Review Reports - Efficient Task Scheduling Using Constraints Programming for Enhanced Planning and Reliability

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a constraint programming (CP) algorithm for efficient task scheduling in aircraft engine Maintenance, Repair, and Overhaul (MRO) operations. By utilizing data from Korean Air’s maintenance logs, the study demonstrates how CP can optimize scheduling by minimizing downtime, adhering to task dependencies, and maximizing resource utilization. Experimental results indicate near-optimal solutions with an average resource utilization of 99.34%, making the approach computationally efficient for small to medium-sized MRO problems. The paper highlights CP’s advantages over heuristic and machine learning methods, emphasizing its suitability for deterministic environments.
It can be accepted after the following improvements are made:

1. Provide a deeper comparison of CP with other methods, such as genetic algorithms, reinforcement learning, and dynamic programming. Relevant articles: Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies; Multi-policy deep reinforcement learning for multi-objective multiplicity flexible job shop scheduling

2. MRO problem for aircraft engines is resource constraints project scheduling problem referred to article Integrated planning and scheduling of multiple manufacturing projects under resource constraints using raccoon family optimization algorithm; Digital Twin-Based Smart Manufacturing System for Project-Based Organizations: A Conceptual Framework. It is suggested to add literature review of RCPSP for aircraft engines MRO.

3. Discuss how the model could handle dynamic or stochastic scenarios, such as unexpected maintenance tasks or real-time disruptions.

4. Add a comparative table summarizing CP’s advantages and limitations relative to other scheduling methods.

5. Line 154, 157, 158, reference is missing.

6. It is suggested to add algorithms complexity analysis.

7. Figures, 3 and 4 are not clear.

8. It is suggest to compare the performance to proposed approach with other state of art algorithms

9. The manuscript requires thorough proofreading for language and grammar. It is recommended to perform a detailed language check and proofreading before resubmitting.

Comments on the Quality of English Language

The manuscript requires thorough proofreading for language and grammar. It is recommended to perform a detailed language check and proofreading before resubmitting.

Author Response

Thank you for your valuable commnets.

Provide a deeper comparison of CP with other methods, such as genetic algorithms, reinforcement learning, and dynamic programming. Relevant articles: Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies; Multi-policy deep reinforcement learning for multi-objective multiplicity flexible job shop scheduling

-> We compared with Genetic Algorithm (GA) in Table 4 by setting parameters for similar order of CPU time since it is very difficult to find similar (optimal) results using GA.

Unfortunately, reinforcement learning, and dynamic programming articles provided cannot be directly compared, we added them in related works section.

MRO problem for aircraft engines is resource constraints project scheduling problem referred to article Integrated planning and scheduling of multiple manufacturing projects under resource constraints using raccoon family optimization algorithm; Digital Twin-Based Smart Manufacturing System for Project-Based Organizations: A Conceptual Framework. It is suggested to add literature review of RCPSP for aircraft engines MRO.

-> We referred possible utilization of smart manufacturing framework based on digital twin for aircraft engines MRO in introduction section.

Discuss how the model could handle dynamic or stochastic scenarios, such as unexpected maintenance tasks or real-time disruptions.

-> We can provide dynamic task scheduling when urgent checkup interrupts occur by using a fast automatic task scheduling which can be rescheduled in minutes. We mentioned this point at the last sentence of experimental results secion.

Add a comparative table summarizing CP’s advantages and limitations relative to other scheduling methods.

-> We added comparison with Genetic Algorithm (GA) in Table 4.

Line 154, 157, 158, reference is missing.

-> Fixed missing references

It is suggested to add algorithms complexity analysis.

-> The worst-case complexity of Constraints Programming (CP) is O(dⁿ), where d is the domain size of task start times, and n is the number of tasks. However, CP is well-suited for smaller, structured problems with well-defined constraints. We mentioned this point in section 3.5.1

Figures, 3 and 4 are not clear.

-> We removed Figures 3 and 4 since it cannot be clearly visualized in the paper.

It is suggested to compare the performance to proposed approach with other state of art algorithms

-> Unfortunately, we cannot directly compare the results with other state of art algorithms since the problem and data are different for them. Therefore, we compared with Genetic Algorithm using the same data in Table 4.

