On the tightness of linear relaxations of alternative mixed integer programming formulations for the generator maintenance scheduling problem

TL;DR

This paper compares six MIP formulations for generator maintenance scheduling, analyzing their linear relaxation tightness to identify which models yield better bounds and computational efficiency.

Contribution

It provides a theoretical comparison of multiple formulations, establishing relationships and identifying the most effective models for generator maintenance scheduling.

Findings

Some formulations have tighter relaxations leading to better bounds.

Tighter relaxations correlate with improved computational performance.

Theoretical insights guide practitioners in selecting optimal models.

Abstract

This paper presents a comprehensive theoretical analysis of six distinct Mixed-Integer Programming (MIP) formulations for preventive Generator Maintenance Scheduling (GMS), a critical problem for ensuring the reliability and efficiency of power systems. By comparing the tightness of their linear relaxations, we identify which formulations offer superior dual bound and, thus, better computational performance. Our analysis includes establishing relationships between the formulations through definitions, lemmas, and propositions, demonstrating that some formulations provide tighter relaxations that lead to more efficient optimization outcomes. These findings offer valuable insights for practitioners and researchers in selecting the most effective models to enhance the scheduling process of preventive generator maintenance.