Operations Research for Pediatric Elective Surgery Planning: Example of a Mathematical Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors propose an Integer Linear Programming (ILP) approach for scheduling elective surgeries in a pediatric Teaching Hospital (TH). The model utilizes a "disruption-restoration" framework, generating a Nominal Schedule (NS) alongside pre-computed Backup Schedules (RS) to handle specific disruptions like emergencies and patient no-shows. The study uses a "realistic example" of 54 patients to demonstrate the model's ability to reschedule patients while minimizing deviations from the original plan.

The authors claim novelty in applying the disruption-restoration concept—borrowed from telecommunications and transportation—specifically to the pediatric teaching hospital context. They emphasize a dual-output system where the schedule and its recovery plans are generated simultaneously to ensure resilience against specific scenarios.

While the application area (pediatric surgery resilience) is highly relevant, the manuscript in its current form is scientifically incomplete. The paper relies heavily on a reference to a preprint for the mathematical formulation, effectively treating the core methodology as a "black box." Furthermore, the literature review is severely under-researched (only 9 references), and the validation lacks a comparative baseline against current hospital practices or standard heuristics

1. The manuscript fails to present the mathematical model it claims to validate. The text states: "A detailed description of the model and optimization approaches to solve it can be found in [9]". Reference [9] is a preprint (arXiv) by the same authors. A standalone scientific research article must be self-contained. You cannot ask reviewers or readers to consult an external preprint to understand the core constraints and variables of the proposed ILP.
2. The results section relies on a "realistic example" and demonstrates that the model produces a schedule. There is no evidence that this schedule is better than the status quo. Does this model reduce overtime compared to manual scheduling? Does it improve patient waiting list turnover compared to First-Come-First-Served (FCFS)? You must compare your model's output against a baseline. Ideally, use historical data from the "high-volume Pediatric Surgery Department" mentioned in the introduction to simulate how your model would have handled past weeks versus what actually occurred.
3. The bibliography contains only 9 references. Operations Research in surgery scheduling is a mature field with hundreds of papers. Citing only 9 sources suggests a lack of familiarity with the State-of-the-Art (SOTA). You fail to cite key works in robust optimization, stochastic programming for ORs, or recent reviews on pediatric scheduling. Conduct a proper literature search. Contextualize your "disruption-restoration" approach against Stochastic Programming (SP) and Robust Optimization (RO) approaches common in healthcare engineering.
4. In the Introduction, the motivation regarding the specific challenges of pediatric hospitals (higher cancellation rates due to respiratory infections, etc.) is well-articulated. The "Research Question" is phrased somewhat informally. Clearly define the gap. Why do existing robust scheduling models fail for pediatric teaching hospitals specifically?
5. In the Materials and Methods, the description of "Blocks A through H" is too abstract. The penalty function provided ($p_{id}$) includes the term $max\{m_{i}+d-l_{i};0\}$. This implies a penalty only if the deadline is breached. Is there no benefit to scheduling earlier than the deadline? Also, the solver specifications are vague ("commercial solver"). State the specific software (e.g., CPLEX, Gurobi, Xpress) and the version used.
6. The Gantt charts (Figures 2-5) appear to be screenshots from a custom interface. While helpful, they are difficult to read in standard print.
7. The paper claims the approach "shows to be effective". However, in Example 3 (Long-length emergency), the solution involves postponing multiple patients (P24, P26, P68, P66). Discuss the trade-off. In a real hospital, postponing 4 patients to accommodate 1 emergency is a major dissatisfaction event. Is the model tunable to prioritize minimizing cancellations over minimizing overtime?
8. The cost savings calculation is purely theoretical ("back-of-the-envelope"). It assumes 3 hours of vacant time per week without providing data to support this assumption.
9. You mention an "Excel-type interface"^. If usability is a key contribution, provide a figure or screenshot of this interface to prove it is "easily usable by administrative staff."
10. Figure 6 (Histogram) is very low quality. The x-axis labels are crowded.
    -> Triggering this concept to suggest you replace the Excel chart with a professional statistical plot (e.g., Kernel Density Estimation or a clean histogram).
11. The term "Decision Science experts" is used somewhat strangely in the third person ("we asked Decision Science experts"). Since the authors are from the Department of Electronics, Information and Bioengineering, this phrasing is odd. Rephrase to "We developed a mathematical model..."
12. Ensure all mathematical variables (like $u_{ij}$) are defined immediately upon first use.
13. The paper mentions a "realistic example". If this data is derived from actual patient records (even anonymized), you must state the IRB/Ethics Committee approval code or explicitly state that the data is synthetic/simulated.
14. The reliance on the author's own preprint for the methodology is a borderline integrity issue if not rectified by including the methods in this paper.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a pediatric elective surgery scheduling model based on integer linear programming and disruption restoration. There are still some defects in the method details and experimental verification, and the specific comments are as follows:

