# On the Local Dominance Properties in Single Machine Scheduling Problems

### Natalia Jorquera-Bravo, Natalia Jorquera-Bravo, Óscar C. Vásquez, Óscar C. Vásquez

#### 2022

#### Abstract

We consider a non-preemptive single machine scheduling problem for a non-negative penalty function f . For this problem every job j has a priority weight wj and a processing time pj , and the goal is to find an order on the given jobs that minimizes ∑wj f(C j), where Cj is the completion time of job j. This paper explores the local dominance properties in this problem, which provide a powerful theoretical tool to better describe the structure of optimal solutions by identifying rules that at least one optimal solution must satisfy, reducing the search space from n! to n!/3^{n/3} schedules and providing insights to show the computational complexity status for problem with a convex penalty from a general framework, such as the problem of minimizing the sum of weighted mean squared deviation of the completion times with respect to a common due date and jobs with arbitrary weights.

Download#### Paper Citation

#### in Harvard Style

Jorquera-Bravo N. and Vásquez Ó. (2022). **On the Local Dominance Properties in Single Machine Scheduling Problems**. In *Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-548-7, pages 208-213. DOI: 10.5220/0010871600003117

#### in Bibtex Style

@conference{icores22,

author={Natalia Jorquera-Bravo and Óscar C. Vásquez},

title={On the Local Dominance Properties in Single Machine Scheduling Problems},

booktitle={Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2022},

pages={208-213},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010871600003117},

isbn={978-989-758-548-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - On the Local Dominance Properties in Single Machine Scheduling Problems

SN - 978-989-758-548-7

AU - Jorquera-Bravo N.

AU - Vásquez Ó.

PY - 2022

SP - 208

EP - 213

DO - 10.5220/0010871600003117