Aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraint
By modeling aircraft maintenance task scheduling as a cuttable, variable-size packing problem, and combining time bins and cutting allocation strategies, resource allocation is optimized, solving the scheduling challenges under resource constraints and time constraints, and achieving efficient resource utilization and cost control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2026-02-04
- Publication Date
- 2026-05-15
AI Technical Summary
Existing aircraft maintenance task scheduling methods are difficult to effectively utilize fragmented resources under resource constraints, ignore time constraints and advance maintenance costs, resulting in infeasible plans and wasted resources.
The scheduling of aircraft maintenance tasks is modeled as a time-constrained, divisible, variable-size packing problem. Time bins and divisible allocation strategies are introduced, and resource allocation and time utilization are optimized through a mixed-integer linear programming model and a mathematical heuristic solution algorithm.
It improved the feasibility of maintenance plans and resource utilization, reduced total operating costs, significantly improved scheduling success rate under complex constraints, and reduced the average waste interval of maintenance tasks.
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Figure CN122047894A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aircraft maintenance management and operations optimization technology, specifically to a method for aircraft maintenance task allocation and scheduling based on a segmentation strategy and time constraints. Background Technology
[0002] Aircraft maintenance is a critical activity ensuring the safe operation and reliability of aircraft. Maintenance tasks typically have prescribed execution intervals, such as flight hours, flight cycles or calendar days, specific durations, and resource requirements. Current aircraft maintenance task scheduling faces the following challenges: Firstly, resource constraints and task conflicts: In actual operation, maintenance resources (such as man-hours and hangar capacity) are limited; when maintenance tasks for multiple aircraft overlap in time, intense resource competition arises, such as... Figure 1 As shown in the figure; secondly, the limitations of existing models: traditional maintenance planning usually treats a maintenance task as an indivisible whole. When faced with resource constraints, this "whole allocation" approach often leads to the plan being infeasible because it cannot flexibly utilize fragmented idle resources; thirdly, the shortcomings of the bin packing problem: although the variable-size bin packing problem has been used for maintenance scheduling, existing research often ignores the special time constraints of maintenance tasks (such as deadlines and arrival times) and the application of cutting strategies; fourthly, the cost of early maintenance is ignored: in order to make do with scheduling, tasks are often executed early, but this leads to a shortened actual maintenance interval, thereby increasing the maintenance frequency and total cost in the long run. Existing methods often ignore this implicit cost; therefore, there is an urgent need for an integrated intelligent scheduling method that can comprehensively consider resource constraints, task divisibility, time constraints, and the cost of early maintenance. Summary of the Invention
[0003] To achieve the above objectives, the present invention provides the following technical solution:
[0004] A method for aircraft maintenance task allocation and scheduling based on a cutting strategy and time constraints is proposed. This method models the aircraft maintenance task scheduling problem as a time-constrained, cuttable, variable-size packing problem, which is particularly suitable for solving complex combinatorial optimization problems involving multiple aircraft under limited maintenance resources and strict time window constraints. The aim is to improve the feasibility, resource utilization, and economic efficiency of airline maintenance plans. The method's steps are as follows: Environment and parameter initialization: Based on the known flight schedule, determine the maintenance opportunities for each aircraft that are grounded and meet the maintenance resource conditions. Furthermore, for situations where multiple aircraft are simultaneously parked at the same maintenance base, time boxes are defined; task items are generated based on each maintenance task, and cost parameters are obtained synchronously.
[0005] Constructing an optimization model: Input the data obtained after environment and parameter initialization into a pre-constructed mixed-integer linear programming model; wherein, the mixed-integer linear programming model includes at least: decision variables, objective function, and a set of constraints;
[0006] Solution Algorithm: A step-by-step algorithm is used to solve the mixed-integer linear programming model, including: initialization, allocation confirmation, resource monitoring, airworthiness monitoring, and iterative iteration. Initialization: Based on the lower bound of each maintenance task within the planned scope, a set of task items is created using the minimum number of executions. Allocation Confirmation: For each solution, a solver is used to calculate whether the allocation meets the resource capacity constraint. Resource Monitoring: If the resource capacity constraint is not met or violated, the resource monitoring program is triggered to delete task items from the violation timebox to meet the capacity constraint. Airworthiness Monitoring: Whenever the interval between two consecutive executions of a maintenance task violates its specified maximum time interval, the airworthiness monitoring program is activated. Iterative Iteration: After initialization, allocation confirmation, resource monitoring, and airworthiness monitoring are repeated until there are no violations or the maximum number of iterations is reached. If violations exist, the violating task items are added to the virtual machine and an alarm is issued.
