An Algebraic Approach to the Solutions of the Open Shop Scheduling Problem

The open shop scheduling problem (OSSP) is one of the standard scheduling problems. It consists of scheduling jobs associated with a finite set of tasks developed by different machines. In this case, each machine processes at most one operation at a time, and the job processing order on the machines...

Full description

Saved in:
Bibliographic Details
Published in2023 IEEE 13th International Conference on Pattern Recognition Systems (ICPRS) pp. 1 - 8
Main Authors Canadas, Agustin Moreno, Mendez, Danna Odette Moreno, Rojas, Juan Carlos Riano, Pantoja, Juan David Hormaza
Format Conference Proceeding
LanguageEnglish
Published IEEE 04.07.2023
Subjects
Algebra
Brauer configuration algebra
Job shop scheduling
open shop scheduling problem
Pattern recognition
quiver representation
Task analysis
Online AccessGet full text

Cover

More Information
Summary:The open shop scheduling problem (OSSP) is one of the standard scheduling problems. It consists of scheduling jobs associated with a finite set of tasks developed by different machines. In this case, each machine processes at most one operation at a time, and the job processing order on the machines does not matter. The goal is to determine the completion times of the operations processed on the machines to minimize the largest job completion time, called C_{max} . This paper proves that each OSSP has associated a path algebra called Brauer configuration algebra whose representation theory (particularly its dimension and the dimension of its center) can be given using the corresponding C_{max} value. It has also been proved that the dimension of the centers of Brauer configuration algebras associated with OSSPs with minimal C_{max} are congruent modulo the number of machines.
DOI:10.1109/ICPRS58416.2023.10179081