A parallel scheduling method for aircraft multi-station support operations

Abstract

The invention discloses a parallel scheduling method for aircraft multi-station support operations, which belongs to the field of operations research and optimization; specifically, first, initialize the stage variables and parking position status, then, in the current scheduling stage, respectively calculate the scheduled, ongoing and schedulable process sets; arrange the M processes in the schedulable process set according to priority; for the kth schedulable process, determine whether a parking position to support the process can be found, if so, add the current process to the ongoing process set, set the start and end time, and update the parking position status; let the number k increase by 1 to continue to judge; otherwise, the current process is not processed, and the sequence number k of the process is directly increased by 1, and the next one is selected to continue to judge; until k is greater than M, let the stage variable g increase by 1, and transfer to the next scheduling stage; when all processes are scheduled, output the scheduling plan. The invention is used to formulate a detailed and thorough scheduling plan to complete the support operation safely and efficiently.

Description

Technical Field

[0001] The invention belongs to the field of operations research and optimization, and in particular is a method for parallel scheduling of aircraft multi-station support operations. Background Art

[0002] Before taking off, the aircraft needs to complete a series of support operations such as refueling, charging and inspection at the support site. Due to the length of the pipeline at the resource site, a single parking stand may not be able to provide all the resources such as fuel, oxygen and nitrogen required for aircraft support. Therefore, during the operation, the aircraft needs to switch between multiple parking stands to complete all support operations, which is the "multi-station" support mode.

[0003] The "multi-stop" aircraft support process involves switching between different support positions. The operation is dangerous and difficult to dispatch. Traditional manual dispatch is inefficient and prone to risks due to personnel decision-making errors. Therefore, it is necessary to study scientific aircraft "multi-stop" support operation dispatching methods and formulate detailed and thorough dispatching plans in order to complete the support operations safely and efficiently. Summary of the invention

[0004] Aiming at the problem that the scheduling of aircraft "multi-stop" support operations based on traditional manual experience is inefficient and prone to risks caused by personnel decision-making errors, the present invention proposes a parallel scheduling method for aircraft multi-stop support operations, which can be used to formulate detailed and careful scheduling plans to complete the support operations safely and efficiently.

[0005] The specific steps are:

[0006] Step 1: Set the phase variable to g = 1, initialize the scheduled process set and the ongoing process set, and set the status of all parking positions to idle;

[0007] The fleet to be supported includes n aircraft, represented by I = {1, 2, ..., i, ..., n}; the set of operating procedures for the i-th aircraft is J i ={1,2,...,|J i |}, and the symbol (i,j) is used to represent the j-th process of the i-th aircraft.

[0008] Ongoing process set A g Initialized as the first process set of each aircraft,

[0009] Scheduled process set S g Initialize to an empty set;

[0010] There are m parking spaces on the support site, and the set is PS = {1, 2, ...p, ..., m}; the state of parking space p at time t

[0011] Step 2: Let g = g + 1. In the current scheduling stage g, calculate the scheduled process set, the process set being scheduled, and the process set that can be scheduled respectively.

[0012] The scheduling time t of the current stage g g :t g =min{S ij +d ij |(i,j)∈A g-1};

[0013] S ij is the start time of the process, d ij It represents the duration of the j-th process (i, j) of the i-th aircraft.

[0014] The calculation formula for the set of processes that have completed scheduling is: S g =S g-1 ∪{(i,j)|(i,j)∈A g-1 ∧t g =E ij};

[0015] E ij is the end time of process (i,j).

[0016] The calculation formula for the ongoing process set is: A g =A g-1 -{(i,j)|(i,j)∈A g-1 ∧t g =E ij}

[0017] The calculation formula of the schedulable process set is:

[0018] P ij is the set of immediate predecessor processes of process (i, j).

