Bi-Level Scheduling for Beijing-Tianjin-Airport Cluster Departures

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study presents a solid and well-structured methodological contribution to the field. However, to further strengthen the manuscript, I have a few specific suggestions for the authors to consider during their revision.

First and foremost, while the bi-level framework is logically sound, it is crucial to explicitly address its inherent structural limitations within the main text. Specifically, I recommend that the authors acknowledge the absence of a dynamic feedback loop between the upper and lower-level models. It should be clearly stated, perhaps in the Discussion or Conclusion, how this lack of real-time interaction might restrict the model's effectiveness in highly stochastic or real-time operational environments. Providing this honest appraisal will significantly improve the paper's transparency and academic rigor.

In addition to this, the manuscript would benefit from a more robust justification of the core modeling assumptions, such as fixed arrival sequences and deterministic taxi times. Rather than just reporting the impressive percentage gains in a descriptive manner, I encourage the authors to dig deeper into the "why" behind these results, explaining the specific conditions under which these benefits emerge. It would also be helpful to see a more distinct comparison with existing bi-level approaches, perhaps highlighting the conceptual novelty of this work beyond just the technical implementation.

Finally, I noticed that the writing in several sections -- particularly 1. Introduction, 2. Literature Review, 3.2 Model Architecture, and 3.3 Algorigthms -- tends to be quite dense with long, repetitive sentence structures. Revising these for conciseness and flow would make the complex methodological details much more accessible to a global audience. I also suggest briefly outlining how this offline optimization might eventually transition into a rolling-horizon or real-time decision support system in future studies.

Addressing these points, particularly the clarity regarding the feedback mechanism and real-time limitations, will greatly enhance the robustness and practical relevance of your work.

Comments on the Quality of English Language

On the whole, the manuscript is written in an accessible manner, with technical terms used correctly throughout. Readers shouldn't have major issues grasping the methodology. The main drawback, however, is a lack of stylistic variety. The prose tends to rely on formulaic patterns, which makes the reading experience feel a bit stagnant. By breaking up the longer, more cumbersome sentences and trimming down the wordier parts, the authors could significantly improve the paper's impact. I wouldn't recommend rejection based on language alone, but a deep revision focused on conciseness and flow is highly encouraged.

Author Response

Reviewer 1

Thank you for your valuable feedback! Based on your suggestions, we have made the following modifications to the manuscript.

Comment 1: “First and foremost, while the bi-level framework is logically sound, it is crucial to explicitly address its inherent structural limitations within the main text. Specifically, I recommend that the authors acknowledge the absence of a dynamic feedback loop between the upper and lower-level models”

Response 1:

Thank you for pointing out this important limitation. We agree that the current implementation does not include a dynamic feedback loop between the upper and lower levels. We revised the Introduction (and further emphasized in the Conclusions) to explicitly state that the proposed framework is implemented as an offline sequential coupling, and we discussed how the lack of real-time interaction may restrict applicability in highly stochastic operational settings. We also outlined a rolling-horizon feedback extension as future work.

The specific revisions and additions in this article are on Line 70 as follows.

“A key objective is to ensure consistency between the two levels, i.e., the lower-level surface schedules comply with the upper-level TTOT assignments. In this study, the two levels are coupled in an offline sequential manner: the upper level assigns TTOTs and the lower level seeks a feasible surface plan consistent with these TTOTs. A real-time feedback loop (e.g., rolling-horizon re-optimization when disturbances occur) is left for future work.”

 

Comment 2: “In addition to this, the manuscript would benefit from a more robust justification of the core modeling assumptions, such as fixed arrival sequences and deterministic taxi times. Rather than just reporting the impressive percentage gains in a descriptive manner, I encourage the authors to dig deeper into the "why" behind these results, explaining the specific conditions under which these benefits emerge. It would also be helpful to see a more distinct comparison with existing bi-level approaches, perhaps highlighting the conceptual novelty of this work beyond just the technical implementation.”

Response 2:

We appreciate this suggestion. We strengthened the justification and interpretation of our modeling assumptions by clarifying their operational meaning (e.g., using unimpeded taxi time as a baseline) and by explicitly discussing the limitations introduced by uncertainties. We also added a discussion in Section 4.4.3 to explain why the performance gains emerge.

For the “In addition to this, the manuscript would benefit from a more robust justification of the core modeling assumptions, such as fixed arrival sequences and deterministic taxi times.…”

The specific revisions and additions in this article are in Section 3.3.1 Model Assumptions as follows.

“

1) Aircraft follow standard SIDs/STARs. Segment flight times are modeled as deterministic baseline values estimated from historical averages by aircraft category; deviations caused by winds or ATC vectoring are not explicitly optimized and are dis-cussed as a limitation.

2) Taxi movements are constrained by airport topology. For each flight, a small candidate set of feasible departure (gate–runway) or arrival (runway–gate) routes is generated via a k-shortest-path method and used as the decision space in the lower-level model.

