SCLP-Simplex Algorithm for Robust Fluid Processing Networks

TL;DR

This paper introduces a novel algorithmic approach for solving robust fluid processing network models formulated as Separated Continuous Linear Programming problems, addressing scalability and degeneracy issues in stochastic environments.

Contribution

The paper develops theoretical results and an algorithm that maintains the size of the nominal SCLP problem and avoids degeneracy in its robust counterpart.

Findings

The proposed method preserves problem dimensions.

It effectively handles stochastic variability in processing networks.

The algorithm avoids degeneracy issues in robust SCLP solutions.

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.