[0019] Step 3: Assume that the size of the schedulable process set is M, that is, |D g |=M|, for the M processes in the schedulable process set, arrange them from high to low priority, and select each process as the process to be scheduled one by one;

[0020] Step 4: For the kth process to be scheduled (μ, ν), determine whether a parking position can be found to guarantee the process (μ, ν). If so, add the current process (μ, ν) to the ongoing process set A. gIn the process (μ, ν), the start and end time of the process (μ, ν) are set, and the parking position state variable is updated; the sequence number k of the process is incremented by 1, and the next process is selected for further judgment; otherwise, the current process (μ, ν) is not processed, the sequence number k of the process is directly incremented by 1, and the next process is selected for further judgment;

[0021] Initialize k=1;

[0022] The specific process of finding the parking position that guarantees the current scheduled process (μ, ν) includes the following steps:

[0023] Step 4.1, determine whether the parking space where the aircraft μ to be scheduled is currently located can be used to support the process (μ, ν) to be scheduled. If so, set the process (μ, ν) to be scheduled to be supported at the current parking space, set its start and end time, update the parking space state variable, and end the search process; otherwise, proceed to step 4.2;

[0024] Specifically:

[0025] First, according to the parking position state variables, determine the aircraft μ at time t g The parking position p,

[0026] Then, determine whether parking position p can guarantee (μ, ν). If so, there are resources r required for the execution of process (μ, ν) μν ∈c p , c p is the set of resource types that can be provided by the pth parking space; then set the start time of (μ, ν) to S μν =t g , the end time is E μν =t g +d μν , add the step (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, update parking space p in time period [t g +1,t g +d μν ] is occupied by aircraft μ, that is, T p (t g +1:t g +d μν )=μ, end.

[0027] If parking space p cannot be used for (μ, ν) protection, then Finish;

[0028] Step 4.2, determine whether there is an idle parking space available for the process to be scheduled. If yes, transfer the aircraft to be scheduled to the idle parking space found, set the process to be scheduled to be guaranteed at the idle parking space, set its start and end time, update the parking space state variable, and end the search process; otherwise, proceed to the next step;

[0029] Specifically:

[0030] First, according to the parking space state variables, find g The parking stands that are free and can provide the resources required by the process (μ, ν) are numbered and saved in the set EM. At the same time, the last time each parking stand was occupied by an aircraft is found.

[0031] EM is initially an empty set; Indicates the last time parking stand s was occupied by an aircraft;

[0032] Then, the parking space numbers in the set EM are sorted according to Arrange in order from small to large, and judge whether each parking position in the set EM can be used to ensure the process (μ, ν);

[0033] That is, it is determined whether the time when the aircraft μ is untied from the current parking position p and transferred to an empty parking position q in EM is greater than the last time that the parking position is occupied by an aircraft, and whether the time when the aircraft μ is transferred to the new parking position q and the tethering is completed is less than the scheduling time t g If yes, it means that the parking position q can be used to guarantee the process (μ, ν), then the start time of (μ, ν) is set to: the time when the aircraft μ is transferred from the current parking position p to the parking position q and the mooring is completed, that is, End time is E μν =S μν +d μν ;

[0034] And update the parking space p in the time period The state is untethered, that is Update parking space q in time period [S μν -tx+1,S μν ] is tethered, that is, T q (S μν -tx+1:S μν )=-2, update parking space q in time period [S μν +1,E μν ] is occupied by aircraft μ, that is, T q (S μν +1:E μν )=μ, adding the process (μ, ν) to A g , that is, A g =Ag ∪{(μ,ν)}, end.

[0035] Step 4.3, determine whether there is a non-idle parking position A that can be used to support the process to be scheduled. If so, first transfer the aircraft on the non-idle parking position A to the nearest idle parking position B, then transfer the aircraft to be scheduled to the non-idle parking position A, set the process to be scheduled to be supported at the idle parking position A, set its start and end time, update the state variable of parking position A, and end the search process; otherwise, exit directly and end;

[0036] A non-vacant parking stand is a parking stand currently occupied by other aircraft;

[0037] Specifically:

[0038] First, according to the parking space state variables, we find: g The numbers of the parking stands that are not idle and can provide the resources required for the process (μ, ν) are saved in the set UM, and the last moment when each parking stand was occupied by an aircraft is found;

[0039] Then, the parking stand numbers in the set UM are sorted according to Arrange them in order from small to large, and judge whether each parking position in the set UM can be used to guarantee the process (μ, ν).

