SCLP-Simplex Algorithm for Robust Fluid Processing Networks

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Détails bibliographiques
Auteurs principaux:	Shindin, Evgeny, Gigi, Roi Ben, Boni, Odellia
Format:	Preprint
Publié:	2024
Sujets:	Optimization and Control
Accès en ligne:	Acceder al recurso
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author	Shindin, Evgeny Gigi, Roi Ben Boni, Odellia
author_facet	Shindin, Evgeny Gigi, Roi Ben Boni, Odellia
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2412_00901
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	SCLP-Simplex Algorithm for Robust Fluid Processing Networks Shindin, Evgeny Gigi, Roi Ben Boni, Odellia Optimization and Control 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.
title	SCLP-Simplex Algorithm for Robust Fluid Processing Networks
topic	Optimization and Control
url	https://arxiv.org/abs/2412.00901

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