[0007] Furthermore, maintenance opportunities and timeboxes are defined as follows: if aircraft A1 lands at a maintenance facility with maintenance capabilities, and the duration of this stoppage meets the conditions for performing a specific maintenance task on aircraft A1, then this stoppage is classified as a maintenance opportunity for that task. To address the situation where multiple aircraft are simultaneously parked at the same maintenance facility, timebox technology is applied: after creating all time periods, a fixed duration is assigned to each time period, thus different aircraft are assigned to different timebox groups, resulting in timeboxes. It has a fixed available resource capacity. and labor hours Task item generation: For each maintenance task According to its planned interval The interval that has been consumed since the start of the planning period will be instantiated into the corresponding maintenance task. Each task item m represents a specific maintenance execution; the cost parameters obtained include at least the set planning period and labor costs.
[0008] Furthermore, the decision variables are represented as follows:
[0009] When task item Assigned to maintenance opportunities To execute, decision variables The value is 1; otherwise it is 0.
[0010] (1)
[0011] In equation (1), Belongs to the collection of all planned aircraft The aircraft number; Belongs to aircraft Corresponding maintenance tasks task item set ; Belongs to aircraft Repair opportunity collection ;
[0012] Decision variables Indicates airplane Tasks In the time box The allocation ratio in;
[0013] (2)
[0014] In equation (2), Belongs to aircraft Repair opportunities medium timebox collection ;
[0015] When the plane Tasks Assigned to timebox Execution, decision variables The value is 1; otherwise it is 0.
[0016] (3).
[0017] Furthermore, the objective function is expressed as:
[0018] Define an objective function, namely equation (4), to minimize the total maintenance cost. This includes normal costs and additional costs; cost function The calculation is performed using equation (5), where the first term is the normal cost and the second term is the additional cost, based on the following:
[0019] (4)
[0020] (5)
[0021] (6)
[0022] In equations (4) to (6), It's an airplane. Execute task items Normal costs; It's an airplane. In maintaining opportunities Execute task items The additional ratio is reflected in the difference between the actual maintenance interval and the planned maintenance interval; It's an airplane. Tasks Planned maintenance intervals are measured by the maximum permissible flight hours; Indicates airplane Tasks Assigned to maintenance opportunities The actual maintenance interval during the execution is measured by the cumulative flight hours.
[0023] Furthermore, the set of constraints includes at least: uniqueness constraints, partitioning strategy constraints, resource capacity constraints, and time interval constraints; among which, the basis for the uniqueness constraint is:
[0024] (7)
[0025] The cut-off strategy constraint states that, given maintenance opportunities, the total cut-off rate matches the task allocation status. Specifically, when a task is assigned to a maintenance opportunity, the sum of the cut-off ratios for the time bins belonging to that maintenance opportunity equals 1; otherwise, it equals 0. The specific basis for this is:
[0026] (8)
[0027] To ensure the continuity of task execution, the cutting ratio of each task item must be greater than the preset minimum allowable cutting ratio. The basis is as follows:
[0028] (9)
[0029] In equation (9), Indicates airplane Tasks Minimum allowable cutting ratio during execution;
[0030] Resource capacity constraints are expressed as follows: within the area belonging to the airport Time Box All tasks assigned in the process cannot exceed their available working hours, based on the following:
[0031] (10)
[0032] In equation (10), Indicates airplane Assign task items Required working hours It is a set of airport numbers;
[0033] Within the airport Time Box All tasks allocated in the system cannot exceed their available capacity, based on the following:
[0034] (11)
[0035] In equation (11), Indicates airplane In the time box Internal space occupied capacity, Airport In the time box Available machine space capacity.
[0036] Furthermore, the time interval constraint means that equations (12), (13), and (14) ensure that any mission of each aircraft must comply with the maximum flight limit, which corresponds to calendar day, flight hour, or flight cycle, respectively, and all of them should be less than or equal to the corresponding maximum time limit, based on the following:
[0037] (12)
[0038] (13)
[0039] (14)
[0040] In equations (12) to (14), Indicates airplane Repair opportunities Time task item The cumulative calendar days from the start of the planning period, Indicates airplane Repair opportunities Time task item Cumulative flight hours from the start of the planning period Indicates airplane Repair opportunities Time task item The cumulative flight cycle starting from the planning period, , and They represent airplanes Execute task items The planned maximum calendar days, maximum flight hours, and maximum flight cycle. Indicates airplane Tasks The next set of units immediately following the task item.
[0041] Furthermore, the specific instructions for initialization are as follows: Set up the aircraft. Execute task items The planned maintenance interval is ,airplane Average flight hours are ,airplane Task The number of flight hours executed at the start of the planning period is 0; after setting the planning period, the minimum number of executions required for this mission within the planning period is [number missing]. and will Defined as the corresponding lower bound, i.e. the theoretically optimal number of executions;
[0042] The specific basis for creating a set of task items by minimum execution count is as follows: the planned interval for this task is set to be once every Q flight hours, and the average usage of this aircraft is 0.375Q flight hours per day; the cumulative flight hours since the start of the planning period are extracted from the aircraft's flight schedule; the first execution of this task is assigned to... , or Therefore, the maintenance opportunity for the first task item is... The earliest maintenance opportunity for the first task item is This creates a new task item for the second execution; the maintenance opportunity for the new task item is... If the first task item is assigned to In the middle, the chance of the second task item is Finally, the process loops back to the earliest maintenance opportunity for the first task item. The allocation of tasks for each aircraft is initialized using a strategy that assigns tasks based on the minimum number of executions, until no further maintenance opportunities can be identified within the planned scope.
