# Efficient Task Scheduling Using Constraints Programming for Enhanced Planning and Reliability
## 2 Related Works  
The scheduling of maintenance, repair, and overhaul (MRO) tasks for aircraft engines has been extensively studied, with various methods proposed to address the complexity and resource-intensive nature of these operations. This section reviews the most relevant works in the field, highlighting their contributions and limitations, and provides a comparison with the approach proposed in this paper. Aircraft MRO processes are inherently complex, involving multiple interdependent tasks that must be carefully scheduled to minimize downtime and reduce operational costs. The scheduling challenges in MRO operations, particularly focusing on the relationship between Original Equipment Manufacturers (OEMs) and MRO providers, and the operational difficulties caused by unexpected component failures are described in [2]. While this study provided a comprehensive overview of the key factors influencing MRO efficiency, it primarily relied on qualitative analysis, offering limited solutions for optimizing task scheduling under uncertainty. This paper aims to build upon these insights by proposing a quantitative, constraint-based optimization approach to handle such challenges more effectively. The task scheduling problem with resource constraints, such as job shop scheduling, is a NP-hard problem, as proved in [3]. There are many heuristic approaches to solve NP-hard problems. Many studies have employed heuristic and metaheuristic methods to solve this NP-hard scheduling problem. For example, a genetic algorithm was used to optimize long-term aircraft maintenance scheduling under uncertainty, demonstrating a 7% reduction in heavy maintenance checks and a 4.4% increase in aircraft utilization [4]. Although this approach showed promising results, heuristic methods like genetic algorithms often struggle with finding truly optimal solutions, especially in dynamic environments where task dependencies and resource availability fluctuate frequently. Metaheuristic approaches like genetic algorithms, simulated annealing, or particle swarm optimization often provide near-optimal solutions but are computationally expensive and may require the fine-tuning of parameters for specific cases. In contrast, our study leverages constraint programming, which, while computationally more straightforward for certain problem sizes, guarantees optimal solutions within a reasonable time for the given MRO task size. By focusing on a more structured optimization approach, our model efficiently handles task dependencies and resource constraints, which are crucial in real-world MRO settings. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm for dynamic hybrid flow shop scheduling problems characterized by uncertain processing times, dynamic job arrivals, and flexible maintenance was proposed in [5]. The study introduced a multi-agent framework for efficient scheduling policy development and demonstrated that the NEAT algorithm outperforms traditional dispatching rules and Deep Q-Network (DQN) in terms of robustness, adaptability, and generalization across diverse test cases. This approach emphasizes real-time decision making and provides a robust methodology for addressing scheduling challenges in smart manufacturing environments. Machine learning and deep learning methods have gained popularity in MRO scheduling for their ability to model complex relationships in large datasets. A reinforcement learning (RL) was applied to optimize aircraft maintenance scheduling, showing that RL could outperform traditional methods in certain stable environments [6]. Similarly, adaptive RL for task scheduling in aircraft maintenance, introducing a dynamic rescheduling mechanism that responds to real-time changes in task requirements was explored in [7]. A Multi-Policy Deep Reinforcement Learning (DRL) framework for solving the multi-objective multiplicity flexible job shop scheduling problem (MOMFJSP) was introduced in [8].