Revised SCLP-simplex Algorithm with Application to Large-Scale Fluid Processing Networks

TL;DR

This paper presents an efficient implementation of a simplex-type algorithm for solving separated continuous linear programs, demonstrating significant improvements over previous methods and discretization approaches in large-scale fluid processing network applications.

Contribution

The paper introduces a robust, accurate, and faster implementation of a recent simplex-type algorithm tailored for large-scale continuous linear programs, outperforming existing methods.

Findings

Achieves several orders of magnitude speedup and accuracy improvements.

Effectively solves large and very large scheduling and fluid control problems.

Provides insights into online and offline optimization applications.

Abstract

We describe an efficient implementation of a recent simplex-type algorithm for the exact solution of separated continuous linear programs, and compare it with linear programming approximation of these problems obtained via discretization of the time horizon. The implementation overcomes many numerical pitfalls often neglected in theoretical analysis allowing better accuracy or acceleration up to several orders of magnitude both versus previous implementation of the simplex-type algorithms and versus a state-of-the-art LP solver using discretization. Numerical study includes medium, large, and very large examples of scheduling problems and problems of control of fluid processing networks. We discuss online and offline optimization settings for various applications and outline future research directions.