[0043] Furthermore, the specific details of the allocation processing are as follows: After the solver calculates and maintains the allocation feasibility, at least two scenarios exist: Scenario 1: The current task allocation satisfies the available resource constraints for each time period; Scenario 2: The current allocation violates the available resource constraints for at least one time period. For Scenario 1, the current solution is taken as the final solution; for Scenario 2, the information on constraint violations in the solution includes: the aircraft violating the constraints, the task item, and the time period, which must be stored in the resource capacity violation set. and time interval violation set middle; Including information related to resource capacity violations , indicating time box China Aircraft Tasks This violated resource capacity constraints. Including information related to time interval violations , indicating airplane Repair opportunities Time task item The time interval constraint was violated.
[0044] Furthermore, the specific details of resource monitoring are as follows: When resource capacity constraints are violated, the monitoring program is triggered: from the violation time box... Exclude tasks from the list to meet capacity constraints; prioritize all tasks within the timebox based on their scheduled deadlines; consider tasks in reverse order of priority, starting with the lowest priority task and working backwards from the priority list. For indexing; after identifying task items Afterwards, Delete ,in For time boxes The task item set in;
[0045] The process of deleting a task item is as follows: First, calculate... If the cumulative flight interval exceeds its execution deadline, proceed to step three; otherwise, if the project... If the task interval is still within the deadline, remove it from this timebox and priority list and proceed to step two; otherwise, select the task from the list... The task item with the second lowest priority is designated as the priority item. Then restart the first step; the second step is to recalculate the occupied working hours and machine space capacity in this box; if the occupied resources are less than or equal to the maximum available maintenance resources, the program terminates; otherwise, select from the list... The task item with the second lowest priority is designated as the priority item. Then return to step one; step three, remove the task from the timebox and priority list. Then, the occupied working hours and machine capacity within the time box are recalculated; if the total occupied resources are less than or equal to the available maintenance resources, the program terminates; otherwise, a time box is selected from the list. The task item with the second lowest priority is designated as... Then, it will return to the first step and continue the iterative loop until the resource capacity constraint is met.
[0046] Furthermore, the specific details of airworthiness monitoring are as follows: Whenever the interval between two consecutive executions of a maintenance task violates its specified maximum time interval, the corresponding airworthiness monitoring procedure is activated to determine the feasible maintenance opportunities for packaging the task item. The first step is to check whether the removal of a task from the resource monitoring procedure results in a maintenance interval violation. The second step, if a violation occurs, is to search for the set of feasible maintenance opportunities prior to the removal location. ,like If this task is not assigned, it will be reassigned to the nearest repair opportunity before the removal location; where, This represents the empty set.
[0047] This invention provides an aircraft maintenance task allocation and scheduling method based on a cutting strategy and time constraints, which has the following beneficial effects: (1) The scheme models the aircraft maintenance task allocation problem as a time-constrained, divisible, variable-size bin packing problem, regards maintenance opportunities as "bins" and maintenance tasks as "items", and introduces the concept of "time bins" to subdivide overlapping aircraft maintenance opportunities; at the same time, it also introduces a cutting allocation strategy, drawing on the work breakdown structure in project management, which allows a large maintenance task to be allocated to multiple consecutive time bins with different resource capacities by vertical cutting, under the premise of satisfying the "safe suspension" point and the smallest atomic unit, thereby maximizing resource utilization. Figure 3 An example diagram of a segmentation strategy is provided, which enables the present invention to reassign tasks that are deemed "infeasible" due to resource limitations in traditional methods to fragmented time boxes through reasonable segmentation, thereby significantly improving the scheduling success rate under complex constraints.
[0048] (2) This scheme establishes a cost function that takes into account early maintenance and defines an objective function that includes normal execution costs and additional costs. The additional costs are calculated based on the difference between the actual maintenance interval and the planned interval, and are used to quantify the waste of maintenance interval caused by early execution of tasks. By incorporating the impact of early maintenance into the cost model, this scheme can reduce total operating costs and significantly reduce the average waste interval of maintenance tasks.
[0049] (3) This scheme develops a hybrid algorithm that combines constructive heuristic algorithm and exact solution technology by designing a mathematical heuristic solution algorithm. The algorithm dynamically repairs infeasible solutions through two core processes: resource monitoring and airworthiness monitoring, and quickly finds the approximate optimal solution in a large search space. The proposed mathematical heuristic algorithm has a significantly improved speed compared to directly using commercial solvers when solving large-scale problems, and the difference in optimality is very small.