3) Taxiing is represented using unimpeded (no-stop) travel times as a baseline. Potential stops and conflicts are mitigated indirectly through pushback holding and route switching decisions, rather than being modeled as explicit stop-and-go dynamics; the impact of disturbances is discussed as a limitation.

4) Arrival sequences are treated as exogenous inputs (FCFS in this study) and are not optimized. Departure sequences are optimized based on available runway slots.

”

For the “…Rather than just reporting the impressive percentage gains in a descriptive manner, I encourage the authors to dig deeper into the "why" behind these results, explaining the specific conditions under which these benefits emerge…”

The specific revisions and additions in this article are at the end of Section 4.4.3 Departure Handover Point Resource Allocation Analysis as follows.

“The delay reduction mainly stems from two coupled effects. First, the upper-level metroplex sequencing redistributes departure demand across airports while enforcing separations at shared handover fixes, which mitigates queue spillback and compression at bottleneck fixes. Second, the lower-level gate holding and route switching convert the assigned TTOTs into conflict-free surface trajectories, reducing stop-and-go taxiing and runway-threshold waiting. Therefore, the benefits are most pronounced during peak periods when handover-point and runway constraints are binding; under light traffic, FCFS and the optimized strategy tend to perform similarly.”

For the “…It would also be helpful to see a more distinct comparison with existing bi-level approaches, perhaps highlighting the conceptual novelty of this work beyond just the technical implementation.”

The specific revisions and additions in this article are at the end of Section 2.4 Summarize as follows.

“…Different from existing bi-level studies that primarily optimize slot times or sequencing at one layer, our framework explicitly enforces separations at shared handover fixes across three airports and couples TTOT assignment with airport-surface realizability, while also embedding airport-level equity as an explicit objective.”

Comment 3: “Finally, I noticed that the writing in several sections -- particularly 1. Introduction, 2. Literature Review, 3.2 Model Architecture, and 3.3 Algorigthms -- tends to be quite dense with long, repetitive sentence structures….”

Response 3:

The specific revisions and additions in this article are as follows. (The specific line numbers of the following modifications in the text correspond to the line numbers in the closed revision mode)

Before:

“Because this dynamic undermines punctuality, regional throughput, and fairness, addressing it is essential: smoothing departure flows and reducing inter-airport conflicts can raise on-time performance and prevent any single airport from monopolizing departure slots.”

Now:

“This dynamic undermines punctuality, regional throughput, and fairness. Therefore, addressing it is essential. Smoothing departure flows and reducing inter-airport conflicts can raise on-time performance and ensure that no single airport monopolizes the departure slots.”

The specific revisions and additions in this article are on Line 38.

Before:

“Accordingly, this paper concentrates on the departure side of multi-airport terminal operations and intentionally excludes arrival sequencing, since arrivals are governed by strict ATC safety procedures and inter-airport arrival coordination (for example, merging inbound streams) adds complexity and controller workload.”

Now:

“Accordingly, this paper focuses on the departure side of multi-airport terminal operations. We intentionally exclude arrival sequencing, because arrivals are governed by strict ATC safety procedures, and coordinating arrivals across airports (e.g., merging inbound streams) adds significant complexity and increases controller workload [5].”

The specific revisions and additions in this article are on Line 41.

Before:

“By focusing on departures, we posit that substantial efficiency gains are achievable through improved surface and takeoff scheduling without interfering with critical arrival management.”

Now:

“By focusing on departures, we posit that substantial efficiency gains are achievable through improved surface and takeoff scheduling without interfering with critical arrival management [6].”

The specific revisions and additions in this article are on Line 45.

Before:

“We further assume that small, coordinated adjustments to each airport’s departure sequence can reduce overall system delay while maintaining safety, and that aligning planned takeoff time with actual taxi-out trajectories can prevent unnecessary holding at gates and on taxiways.”

Now:

“We further assume that small, coordinated adjustments to each airport’s departure sequence can reduce overall system delay while maintaining safety. Additionally, aligning the planned takeoff times with actual taxi-out trajectories can prevent unnecessary holding at gates and on taxiways.”

The specific revisions and additions in this article are on Line 49.

Before:

“Conditioned on the upper-level TTOTs, it jointly determines for each departure flight the pushback timing, pushback order (including holding at gate when necessary), and conflict-free taxi routes to reach the runway in time for the assigned slot; simultaneously, and without altering arrival sequencing, it computes conflict-free taxi routes for arriving flights from runway to gate so that surface movements remain deconflicted across arrivals and departures.”

Now:

“Given the upper-level TTOT assignments, the lower-level model determines each departure flight’s pushback timing, pushback order (holding at the gate if necessary), and a conflict-free taxi route to reach the runway in time for its assigned slot. At the same time, without altering the arrival sequence, the model computes conflict-free taxi routes for arriving flights from the runway to the gate, ensuring that surface movements for arrivals and departures do not conflict.”

The specific revisions and additions in this article are on Line 60.