[0040] For a non-free parking stand q in the set UM, the aircraft occupying the parking stand is e, and the nearest free parking stand to parking stand q is v, if the following conditions are met:

[0041] 1) The time when aircraft μ is untied from its current parking position p and transferred to parking position q is greater than the time when aircraft e at parking position q is untied, and the time when aircraft μ is transferred to the new parking position and the time when it is untied is less than the scheduling time t g ;

[0042] 2) The time when aircraft e is untied from its current parking position q and transferred to parking position v is greater than the last time parking position v was occupied by an aircraft, and the time when aircraft e is tied up after transferring to the new parking position is less than the scheduling time t g .

[0043] If a non-idle parking space q is found for process (μ, ν), update the parking space q in the time period The state is untethered, that is

[0044] Let t a represents the time when aircraft e arrives at parking position v, then

[0045] Update the parking space v in the time period [t a+1,t a +tx] is tethered, that is, T v (t a +1:t a +tx)=-2,

[0046] Update parking slot v at t a +tx+1 is occupied by aircraft e, that is, T v (t a +tx+1)=e.

[0047] The start time of (μ, ν) is set to the time when the aircraft μ is untied from the current parking position p and transferred to the parking position q and the tethering is completed, that is, Set the end time E of (μ,ν) μν =S μν +d μν ;

[0048] Update parking space p in time period The state is untethered, that is

[0049] Update parking space q in time period [S μν -tx+1,S μν ] is tethered, that is, T q (S μν -tx+1:S μν )=-2,

[0050] Update parking space q in time period [S μν +1,E μν ] is occupied by aircraft μ, that is, T q (S μν +1:E μν )=μ,

[0051] Add the step (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, end.

[0052] If no non-idle parking position can be found to guarantee the process (μ, ν), it means that the process (μ, ν) cannot be executed at the current moment and the process ends.

[0053] Step 5: Determine whether the process number k in the schedulable process set is greater than M. If so, increment the stage variable g by 1, return to step 2, and proceed to the next stage; otherwise, continue to increment k by 1, select the next process and return to step 4 for judgment until all processes are scheduled, and then output the scheduling plan.

[0054] The advantages of the present invention are:

[0055] 1) A parallel scheduling method for aircraft multi-station support operations, by setting a scheduled process set, a process set being scheduled and a process set that can be scheduled, the three do not overlap with each other, thereby avoiding process conflicts caused by unclear scheduling operations and ensuring that the process scheduling is not repeated or missed.

[0056] 2) A parallel scheduling method for aircraft multi-station support operations adopts a parallel scheduling framework, uses the scheduling time as the division mark of the scheduling stage, arranges resources for the processes that meet the constraints at the current scheduling time, and avoids operational risks caused by resource conflicts.

[0057] 3) A parallel scheduling method for aircraft multi-stop support operations. The parallel scheduling framework generates a non-delayed scheduling solution, which is suitable for handling large-scale "multi-stop" support operation scheduling problems, can shorten the global completion time as much as possible, and improve scheduling efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of a method for parallel scheduling of aircraft multi-station support operations of the present invention;

[0059] Figure 2 It is a flow chart adopted by the embodiment of parallel scheduling of aircraft multi-station support operations of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0061] The present invention discloses a parallel scheduling method for aircraft multi-station support operations, which first initializes the phase variables, the scheduled process set, the ongoing process set and all parking position states, and then arranges the processes in the schedulable process set according to the priority for the current scheduling phase, sets the start and end time for the schedulable processes of all available parking positions at the current scheduling moment, and updates the parking position state variables. Then, the next scheduling phase is entered until all operation processes are scheduled.