[0050] (4) This solution handles fictitious maintenance opportunities. To prevent program crashes in unsolvable situations, a "fictitious maintenance opportunity" is set after the planning period ends. This is used to temporarily store unassignable tasks and generate warning signals due to insufficient resources. At the same time, the application of the overall solution ensures the feasibility of actual operation through strict modeling and constraints on hourly maintenance capabilities and time windows, thus fundamentally guaranteeing operational safety. Attached Figure Description
[0051] Figure 1 This is a schematic diagram illustrating a case of overlapping maintenance between aircraft.
[0052] Figure 2 An example diagram showing the cutting of multiple timeboxes within an overlapping stop time;
[0053] Figure 3 Example diagram of task item splitting strategy;
[0054] Figure 4 This is a diagram illustrating recurring task items and maintenance opportunities for a maintenance task; where, in Figure 4 Note: 1st-7th represent all possible repair opportunities to perform this task. This indicates the optional cumulative flight hours (at which point the aircraft is parked at the airport) for performing this mission, corresponding to 6, 12, 20, ..., 46 flight hours (FHs). Detailed Implementation
[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0056] Please see Figures 1 to 4 This embodiment provides a method for aircraft maintenance task allocation and scheduling based on a segmentation strategy and time constraints. The technical solution described in this embodiment is based on real flight schedule data from a certain airline, including 30 aircraft, 3301 flight segments, 106 airports, and 9 maintenance bases. The specific steps of this method are as follows:
[0057] S1. Environment and parameter initialization:
[0058] Based on the known flight schedules, identify maintenance opportunities for each aircraft that are grounded and meet maintenance resource requirements. Furthermore, for situations where multiple aircraft are simultaneously parked at the same maintenance base, time boxes are defined; task items are generated based on each maintenance task, and cost parameters are obtained synchronously.
[0059] Regarding the definition of repair opportunities and time boxes: such as Figure 2 As shown, if aircraft A1 lands at a maintenance facility with maintenance capabilities, and the stoppage has sufficient duration to perform a specific maintenance task on aircraft A1, then this stoppage is classified as a maintenance opportunity for that task. For situations where multiple aircraft are simultaneously parked at the same maintenance facility, timeboxing technology is applied, similarly... Figure 2 As shown, the first overlap between aircraft A3 and A4 is from 16:00 to 18:00, prompting the creation of a 16:00-18:00 overlap. The time period is 18:00; the subsequent overlapping area occurs at 18:00 and ends at 20:00, which results in 18:00-20:00 ( The establishment of time periods; after creating all the necessary time periods, a fixed duration is assigned to each time period, so aircraft A1-A4 are assigned to different box groups: A1 contains four boxes ( - A2 contains four boxes ( - A3 contains three boxes ( - A4 contains three boxes ( - Timebox It has a fixed available resource capacity. and labor hours It should be noted that the individual boxes in the aforementioned box group are time boxes; Task item generation: For each maintenance task According to its planned interval The interval that has been consumed since the start of the planning period will be instantiated into the corresponding maintenance task. Each task item m represents a specific maintenance execution; the cost parameters obtained include at least the set planning period and labor costs, for example: the planning period is 30 days and the labor cost is $55 / hour.
[0060] S2. Constructing an optimization model:
[0061] The data obtained from S1 after environment and parameter initialization is input into the pre-constructed mixed-integer linear programming model; wherein, the mixed-integer linear programming model includes at least: decision variables, objective function and constraint set;
[0062] Specifically, decision variables:
[0063] When task item Assigned to maintenance opportunities To execute, decision variables The value is 1; otherwise it is 0.
[0064] (1)
[0065] In equation (1), Belongs to the collection of all planned aircraft The aircraft number; Belongs to aircraft Corresponding maintenance tasks task item set ; Belongs to aircraft Repair opportunity collection .
[0066] Decision variables Indicates airplane Tasks In the time box The allocation ratio in;
[0067] (2)
[0068] In equation (2), Belongs to aircraft Repair opportunities medium timebox collection .
[0069] When the plane Tasks Assigned to timebox Execution, decision variables The value is 1; otherwise it is 0.
[0070] (3)
[0071] Objective function:
[0072] Define an objective function, namely equation (4), to minimize the total maintenance cost. This includes normal costs and additional costs; cost function The calculation is performed using equation (5), where the first term is the normal cost and the second term is the additional cost, based on the following:
[0073] (4)
[0074] (5)
[0075] (6)
[0076] In equations (4) to (6), It's an airplane. Execute task items Normal costs; It's an airplane. In maintaining opportunities Execute task items The additional ratio is reflected in the difference between the actual maintenance interval and the planned maintenance interval; It's an airplane. Tasks Planned maintenance intervals are measured by the maximum permissible flight hours; Indicates airplane Tasks Assigned to maintenance opportunities The actual maintenance interval during the execution is measured by the cumulative flight hours.