Before:

“Li et al. [7] propose a multi-agent reinforcement learning (MARL) framework: first they jointly optimize departure times across all airports to minimize overall delay and queue congestion, then assign optimal departure routes (SIDs) for each flight.”

Now:

“Li et al. [7] propose a multi-agent reinforcement learning (MARL) framework. In this approach, departure times across all airports are first optimized jointly to minimize overall delay and taxi queue congestion. Next, optimal departure routes (SIDs) are assigned to each flight.”

The specific revisions and additions in this article are on Line 103.

Before:

“Fairbrother et al. [14] propose a two-stage slot-assignment mechanism: stage one builds a “fair” baseline schedule across airlines, then stage two lets each airline adjust allocation among its flights according to its own preferences.”

Now:

“Fairbrother et al. [14] propose a two-stage slot assignment mechanism. In stage one, a ‘fair’ baseline schedule is constructed across all airlines. In stage two, each airline then adjusts its allocated slots among its flights according to its own preferences.”

The specific revisions and additions in this article are on Line 124.

Before:

“Critically, taxi studies have not generally considered full MAS contexts or tactical equity, i.e., fair resource allocation among airports - they focus on single airports with simplified path/routing assumptions, and lack coupling to airspace constraints.”

Now:

“Critically, most taxi scheduling studies have not considered the full multi-airport system context or tactical equity (fair resource allocation among airports). They tend to focus on single airports with simplified taxi-routing assumptions and lack integration with airspace slot allocation constraints.”

The specific revisions and additions in this article are on Line 155.

Before:

“In tests this cut total taxi-engine-on time significantly: fuel burn was reduced by 12,250–14,500 kg (4000–4700 US gallons) over 4-hour peak periods, at the cost of only a few minutes of gate delay per flight.”

Now:

“In field tests, this strategy significantly reduced total taxi engine-on time. Fuel burn dropped by approximately 12,250–14,500 kg (4000–4700 US gallons) over 4-hour peak periods, at the cost of only a few extra minutes of gate delay per flight.”

The specific revisions and additions in this article are on Line 164.

Before:

“Simaiakis & Balakrishnan [26] showed via simulation that gate-holding can decouple gate supply from runway demand, smoothing peaks; Khadilkar & Balakrishnan [27] formalized the CVQ protocol to manage congested ramps fairly. These methods consistently find that controlled gate queues yield large fuel/emission savings and can scale effectively to high-demand scenarios.”

Now:

“Simaiakis and Balakrishnan [28] demonstrated via simulation that gate-holding can decouple gate pushbacks from runway departures, thereby smoothing departure peaks. Khadilkar and Balakrishnan [29] later formalized the Collaborative Virtual Queue (CVQ) protocol to manage congested ramps more fairly. These methods consistently find that controlling gate queues yields large fuel and emission savings, and can scale effectively even under high-demand scenarios.”

The specific revisions and additions in this article are on Line 174.

Before:

“This fragmented approach causes three main issues: (1) congestion and inefficient airspace utilization due to unplanned merging, (2) elevated controller workload from frequent manual interventions, and (3) systemic inequities where certain airports gain persistent timing advantages.”

Now:

“This fragmented approach causes three main issues. First, it leads to congestion and inefficient airspace utilization due to unplanned merging at shared waypoints. Second, it elevates controller workload because frequent manual interventions are required. Third, it creates systemic inequities in which certain airports gain persistent timing advantages.”

The specific revisions and additions in this article are on Line 214.

Before:

“where  is a binary variable, and  is a sufficiently large constant. This ensures temporal separation between conflicting direction flights.”

Now:

“where  is a binary variable, and  is a sufficiently large constant. This ensures temporal separation between conflicting direction flights. This constraint enforces temporal separation on the shared segment so that two flights cannot traverse it in opposite directions at the same time, thereby preventing head-on conflicts.”

The specific revisions and additions in this article are on Line 390.

Before:

“The proposed integrated scheduling model adopts a bi-level optimization structure, with its solution process divided into three sequential stages to ensure feasibility, efficiency, and consistency between airspace sequencing and surface operations:”

Now:

“The proposed integrated scheduling model adopts a bi-level optimization structure. Its solution process is divided into three sequential stages to ensure feasibility, efficiency, and consistency between airspace sequencing and surface operations:”

The specific revisions and additions in this article are on Line 400.

Before:

“The surface scheduling problem is addressed through a Genetic-Simulated Annealing (GSA) hybrid algorithm that integrates the global search capacity of Genetic Algorithms with the local refinement capability of Simulated Annealing to effectively balance exploration and exploitation while avoiding premature convergence.”

Now:

“We address the surface scheduling problem using a Genetic–Simulated Annealing (GSA) hybrid algorithm, which combines the global search capability of Genetic Algorithms with the local refinement capability of Simulated Annealing. This combination effectively balances exploration and exploitation while also avoiding premature convergence.”

The specific revisions and additions in this article are on Line 458.