The manuscript requires thorough proofreading for language and grammar. It is recommended to perform a detailed language check and proofreading before resubmitting.

-> We thoroughly proofread again.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

-What is the average number of different MRO tasks in Korean Air's operations over the course of a year?

-The manuscript contains numerous messages such as "Error! Reference 158 source not found."

-In Table 1, explain the abbreviations for Work Scope and the meaning of the different levels. Additionally, indicate the unit of measure for levels (days).

-The authors mention using the mean to estimate the duration of individual tasks and subtasks. One drawback of using the mean is its sensitivity to outliers. In such cases, the median is a more robust measure as it is not influenced by extreme values. Problems also arise from applying the mean due to excessive standard deviation, data non-linearity, etc. A thorough analysis of input data is required before applying the optimization model. The authors must recognize that an optimization algorithm will provide optimal results even for incorrect input data! Consequently, the final result (scheduling) could be completely inaccurate.

-Provide descriptive statistics (mean, median, mode, standard deviation, variance, minimum and maximum values, kurtosis, and skewness) for historical data on individual MRO tasks/subtasks. Determine the distribution of the data and visualize it with a "Task/Subtask vs. time" graph.

-Table 2 and Table 3 have the same title. Does Table 2 illustrate the structure of the "csv" files? Table 3 should be omitted. Alternatively, the structure of the files containing optimization input data should be presented differently.

-What is the difference in presentation between Table 1 and Table 2? It seems Table 2 contains the same data as Table 1. Consider omitting Table 2 for simplicity.

-The mathematical model in section "3.3.3. Mathematical Model" should be visualized with a diagram and the final mathematical model presented.

In Table 4, clarify the meaning of the columns "horizon" and "#Days" and their units (days). Are these optimized values? It would be helpful to compare unoptimized and optimized horizon values for the same tasks and workplaces.

-Since the authors claim that their CP algorithm provides faster and better results than a genetic algorithm for optimization, the manuscript should compare CP vs. genetic algorithms using the same dataset to substantiate this claim.

-Additionally, the authors should explain how the application of the CP algorithm for MRO differs from conventional optimization of operations scheduling on machines, i.e., what is the originality of their work?

Author Response

Replay to Reviewer 2

-What is the average number of different MRO tasks in Korean Air's operations over the course of a year?

-> We are sorry but the average number of different MRO tasks in Korean Air's operations over the course of a year is not disclosed. We were provided a typical MRO tasks example from Korean Air.

-The manuscript contains numerous messages such as "Error! Reference 158 source not found."

-> Fixed all the Error References

-In Table 1, explain the abbreviations for Work Scope and the meaning of the different levels. Additionally, indicate the unit of measure for levels (days).

-> We added explanations on levels and measure for levels.

-> The average duration values are given by Korean Air not decided by the authors, where they are currently using for their MRO. It can be easily changed to use median or any measure by modifying Table 1.

-> We are sorry but Korean Air didn’t provide historical data but only provided average values.as shown in Table 1.

-> Modified titles of Table 2 and Table 3. Table 2 illustrate the structure of the ‘csv” file. Table 3 illustrates expected tasks for a period.

-What is the difference in presentation between Table 1 and Table 2? It seems Table 2 contains the same data as Table 1. Consider omitting Table 2 for simplicity.

-> Table 1 is an example table for the working days for all the subtasks depending on the difficulty of the subtask of an example engine type PW1100G. Table 2 is an example checkup task table for engine type PW1100G. Days of Table 2 are extracted from Table 1.

-The mathematical model in section "3.3.3. Mathematical Model" should be visualized with a diagram and the final mathematical model presented.

-> We inserted Figure 1 for the visualization of the mathematical model and added explanation on it.

-> In Table 4, horizon is the maximum days boundary expected when all the tasks are assigned consecutively.

-> We compared with Genetic Algorithm (GA) in Table 4 by setting parameters for similar order of CPU time since it is very difficult to find similar (optimal) results using GA.

-> The main contribution is mathematical modeling of the MRO problem for CP algorithm where CP algorithm can find near optimal solution. In practical applications, we can provide dynamic task scheduling when urgent checkup interrupts occur by using a fast automatic task scheduling which can be rescheduled in minutes.