[0077] The set of constraints includes at least: uniqueness constraints, cutting strategy constraints, resource capacity constraints, and time interval constraints; among which, the uniqueness constraint ensures that each task item is assigned only once by equation (7), either to a maintenance opportunity within the planning period or to a virtual maintenance opportunity after the planning period, based on the following:
[0078] (7)
[0079] Cutting strategy constraint: According to equation (8), in a given maintenance opportunity, the total cutting rate is matched with the allocation status of the task item. That is, when a task item is assigned to a maintenance opportunity, the time cutting ratios of the time bins to which this maintenance opportunity belongs are added together to equal 1, otherwise, they are equal to 0.
[0080] (8)
[0081] To ensure the continuity of task execution, the cutting ratio of each task item must be greater than the preset minimum allowable cutting ratio. The definition is as shown in equation (9):
[0082] (9)
[0083] In equation (9), Indicates airplane Tasks Minimum allowable cutting ratio during execution.
[0084] Resource capacity constraints: According to equation (10), within the airport Time Box All tasks assigned in the process cannot exceed their available working hours:
[0085] (10)
[0086] In equation (10), Indicates airplane Assign task items Required working hours It is a set of airport numbers.
[0087] According to equation (11), in the case of an airport Time Box All task items allocated in the middle cannot exceed their available capacity:
[0088] (11)
[0089] In equation (11), Indicates airplane In the time box Internal space occupied capacity, Airport In the time box Available machine space capacity.
[0090] Time interval constraints: Equations (12), (13), and (14) ensure that any mission of each aircraft must comply with the maximum flight limits, corresponding to calendar days, flight hours, or flight cycles (cycles), which should all be less than or equal to the corresponding maximum time limits.
[0091] (12)
[0092] (13)
[0093] (14)
[0094] In equations (12) to (14), Indicates airplane Repair opportunities Time task item The cumulative calendar days from the start of the planning period, Indicates airplane Repair opportunities Time task item Cumulative flight hours from the start of the planning period Indicates airplane Repair opportunities Time task item The cumulative flight cycle starting from the planning period, , and They represent airplanes Execute task items The planned maximum calendar days, maximum flight hours, and maximum flight cycle. Indicates airplane Tasks The next set of units immediately following the task item.
[0095] S3. Solution Algorithm (Mathematical Heuristic):
[0096] A step-by-step algorithm is used to solve the mixed-integer linear programming model, including: initialization, allocation confirmation, resource monitoring, airworthiness monitoring, and iterative iteration. Initialization involves creating a set of task items based on the lower bound of each maintenance task within the planned scope, using the minimum number of executions. Allocation confirmation involves using a solver to calculate for each solution to determine if the allocation meets resource capacity constraints. Resource monitoring involves triggering a resource monitoring program when resource capacity constraints are not met or violated, starting from the violation timebox. The process involves: deleting task items to meet capacity constraints; airworthiness monitoring: activating the airworthiness monitoring program whenever the interval between two consecutive maintenance tasks violates the maximum specified time interval, and determining feasible maintenance opportunities for packaging the task item; iterative loop: after initialization, repeatedly verify allocation processing, resource monitoring, and airworthiness monitoring until no violations are detected or the maximum number of iterations is reached; if violations are detected, all violating task items are added to the virtual machine and an alarm is issued.
[0097] The specific instructions for initialization are as follows:
[0098] For each maintenance task within the planned scope, there exists a lower bound, which represents the basic number of executions based on its planned interval; for example, assuming an aircraft... Execute task items The planned maintenance interval is 20 flight hours. ),airplane The average flight hours are 160 hours / 30 days. ),airplane Task The number of flight hours executed at the start of the planning period was 0 ( Within the 30-day planning period, the minimum number of times this task should be executed within the planning period is: Therefore, using A lower bound is defined, which is the theoretically optimal number of executions assuming no other constraints are considered.
[0099] Based on this lower bound, the solution initialization begins by creating a set of task items using the minimum number of executions. For a better illustration of the initialization and allocation process, please refer to [link / reference]. Figure 3 There are 7 parking events, indicating that the aircraft is parked at a certain airport. Assume the planned interval for this task is once every 20 flight hours, and the average usage of the aircraft is 7.5 flight hours per day. Extract the cumulative flight hours from the start of the planning period from the aircraft's flight schedule, representing them as 6 flight hours, 12 flight hours, ..., 46 flight hours respectively. S3.1, the first execution of this task can be assigned to... , or In this case, because the accumulated flight hours prior to this maintenance are within its scheduled maintenance interval, i.e., less than or equal to 20 flight hours, the maintenance opportunity for the first task item is... Indexed using "*"; S3.2, it can be found that the earliest maintenance opportunity for the first task item is Therefore, a new task item can be created for the second execution; S3.3, the maintenance opportunity for the new task is... If the first project is assigned to In the middle, the opportunity for the second task item is... Finally, the process loops back to S3.2 until no further maintenance opportunities can be identified within the planned scope.