Before:

“Each solution encodes pushback times and taxi route selections for all departures, along with taxi routes for arrivals, with repair procedures ensuring feasibility regarding safety separations, runway-entry windows, and conflict constraints.”

Now:

“Each feasible solution encodes the pushback times and selected taxi routes for all departures, as well as the taxi routes for all arriving flights. A repair procedure is applied to ensure that safety separation requirements, runway entry time windows, and other conflict constraints are all satisfied.”

The specific revisions and additions in this article are on Line 462.

Before:

“The Metropolis criterion governs acceptance: improved solutions are always accepted, while inferior solutions may be accepted with probability  to escape local optima.”

Now:

“The Metropolis criterion governs solution acceptance. Improved solutions are always accepted, whereas inferior solutions may still be accepted with a certain probability  to escape local optima.”

The specific revisions and additions in this article are on Line 485.

Delete：

“Each airport surface is modeled as a directed graph : nodes U represent stands, taxiway intersections, and runway entry/exit points; edges  denote taxiway segments (defined by length  and maximum speed ). For every departure flight (route: stand → runway entry) and arrival flight (route: runway exit → stand), Yen’s k-shortest paths algorithm generates a candidate set of feasible taxi routes. Here, , though the actual number of feasible routes per flight may be ≤ 4 due to airport topology constraints. The output is a path set  for each flight  which constrains the lower-level optimization’s decision variables.”

Comment 4: “…I also suggest briefly outlining how this offline optimization might eventually transition into a rolling-horizon or real-time decision support system in future studies.”

Response 4:

We revised the manuscript for conciseness and readability, especially in Sections 1–3, by removing redundant descriptions (e.g., repeated explanation of the taxi-route generation step) and simplifying long sentences. We also expanded the Conclusions to briefly describe how the offline framework can be extended into a rolling-horizon, real-time decision-support tool through periodic TTOT updates and feedback signals from the surface layer.

The specific revisions and additions in this article are at the end of Section 5. Conclusions as follows.

“In particular, a rolling-horizon implementation can be developed by updating TTOT assignments every Δt minutes using the latest surface states and predicted uncertainties. The lower level can return feasibility indicators (e.g., minimal required gate holding or in-feasibility penalties) as feedback signals to guide the upper-level re-optimization.”

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article proposes a model that integrates terminal departure sequencing (upper level) with airport surface taxi and push-back scheduling (lower level) to achieve collaborative and efficient operations within a multi-airport system, which demonstrates a certain degree of innovation. However, the following issues exist in the paper:

1.Assumptions such as "continuous taxiing without stops" and "fixed flight times" do not fully account for dynamic uncertainties (e.g., taxi conflicts, weather impacts, air traffic controller interventions). The extent to which such disturbances affect the problem should be analyzed and discussed.

2.The coupling optimization of arrivals and departures is not incorporated. Although the focus is on departures, the mutual influence between arrivals and departures during high-density operations is significant and should be addressed in the paper.

3.The impact of aircraft entering and exiting the runway during ground taxiing is not analyzed or discussed.

4.The current "satisfaction" function is based on delay and sequence deviation, without considering airline interests or flight priorities (e.g., emergency flights, the impact of wide-body aircraft). This should be analyzed and discussed in the paper.

Comments on the Quality of English Language

It is suggested that the expressions in the text be described in the third person.

Author Response

Reviewer 2

Thank you for your valuable feedback! Based on your suggestions, we have made the following modifications to the manuscript.

Comment 1: “Assumptions such as "continuous taxiing without stops" and "fixed flight times" do not fully account for dynamic uncertainties (e.g., taxi conflicts, weather impacts, air traffic controller interventions). The extent to which such disturbances affect the problem should be analyzed and discussed.”

Response 1:

We agree that operational uncertainties (e.g., weather, ATC interventions, and stochastic surface interactions) may affect both feasibility and performance. We added an explicit discussion in the Conclusions to clarify that our current formulation is a deterministic baseline and to explain how disturbances can reduce feasibility margins and alter trade-offs. We also outlined practical extensions, including stochastic buffers, robust optimization, and rolling-horizon re-optimization.

 

The specific additions in this article are at Section 5. Conclusions – Paragraph 2 as follows.

“The proposed model is formulated as a deterministic baseline using historical-average flight times and unimpeded taxi times. In practice, weather, ATC interventions, and stochastic surface interactions may introduce variability that reduces feasibility margins (e.g., tighter runway-entry windows) and changes delay trade-offs. Incorporating stochastic buffers, robust optimization, or online state-updated rolling-horizon re-optimization is an extension.”

The specific revisions and additions in this article are at Section 3.3.1 Model Assumptions as follows.

“5) This article does not consider the impact of weather or unexpected flight events (such as special flights, flight emergencies, air force training, airport surface maintenance, etc.) on airport operations.”

Comment 2: “The coupling optimization of arrivals and departures is not incorporated. Although the focus is on departures, the mutual influence between arrivals and departures during high-density operations is significant and should be addressed in the paper.”

