algorithm. In this paper we develop theoretical results and a corresponding algorithm that allows to preserve dimensions of nominal SCLP problem and avoid degeneracy issues during solution of its robust counterpart.

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BibTeX RIS

Evgeny Shindin, Roi Ben Gigi, Odellia Boni. 2024-12-01. SCLP-Simplex Algorithm for Robust Fluid Processing Networks. https://arxiv.org/abs/2412.00901

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