1. The mathematical model description is seriously insufficient and difficult to reproduce. Although the author claims to have proposed an ILP model, the set of decision variables and the mathematical expression of constraints are not given. Block A-H only gives A literal overview, without any formal formula
2. The scenario assumption is too strong, and the rationality needs to be demonstrated. The key assumptions in this paper include that there is at most one emergency room or one no-show per day, and the length of emergency room only takes three discrete values of 1h / 2h / 4h. These assumptions are highly idealized in reality.
3. Lack of real data or controlled experiments, it is recommended to use real historical data for verification.
4. The reference order of Figure 1/2/3/4/5 is not consistent with the main text, and should be unified.
5. The clinical plausibility of the urgency parameter needs further explanation.
6. The related work section lacks the latest intelligent medicine papers, such as "Vision-Language Models in medical image analysis: From simple fusion to general large models",  and "Knowledge distillation and teacher-student learning in medical imaging:  Comprehensive overview, pivotal role, and future directions".

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

Authors addressed the problem of optimizing surgical programme scheduling in a teaching paediatric hospital, also addressing the possible eventualities that disrupt daily programming, using a mathematical model developed by Decision Science experts.

Comments:

i. The organization of the manuscript is very good.

ii. Provide the detailed contribution and novelty of this research work in a more comprehensive way.

iii. A lot of software has already been developed by vendors related to this problem, and similar research papers have also been published. Eg: "Clavel, D.; Mahulea, C.; Albareda, J.; Silva, M. A Decision Support System for Elective Surgery Scheduling under Uncertain Durations. Appl. Sci. 2020, 10, 1937. https://doi.org/10.3390/app10061937"

iv. In the manuscript, it is mentioned: “An Integer Linear Programming-based approach is proposed for the problem.” How will this linear approach support uncertain data management and immediate scheduling requirements (e.g., emergency surgery needs or sudden operation requests)?

v. How can surgical urgency and resource availability be mapped for immediate scheduling? Provide the detailed mathematical representation.

vi. Provide the complete mathematical flow and process flow of the proposed work using a flowchart for better understanding.

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

This manuscript addresses a relevant problem in pediatric operating room scheduling and presents a clear and technically sound optimization model. The pediatric and teaching hospital context is well motivated, and the formulation is generally well described.

To strengthen the contribution, the authors should clarify the novelty of the work relative to recent disruption-aware and stochastic OR scheduling literature. The evaluation relies mainly on illustrative examples; including baseline comparisons and sensitivity analyses (e.g., emergency rates, no-show probabilities, OR capacity) would substantially improve the empirical support. The choice of objective-function weights should also be better justified or analyzed.

Author Response

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Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I am satisfied with the authors’ revisions; the manuscript is ready for publication.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The paper has been well revised.

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Reviewer 3 Report

Comments and Suggestions for Authors

The authors have completely revised the manuscript, and its quality has significantly improved compared to the initial version.

Comments:

i. Please check the overall presentation of the manuscript, including all equations.

ii. The equations are not described properly. Please define the variables after each equation or provide them in a table format.

iii. Please provide a detailed comparison of your proposed method with state-of-the-art techniques and include this in the Results and Discussion section.

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The authors have addressed all my comments

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