Respose 2:

Thank you for this comment. While our study focuses on departure-centric coordination and treats arrival sequences as fixed inputs, we clarified in the Introduction that arrival–departure interactions are still incorporated through mixed-mode runway separation and runway-occupancy constraints in the upper-level model. We also explicitly noted that extending the framework to joint arrival–departure sequencing is an important direction for future work.

 

The specific revisions and additions in this article are on Page 2 Line 65 as follows.

“…Although arrival sequences are treated as fixed inputs, arrival–departure interactions are still captured through mixed-mode runway separations and runway-occupancy constraints in the upper-level model. By splitting the problem…”

Comment 3: “The impact of aircraft entering and exiting the runway during ground taxiing is not analyzed or discussed.”

Response 3:

We clarified the role of runway entry/exit effects in the lower-level model by explicitly interpreting the runway-entry window constraint and the runway holding-time objective as runway-threshold management. We also acknowledged that runway crossings and detailed runway–taxiway intersection constraints are not explicitly modeled in the current study and are left as future extensions.

The specific revisions and additions in this article are at the of 3.3.4 Lower-Level Model: Surface Scheduling and Conflict Resolution - Paragraph 1 as follows.

“…Here, the runway entry time window and the runway holding-time term explicitly represent runway-threshold management (i.e., controlling how aircraft enter the runway system and how long they wait at the runway before takeoff).”

The specific revisions and additions in this article are at the end of Section 3.3.4 Lower-Level Model: Surface Scheduling and Conflict Resolution as follows.

“The surface taxiing structure in the Beijing Terminal Area is well-developed. Detour taxiing routes can be selected to replace runway crossings, thus avoiding conflict risks from runway crossings. Therefore, the impact of runway crossings during ground taxiing is not considered.”

Comment 4: “The current "satisfaction" function is based on delay and sequence deviation, without considering airline interests or flight priorities (e.g., emergency flights, the impact of wide-body aircraft). This should be analyzed and discussed in the paper.”

Response 4:

We added a discussion to clarify that the current satisfaction function is defined at the airport level for inter-airport equity. We also explained how airline interests or flight priorities can be incorporated through flight-specific weighting parameters when such preference/priority data are available, and we stated why this extension is beyond the scope of the current study.

The specific revisions and additions in this article are at the end of Section 3.3.3 Upper-Level Model: Multi-Airport Departure Sequencing 2) Maximizing Overall Airport Satisfaction as follows.

“The satisfaction metric is defined at the airport level to reflect inter-airport equity in terminal resource allocation. If airline preferences or flight priorities (e.g., emergencies, wide-body operations, passenger connections) are available, the formulation can be extended by introducing flight-specific weights in the aggregation, so that higher-priority flights contribute more to the satisfaction score. Such airline-level preference modeling is not included here due to data availability and to keep the focus on airport-level fairness.”

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1.The research contribution needs further exploration.

2. There is a lack of a research framework diagram to explain the relationship between the upper and lower layer models.

3. The expression process of the overall model formula is rather chaotic.

4. The upper and lower layer models do not take into account the runway allocation, which is inconsistent with the calculation examples.

5. Further details of the algorithm need to be provided, including: encoding and the initial population generation process. Furthermore, there is a lack of understanding of how the two algorithms interact.

6. Both the upper and lower layer models are an NP-hard problem. How to ensure the feasibility of the algorithm?

7. A specific scheduling result table for the upper and lower layer models should be provided.

Author Response

Reviewer 3

Thank you for your valuable feedback! Based on your suggestions, we have made the following modifications to the manuscript.

Comment 1: “The research contribution needs further exploration.”

Response 1:

We strengthened the stated contributions by making them more specific and highlighting three key novelties: (i) explicit coordination across airports at shared terminal handover fixes, (ii) an end-to-end coupling between TTOT assignment and surface realizability via pushback/taxi planning, and (iii) airport-level equity as an explicit optimization objective to quantify efficiency–fairness trade-offs.

The specific revisions and additions in this article are on Line 70 as follows.

“The main contributions of this paper are summarized as follows:

1. Metroplex-wide coordination at shared terminal fixes. We formulate a multi-airport departure sequencing model that explicitly enforces separation constraints at shared handover points (e.g., ELKUR/PEGSO), enabling system-wide coordination across three airports.
2. End-to-end linkage from TTOT to surface realizability. We couple TTOT assignment with airport-surface pushback and taxi planning, ensuring that strategic takeoff slots are operationally realizable under surface conflict constraints.
3. Airport-level equity as an explicit optimization objective. We embed an airport-level satisfaction and fairness-deviation objective to quantify and control inter-airport equity–efficiency trade-offs in metroplex departure management.”

Comment 2: “There is a lack of a research framework diagram to explain the relationship between the upper and lower layer models.”

Response 2:

We added a research framework diagram (Figure 2) to clearly illustrate the relationship between the upper-level TTOT assignment and the lower-level surface scheduling, including the information flow and the key decision variables and constraints at each level.