[0062] like Figure 1 As shown, the specific steps are:

[0063] Step 1: Set the phase variable to g = 1, initialize the scheduled process set and the ongoing process set, and set the status of all parking positions to be idle at all times;

[0064] Step 2: Let g=g+1. In the current scheduling stage g, count the scheduled process set, the process set being scheduled, and the process set that can be scheduled.

[0065] Step 3: Assume that the size of the schedulable process set is M, that is, |D g|=M|, for the M processes in the schedulable process set, arrange them from high to low priority, and select each process as the process to be scheduled one by one;

[0066] Step 4: For the kth process to be scheduled, determine whether a parking position can be found to guarantee the process. If so, add the current process to the ongoing process set, set the start and end time of the process, update the parking position state variable, increment the sequence number k of the process by 1, and select the next process to continue the judgment; otherwise, do not process the current process, directly increment the sequence number k of the process by 1, and select the next process to continue the judgment;

[0067] Initialize k=1;

[0068] The specific process of finding a parking space that guarantees the current process to be scheduled includes the following steps:

[0069] Step 4.1, determine whether the parking space where the aircraft to be scheduled is currently located can be used to support the process to be scheduled. If so, set the process to be scheduled to be supported at the current parking space, set its start and end time, update the parking space state variable, and end the search process; otherwise, go to step 4.2;

[0070] Step 4.2, determine whether there is an idle parking space available for the process to be scheduled. If yes, transfer the aircraft to be scheduled to the idle parking space found, set the process to be scheduled to be guaranteed at the idle parking space, set its start and end time, update the parking space state variable, and end the search process; otherwise, proceed to the next step;

[0071] Step 4.3, determine whether there is a non-idle parking position A that can be used to support the process to be scheduled. If so, first transfer the aircraft on the non-idle parking position A to the nearest idle parking position B, then transfer the aircraft to be scheduled to the non-idle parking position A, set the process to be scheduled to be supported at the idle parking position A, set its start and end time, update the state variable of parking position A, and end the search process; otherwise, exit directly and end;

[0072] A non-vacant parking stand is a parking stand currently occupied by other aircraft;

[0073] Step 5: Determine whether the process number k in the schedulable process set is greater than M. If so, increment the stage variable g by 1, return to step 2, and proceed to the next stage; otherwise, continue to increment k by 1, select the next process and return to step 4 for judgment until all processes are scheduled, and then output the scheduling plan.

[0074] Example:

[0075] Assume that the fleet to be supported includes n aircraft, represented by I = {1, 2, ..., n}; the set of operating procedures for the i-th (i∈I) aircraft is J i ={1,2,…,|J i |}, the process must be carried out strictly according to the operation process. The first process of each aircraft is the virtual start process, and the last process is the virtual end process; (i, j) represents the jth process of the i-th aircraft, d ij represents the duration of process (i, j), r ij Indicates the resource type required when executing process (i, j). Each process only requires one type of resource. ij is the set of immediate predecessor processes of process (i, j).

[0076] There are m parking spaces on the support site, the set is PS = {1, 2, ..., m}; the set of resource types that the pth parking space can provide is c p Each parking stand can provide at least one type of resource for aircraft operations; the aircraft needs to be tethered before arriving at the parking stand for operation and needs to be untethered before leaving the parking stand. The tethering and untethering time is tx.

[0077] Before the support operation begins, all aircraft are tied to the initial parking position; The transfer time between two parking positions is ΔT pq . Define the decision variable S ij is the start time of the process, E ij is the end time of the process, T p (t) is the state of parking stand p at time t, and its value meaning is shown in Table 1:

[0078] Table 1

[0079] <![CDATA[T p (t)]]> =i(i∈I) ＝-1 ＝-2 ＝0 meaning Occupied by aircraft Untether Tethered idle

[0080] The goal of aircraft multi-station support operation scheduling is to rationally plan the decision variables S ij 、E ij and T p The value of (t) ensures that there is no conflict in the use of parking spaces and that all processes can be completed smoothly according to the established operating procedures.