[0100] At this point, the strategy of allocating tasks based on the minimum number of executions only applies when... and If a task is executed during the process, it is assigned based on the closest planned interval. The interval for advance maintenance is calculated as follows:
[0101] ;
[0102] By allocating tasks to each aircraft based on the minimum number of executions, this initial allocation method relaxes resource capacity constraints.
[0103] The specific instructions for the allocation process are as follows:
[0104] It employs precise allocation technology. For each solution, a commercial solver can be used for rapid calculation, with the option to incorporate a splitting strategy to precisely determine whether the allocation satisfies resource capacity constraints. After the commercial solver calculates and maintains the feasibility of the allocation, there are two possible scenarios: 1) The current task allocation satisfies the available resource constraints for each time period; 2) The current allocation violates the available resource constraints for at least one time period. In the first case, the current allocation is a feasible solution. However, in reality, it is more likely to face the second scenario. Information regarding constraint violations in the solution, including the violating aircraft, task items, and time periods, needs to be stored in a resource capacity violation set. and time interval violation set middle; Including information related to resource capacity violations , indicating time box China Aircraft Tasks This violated resource capacity constraints. Including information related to time interval violations , indicating airplane Repair opportunities Time task item The time interval constraint was violated.
[0105] The specific details of resource monitoring are as follows:
[0106] This monitoring program is triggered whenever resource capacity constraints are violated; in such cases, the violation must be detected from the time bin. Certain tasks are excluded to meet capacity constraints; all tasks within the timebox are prioritized based on their scheduled deadlines; that is, the closer a task is to its execution deadline, the higher its priority; tasks are then considered in reverse order of priority, starting with the lowest priority task and proceeding upwards. For indexing; after identifying task items Afterwards, Delete ,in For time boxes The task item set in; it is worth noting that, The priority list needs to be reset every time a task item is deleted, so they need to be treated as a dynamic evolution set and a dynamic list.
[0107] Then, perform the following operations to delete the task item:
[0108] Step 1: Calculation If the cumulative flight interval exceeds its execution deadline, proceed to step three; conversely, if the project... If the task interval is still within the deadline, remove it from this timebox and priority list and proceed to step two; otherwise, select the task from the list... The task item with the second lowest priority is designated as... Then restart the first step; the second step is to recalculate the occupied man-hours and machine space capacity in this box; if these occupied resource counts are less than or equal to the maximum available maintenance resource count, this program terminates; otherwise, select from the list... The task item with the second lowest priority is designated as... Then return to step one; step three, remove the task from the timebox and priority list. Then, recalculate the occupied working hours and machine capacity within the time box; if the total occupied resources are less than or equal to the available maintenance resources, the program terminates; otherwise, select from the list... The task item with the second lowest priority is designated as... Then, it will return to the first step and continue the iterative loop until the resource constraints of this box are met.
[0109] The specific instructions for airworthiness monitoring are as follows:
[0110] This procedure is activated whenever the interval between two consecutive executions of a maintenance task violates its specified maximum time interval. The key is to determine the feasible maintenance opportunities that encapsulate the task item. The first step is to check if the removal of the task from the resource monitoring program caused the maintenance interval violation. The second step, if a violation occurs, is to search for the set of feasible maintenance opportunities prior to the removal location. ,like If so, the task will be reassigned to the nearest repair opportunity before it was removed from the location.
[0111] The specific explanation of loop iteration is as follows:
[0112] After step 1 (corresponding to initialization) is executed, repeat steps 2 (corresponding to confirmation and allocation processing) to 4 (corresponding to airworthiness monitoring) until there are no violations or the maximum number of iterations is reached (e.g., 5 times). If there are violations, all violating task items will be placed in the virtual machine and an alarm message will be issued to remind the dispatcher to take other measures to resolve the violations (e.g., extend the aircraft ground parking time or increase the corresponding maintenance resources in the maintenance base).
[0113] Implementation effect verification: Under the condition of limited resources (such as only 60% maintenance resources), the cutting strategy proposed in this invention can still find a feasible solution, while the traditional non-cutting method cannot obtain a feasible solution when the resources are less than 80%; at the same time, the algorithm's solution time (average 251-407 seconds) is much lower than that of the commercial solver Gurobi (1042-11212 seconds), and the difference in optimality is extremely low (0.22%-1.87%).
[0114] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.
[0115] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0116] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.