The specific revisions and additions in this article are at the end of Section 3.4.1 Overall Solution Framework as follows.

“The overall optimization framework is as follows:

Figure 2. Overall Solution Framework”

Comment 3: “The expression process of the overall model formula is rather chaotic.”

Response 3:

We improved the clarity of the model formulation by summarizing the key variables directly in the main text and by better organizing the constraints and their explanations. Complete definitions remain in the Appendix, but the main text now provides a concise variable overview to make the formulation easier to follow.

The specific revisions and additions in this article are at Section 3.3.2 Variable Definitions as follows.

“The model construction involves multiple airports, runways and attributes of individual flight arrivals and departures and so on. Therefore, the formulation introduces many symbols, making it difficult to explain their specific meanings in the main text. The specific meanings of these formula symbols are presented in Appendix A and B.”

Comment 4: “The upper and lower layer models do not take into account the runway allocation, which is inconsistent with the calculation examples.”

Response 4:

We clarified the role of runway allocation by explicitly stating that runway configuration and flight–runway assignments are treated as given inputs in the case study, consistent with the operational mode described in the experimental section.

The specific revisions and additions in this article are on 4.1 Operational Characteristics Table 3 as follows.

“…The "AD" column indicates the arrival and departure attributes of flights.

Table 3. Sample Flight Schedule of BTA

Flight number	AD	airport	Aircraft type	runway	Handover point	Stand	SOBT
KN5215	Departure	ZBAD	L	35R	PEGSO	ZBAD.PP_120	8:10:00
KN5909	Departure	ZBAD	M	11L	ELKUR	ZBAD.PP_148	8:15:00
CA1238	Departure	ZBAA	L	36R	MUGLO	ZBAA.PP_326	8:15:00
CA2987	Departure	ZBTJ	L	34L	MUGLO	ZBTJ.PP_208	8:15:00
CA0182	Arrival	ZBAD	M	35L	BELAX	ZBAD.PP_126	9:00:00
MU0023	Arrival	ZBTJ	L	34R	OMDEK	ZBTJ.PP_218	9:20:00
CA0895	Arrival	ZBAA	M	36R	DUGEB	ZBAA.PP_525	9:25:00
…	…	…	…	…	…	…	…

”

Comment 5: “Further details of the algorithm need to be provided, including: encoding and the initial population generation process. Furthermore, there is a lack of understanding of how the two algorithms interact.”

Response 5:

We expanded the algorithm description by explicitly defining the chromosome/individual encodings, the initialization procedure (FCFS-based seeds plus random permutations), and the decoding/repair process used to construct feasible TTOTs. We also clarified the interaction between the two algorithms: the upper-level NSGA-II outputs TTOTs, which are then enforced as constraints in the lower-level GA–SA surface scheduler.

The encoding procedure of the upper-level model is specifically added on 3.4.3 Upper-Level Optimization: NSGA-II for Departure Sequencing – Paragraph 2 as follows: “In the upper-layer model, to ensure NSGA-II performance, the initial population is generated as follows: First, for each departing flight, a feasible take-off time window is calculated. The earliest take-off time is determined by adding conflict-free taxiing time to the scheduled pushback time. The latest take-off time accounts for a maximum 15-minute delay. Subsequently, within each flight’s time window, take-off times are randomly selected to form multiple random take-off sequences (the initial solution set). The FCFS-derived take-off queue is also incorporated into this set to enhance population diversity.

For encoding, a sort-based integer method is used. Flights are numbered in order of planned pushback time (e.g., 0, 1, 2...), and the chromosome sequence indicates the take-off order.

Subsequently, Partially Mapped Crossover (PMX) generates offspring. Evolution proceeds via non-dominated sorting and elitism strategies, finally yielding the Pareto solution set.”

The encoding procedure of the lower-level model is specifically added on 3.4.4 Lower-Level Optimization: Genetic-Simulated Annealing Hybrid – Paragraph 2 as follows: “In the lower-layer model, each departing flight in the initial population has two at-tributes: pushback time and taxiing route. First, flights are sorted by their initial scheduled pushback times. Within the maximum allowable delay of 15 minutes, a random de-lay duration is generated for each departing flight. This duration is added to the scheduled pushback time to determine the actual pushback time for each flight in the population. Available taxiing routes are encoded as 1, 2, 3, 4. One encoded route is randomly as-signed to each arriving and departing aircraft to define its taxiing path attribute. These steps generate the lower-layer initial population with complete attributes (pushback time and taxiing route). New individuals are created by crossover and mutation of the generated delay durations and route sets. In each iteration, the fitness of newly generated individuals is calculated and used to update the population, allowing the algorithm to gradually converge to the final solution set.”

The specific revisions and additions in this article are at the end of Section 3.4.1 Overall Solution Framework as follows.