Claims
1. A method for aircraft maintenance task allocation and scheduling based on a segmentation strategy and time constraints, characterized in that, The method involves the following steps: Environment and parameter initialization: Based on the known flight schedule, determine the maintenance opportunities for each aircraft that are grounded and meet the maintenance resource requirements. Furthermore, for situations where multiple aircraft are simultaneously parked at the same maintenance base, time boxes are defined; task items are generated based on each maintenance task, and cost parameters are obtained synchronously. Constructing an optimization model: Input the data obtained after environment and parameter initialization into a pre-constructed mixed-integer linear programming model; wherein, the mixed-integer linear programming model includes at least: decision variables, objective function, and a set of constraints; Solution Algorithm: A step-by-step algorithm is used to solve the mixed-integer linear programming model, including: initialization, allocation confirmation, resource monitoring, airworthiness monitoring, and iterative iteration. Initialization: Based on the lower bound of each maintenance task within the planned scope, a set of task items is created using the minimum number of executions. Allocation Confirmation: For each solution, a solver is used to calculate whether the allocation meets the resource capacity constraint. Resource Monitoring: If the resource capacity constraint is not met or violated, the resource monitoring program is triggered to delete task items from the violation timebox to meet the capacity constraint. Airworthiness Monitoring: Whenever the interval between two consecutive executions of a maintenance task violates its specified maximum time interval, the airworthiness monitoring program is activated. Iterative Iteration: After initialization, allocation confirmation, resource monitoring, and airworthiness monitoring are repeated until there are no violations or the maximum number of iterations is reached. If violations exist, the violating task items are added to the virtual machine and an alarm is issued.
2. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 1, characterized in that, Maintenance opportunities and timeboxes are defined as follows: If aircraft A1 lands at a maintenance facility with maintenance capabilities, and the duration of this stoppage meets the conditions for performing a specific maintenance task on aircraft A1, then this stoppage is classified as a maintenance opportunity for that task. To address situations where multiple aircraft are simultaneously stopped at the same maintenance facility, timeboxing technology is applied: after creating all time periods, a fixed duration is assigned to each time period. Therefore, different aircraft are assigned to different timebox groups, resulting in a timebox... It has a fixed available resource capacity. and labor hours Task item generation: For each maintenance task According to its planned interval The interval that has been consumed since the start of the planning period will be instantiated into the corresponding maintenance task. Each task item m represents a specific maintenance execution; the cost parameters obtained include at least the set planning period and labor costs.
3. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 1, characterized in that, Decision variables are represented as follows: When task item Assigned to maintenance opportunities To execute, decision variables The value is 1; otherwise it is 0. ；（1） In equation (1), Belongs to the collection of all planned aircraft The aircraft number; Belongs to aircraft Corresponding maintenance tasks task item set ; Belongs to aircraft Repair opportunity collection ; Decision variables Indicates airplane Tasks In the time box The allocation ratio in; ；（2） In equation (2), Belongs to aircraft Repair opportunities medium timebox collection ; When the plane Tasks Assigned to timebox Execution, decision variables The value is 1; otherwise it is 0. （3）。 4. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 1, characterized in that, Objective function representation: Define an objective function, namely equation (4), to minimize the total maintenance cost. This includes normal costs and additional costs; cost function The calculation is performed using equation (5), where the first term is the normal cost and the second term is the additional cost, based on the following: ；（4） ；（5） ；（6） In equations (4) to (6), It's an airplane. Execute task items Normal costs; It's an airplane. In maintaining opportunities Execute task items The additional ratio is reflected in the difference between the actual maintenance interval and the planned maintenance interval; It's an airplane. Tasks Planned maintenance intervals are measured by the maximum permissible flight hours; Indicates airplane Tasks Assigned to maintenance opportunities The actual maintenance interval during the execution is measured by the cumulative flight hours.
5. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 1, characterized in that, The set of constraints must include at least: uniqueness constraints, partitioning strategy constraints, resource capacity constraints, and time interval constraints; among which, the basis for uniqueness constraints is: ；（7） The cut-off strategy constraint states that, given maintenance opportunities, the total cut-off rate matches the task allocation status. Specifically, when a task is assigned to a maintenance opportunity, the sum of the cut-off ratios for the time bins belonging to that maintenance opportunity equals 1; otherwise, it equals 0. The specific basis for this is: ；（8） To ensure the continuity of task execution, the cutting ratio of each task item must be greater than the preset minimum allowable cutting ratio. The basis is as follows: ；（9） In equation (9), Indicates airplane Tasks Minimum allowable cutting ratio during execution; Resource capacity constraints are expressed as follows: within the area belonging to the airport Time Box All tasks assigned in the process cannot exceed their available working hours, based on the following: ；（10） In equation (10), Indicates airplane Assign task items Required working hours It is a set of airport numbers; Within the airport Time Box All tasks allocated in the system cannot exceed their available capacity, based on the following: ；（11） In equation (11), Indicates airplane In the time box Internal space occupied capacity, Airport In the time box Available machine space capacity.
6. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 5, characterized in that, The time interval constraint means that equations (12), (13), and (14) ensure that any mission of each aircraft must comply with the maximum flight limit, which corresponds to calendar day, flight hour, or flight cycle, respectively, and all of them should be less than or equal to the corresponding maximum time limit, based on the following: ；（12） ；（13） ；（14） In equations (12) to (14), Indicates airplane Repair opportunities Time task item The cumulative calendar days from the start of the planning period, Indicates airplane Repair opportunities Time task item Cumulative flight hours from the start of the planning period Indicates airplane Repair opportunities Time task item The cumulative flight cycle starting from the planning period, , and They represent airplanes Execute task items The planned maximum calendar days, maximum flight hours, and maximum flight cycle. Indicates airplane Tasks The next set of units immediately following the task item.
7. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 1, characterized in that, The specific instructions for initialization are as follows: Set up the aircraft Execute task items The planned maintenance interval is ,airplane Average flight hours are ,airplane Task The number of flight hours executed at the start of the planning period is 0; after setting the planning period, the minimum number of executions required for this mission within the planning period is [number missing]. and will Defined as the corresponding lower bound, i.e. the theoretically optimal number of executions; The specific basis for creating a set of task items by minimum execution count is as follows: the planned interval for this task is set to be once every Q flight hours, and the average usage of this aircraft is 0.375Q flight hours per day; the cumulative flight hours since the start of the planning period are extracted from the aircraft's flight schedule; the first execution of this task is assigned to... , or Therefore, the maintenance opportunity for the first task item is... The earliest maintenance opportunity for the first task item is This creates a new task item for the second execution; the maintenance opportunity for the new task item is... ; If the first task is assigned to In the middle, the chance of the second task item is Finally, the process loops back to the earliest maintenance opportunity for the first task item. Until no further maintenance opportunities can be identified within the planned scope; The strategy of allocating tasks based on the minimum number of executions is used to initialize the assignment of each task for each aircraft.
8. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 6, characterized in that, The specific instructions for confirming the allocation process are as follows: After the solver calculates and maintains the allocation feasibility, there are at least two possible scenarios: Scenario 1: The current task allocation satisfies the available resource constraints for each time period; Scenario 2: The current allocation violates the available resource constraints for at least one time period. Response to scenario 1: Treat the current solution as the final solution; To address scenario 2, the solution should include information on constraint violations, such as the aircraft, task item, and time period involved. This information should be stored in the resource capacity violation set. and time interval violation set middle; Including information related to resource capacity violations , indicating time box China Aircraft Tasks This violated resource capacity constraints. Including information related to time interval violations , indicating airplane Repair opportunities Time task item The time interval constraint was violated.
9. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 6, characterized in that, The specific instructions for resource monitoring are as follows: When resource capacity constraints are violated, the monitoring program is triggered: from the violation time box. Exclude tasks from the list to meet capacity constraints; prioritize all tasks within the timebox based on their scheduled deadlines; consider tasks in reverse order of priority, starting with the lowest priority task and working backwards from the priority list. For indexing; after identifying task items Afterwards, Delete ,in For time boxes The task item set in; The process of deleting a task item is as follows: First, calculate... If the cumulative flight interval exceeds its execution deadline, proceed to step three; otherwise, if the project... If the task interval is still within the deadline, remove it from this timebox and priority list and proceed to step two; otherwise, select the task from the list... The task item with the second lowest priority is designated as... And restart the first step; The second step is to recalculate the occupied man-hours and machine space capacity in this box; If the number of resources used is less than or equal to the maximum number of available maintenance resources, this program will terminate. Otherwise, select from the list. The task item with the second lowest priority is designated as... Then return to step one; The third step is to remove the task from the timebox and priority list. ; Subsequently, the occupied working hours and machine space capacity within the time box were recalculated; If the total number of resources used is less than or equal to the available maintenance resources, the program terminates; otherwise, it selects from the list. The task item with the second lowest priority is designated as... Then, it will return to the first step and continue the iterative loop until the resource capacity constraint is met.
10. The aircraft maintenance task allocation and scheduling method based on cutting strategy and time constraints according to claim 9, characterized in that, The specific instructions for airworthiness monitoring are as follows: Whenever the interval between two consecutive executions of a maintenance task violates its specified maximum time interval, the corresponding airworthiness monitoring procedure is activated to determine the feasible maintenance opportunity for packaging the task item; the first step is to check whether the removal of the task from the resource monitoring procedure has caused the maintenance interval violation. The second step, if violated, is to search for the set of feasible repair opportunities prior to the location being removed. ,like If this task is not assigned, it will be reassigned to the nearest repair opportunity before the removal location; where, This represents the empty set.