“The overall optimization framework is as follows:

Figure 2. Overall Solution Framework”

Comment 6: “Both the upper and lower layer models are an NP-hard problem. How to ensure the feasibility of the algorithm?”

Response 6:

The answer provided in this article is as follows. Specifically, for the upper level, separation violations are repaired by forward time-shifting the affected flights until all runway and handover constraints are satisfied; solutions exceeding maximum delay or time-window limits receive penalty terms. For the lower level, node/edge conflicts are addressed by delaying pushback within the allowable bound and/or switching to alternative taxi routes from the candidate set; remaining violations are penalized to guide the GA–SA search toward feasible regions.

Comment 7: “A specific scheduling result table for the upper and lower layer models should be provided.”

Response 7:

We added representative flight-level scheduling tables for both levels.

The specific revisions and additions in this article are at the end of Section 4.3 Computational Results as follows.

“The optimized scheduling results for the upper and lower level models are shown below.

Table 7 The optimization results of takeoff time of Upper-level model

Flight number	Departure airport	Departure runway	SOBT	TTOT (FCFS)	TTOT (upper model)
CA8639	ZBTJ	11L	7:45:00	8:00:49	7:58:51
CA2887	ZBTJ	34L	8:00:00	8:15:13	8:08:03
MU5102	ZBAA	36R	8:00:00	8:25:36	8:18:05
…	…	…	…	…	…

Table 8 The optimization results of pushback time of Lower-level model (Unit: s)

Flight number	Departure airport	Departure runway	SOBT	Scheduled Taxi Time	AOBT	Actual Taxi Time	Pushback waiting time
CA8639	ZBTJ	11L	7:45:00	879	7:46:26	745	86
CA2887	ZBTJ	34L	8:00:00	850	8:02:17	346	137
MU5102	ZBAA	36R	8:00:00	1536	8:10:22	463	622
…	…	…	…	…	…

“

 

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper introduces two-level scheduling for the multi-airport coordination. This two-level model manages departure sequencing and pushback scheduling. Authors suggest NSGA-II and a Genetic-Simulated Annealing algorithm as the solution and provide experiments and results, having significantly reduced delays and improved satisfaction.

 

I would like to suggest the structural (major) revision as follows:
1. Add Preliminary Section: Explain background knowledge. Introduce the current optimization model.
2. Add a formal problem statement in the problem section: Deliver system-wide optimization.
3. Add a solution (or proposed methodology) section: Propose your two-level optimization.
4. Experiment: Compare the current optimization model with the proposed model.

I also want to see the minor revision as follows:
1. Change the citation format from a plain number to the number in square brackets, like [1].
2. Add reference(s) for the following sentences or phrases:
- ... and inter-airport arrival coordination (for example, merging inbound streams) adds complexity and controller workload.
- By focusing on departures, we posit that substantial efficiency gains are achievable through improved surface and takeoff scheduling without interfering with critical arrival management.
3. Not sure what the following is about. Rewrite this.
Conditioned on the upper-level TTOTs, it jointly determines for each departure flight the pushback timing, pushback order (including holding at gate when necessary), and conflict-free taxi routes to reach the runway in time for the assigned slot; simultaneously, and without altering arrival sequencing, it computes conflict-free taxi routes for arriving flights from runway to gate so that surface movements remain deconflicted across arrivals and departures.

Author Response

Reviewer 4

Thank you for your valuable feedback! Based on your suggestions, we have made the following modifications to the manuscript. 

Comment 1: “I would like to suggest the structural (major) revision as follows: …”

Response 1:

We followed your structural suggestions by adding a short Preliminaries section to introduce the key concepts and the baseline FCFS practice. We also strengthened the problem section by explicitly stating the system-wide optimization goal. The proposed bi-level methodology is then presented as the solution approach, and the experimental section compares the baseline with the proposed model using the same dataset and operational runway modes.

Add the content of 3.1 Preliminaries, with the specific content as follows:

“For each departure flight , SOBT denotes the scheduled off-block time, TTOT denotes the target takeoff time assigned by the upper-level model, and ATOT denotes the realized takeoff time. The runway-entry time refers to the time when the aircraft reaches the runway queue (threshold). A handover point is a terminal-area fix where departure flows from different airports merge into shared routes; separation constraints are enforced at these fixes to prevent downstream conflicts. In current operations, each airport typically applies a first-come-first-served (FCFS) rule locally, which does not explicitly coordinate departures at shared handover points. Our bi-level framework replaces this fragmented practice by jointly sequencing metroplex departures (upper level) and realizing TTOTs through pushback and taxi planning under surface-conflict constraints (lower level).”

Adjust the structure of 3.2 Problem Statement as follows:

“Current tactical departure management operates independently per airport, resulting in uncoordinated convergence at shared waypoints under first-come, first-served (FCFS) principles. This fragmented approach causes three main issues. First, it leads to congestion and inefficient airspace utilization due to unplanned merging at shared waypoints. Second, it elevates controller workload because frequent manual interventions are required. Third, it creates systemic inequities in which certain airports gain persistent timing advantages.

In summary, independent airport scheduling yields suboptimal throughput and fragmented decision-making, failing to achieve system-wide optimization. These limitations necessitate an integrated air-ground coordination framework for the Beijing multi-airport system, which is achieved through a bi-level optimization model. The upper level coordinates departure sequencing across airports to allocate takeoff slots, while the lower level manages surface control (pushback timing and taxi routing) at each individual airport.

This integrated approach aims to minimize total departure delay and improve inter-airport fairness, ensuring no single hub bears disproportionate waiting time, while maintaining tactical-level consistency. Accordingly, our goal is a system-wide optimization that coordinates takeoff slots across airports while ensuring surface-level realizability and inter-airport equity.

The Beijing terminal airspace comprises a multi-airport system with three major hubs: Beijing Capital (ZBAA), Beijing Daxing (ZBAD), and Tianjin Binhai (ZBTJ). These airports share common departure waypoints, particularly ELKUR, IDKEX, and MUGLO, which serve as critical merge points for departures. ELKUR handles approximately one-quarter of total departures (ZBAA: 27.16%, ZBAD: 23.46%, ZBTJ: 25.47%), establishing it as a primary bottleneck during peak operations. While IDKEX and MUGLO accommodate lower traffic volumes, all shared points constrain departure throughput under high demand.

Figure 1. Schematic Diagram of Departure Routes in Beijing Terminal Airspace

Table 1. Proportion of Traffic Volume at Departure Handover Points

Departure handover point	Airport
	ZBAA	ZBAD	ZBTJ
BOTPU	25.14%	/	3.59%
DOTRA	6.82%	9.21%	/
ELKUR	27.16%	23.46%	25.47%
IDKEX	6.90%	10.77%	4.87%
IGMOR	3.11%	/	2.54%
MUGLO	3.77%	3.40%	12.84%
OMDEK	/	22.39%	25.37%
PEGSO	/	30.77%	25.32%
RUSDO	27.11%	/	/

“

 

 

Comment 2: “I also want to see the minor revision as follows: …”

Response 2:

We revised the manuscript to standardize all citations into the required square-bracket format (e.g., [1]) and ensured consistent spacing and punctuation throughout. Meanwhile, we added appropriate references to support the two statements in the Introduction regarding (i) the added complexity/workload of inter-airport arrival coordination and (ii) the potential for substantial efficiency gains via departure-side surface and takeoff scheduling. Finally, we rewrote the long sentence describing the lower-level model by splitting it into two clearer sentences, explicitly stating the decisions for departures and arrivals and clarifying that the arrival sequence remains fixed.

For the “Change the citation format from a plain number to the number in square brackets, like [1]”

The specific revisions and additions in this article are at Section References as follows.

For example:

[1]. Civil Aviation Administration of China, “2024 National Civil Aviation Flight Operation Efficiency Report,” CAAC, Beijing, 2025.

For the “Add reference(s) for the following sentences or phrases:

- ... and inter-airport arrival coordination (for example, merging inbound streams) adds complexity and controller workload.

- By focusing on departures, we posit that substantial efficiency gains are achievable through improved surface and takeoff scheduling without interfering with critical arrival management.”

The specific revisions and supplements to this article are as follows.

“…We intentionally exclude arrival sequencing, because arrivals are governed by strict ATC safety procedures, and coordinating arrivals across airports (e.g., merging inbound streams) adds significant complexity and increases controller workload [5]. By focusing on departures, we posit that substantial efficiency gains are achievable through improved surface and takeoff scheduling without interfering with critical arrival management [6].…”

For the “Not sure what the following is about. Rewrite this.…”

The specific revisions to this article are as follows:

“Given the upper-level TTOT assignments, the lower-level model determines each departure flight’s pushback timing, pushback order (holding at the gate if necessary), and a conflict-free taxi route to reach the runway in time for its assigned slot. At the same time, without altering the arrival sequence, the model computes conflict-free taxi routes for arriving flights from the runway to the gate, ensuring that surface movements for arrivals and departures do not conflict.”

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors propose a two-level collaborative scheduling model that integrates departure sequence planning with ground taxiing and pushback schedulingn for the Beijing-Tianjin airport cluster. Concerns initially raised about the absense of feedback between the upper and lower levels have been properly addressed in the revised version, and the scope is now clearly defined as an offline sequential coupling. The conclusions suggest applying a rolling-horizon approach using periodic TTOT(Target Take-Off Time) updates and feedback, indicating potential for practical application. In addition, the authors have refined dense sentences throughout the manuscript to enhance readability, and Section 4.4.3 explains in detail how the model manages multi-airport constraints, such as separating shared handover points. Since these revisions have been faithfully incoporated and the academic quality improved, final publication is recommended.

Reviewer 4 Report

Comments and Suggestions for Authors

I am satisfied with the current form of the manuscript, and I can say that the paper is ready to publish now. I hope the authors also like what they have.