[0081] like Figure 2 As shown, g is the stage variable, A g is the set of ongoing processes in stage g, S g is the set of processes that have been scheduled in stage g, D g is the set of schedulable processes in stage g, that is, the set of processes whose immediate predecessor processes have been scheduled and which have not been scheduled themselves, t g is the scheduling time of stage g.

[0082] The scheduling process includes the following steps.

[0083] Step 1: Initialize the scheduling phase variable g = 1, and the process set A is in progress g Initialized as the first process set of each aircraft, Scheduled process set S g Initialize to an empty set, and initialize all parking space state variables to be idle at all times.

[0084] Step 2: Calculate the variable t g , S g , A g and D g The value of

[0085] The specific calculation formula is:

[0086] t g =min{S ij +d ij |(i,j)∈A g-1}

[0087] S g =S g-1 ∪{(i,j)|(i,j)∈A g-1 ∧t g =E ij};

[0088] A g =A g-1 -{(i,j)|(i,j)∈A g-1 ∧t g =E ij}

[0089]

[0090] Step 3: D g The processes in are arranged according to priority. The shorter the duration, the higher the priority. Processes with the same duration are arranged in ascending order according to the process number.

[0091] Step 4: Select D g The kth process (μ, ν) is taken as the process to be scheduled.

[0092] Initially, k=1.

[0093] Step 5: Determine whether a parking position can be found to ensure the process (μ, ν). If so, add (μ, ν) to A. g , set its start and end time, and update the parking space status variable.

[0094] The specific process is divided into three steps, as follows:

[0095] Step 5.1: For the process (μ, ν) to be scheduled, determine whether the parking space where the aircraft μ is currently located can be used to support the process (μ, ν) to be scheduled; if so, set the process (μ, ν) to be supported at the current parking space, set its start and end time, update the parking space state variable, and end; otherwise, the parking space p cannot be used to support the process (μ, ν), that is, Then go to step 5.2.

[0096] Specifically:

[0097] First, according to the parking position state variables, determine the aircraft μ at t g The parking position p at the time,

[0098] t g =0, the process to be scheduled is the first process after the virtual start process;

[0099] Then, determine whether parking space p can be guaranteed (μ, ν). If so, then we have r μν ∈c p , then set the start time of (μ,ν) to S μν =t g , the end time is E μν =t g +d μν , add the process (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)},

[0100] Update parking space p in time period [t g +1,t g +d μν ] is occupied by aircraft μ, that is, T p (t g +1:t g +d μν )=μ, end.

[0101] If parking space p cannot be used for (μ, ν) protection, then Then go to step 5.2.

[0102] Step 5.2: Determine whether there is an idle parking space available for the process (μ, ν) to be scheduled. If so, transfer the aircraft to be scheduled to the idle parking space found, set the process to be scheduled to be secured at the idle parking space, set its start and end time, update the parking space state variable, and end; otherwise, proceed to step 5.3.

[0103] Defining variables represents the last time that parking space s was occupied by an aircraft. First, we find the time t according to the parking space state variable. g The parking spaces that are free and can provide the resources required by the process (μ, ν) and the last time they were occupied by an aircraft are as follows:

[0104]

[0105] Among them, the set EM is used to store the g The parking bay number that is idle and can provide the resources required for the process (μ, ν).

[0106] Then, the parking space numbers in the set EM are sorted according to Arrange in order from small to large, and judge whether each parking position in the set EM can be used to guarantee the process (μ, ν), that is, judge whether the time when the aircraft μ is untied from the current parking position p and transferred to a parking position in EM is greater than the last time that the parking position is occupied by the aircraft, and whether the time when the aircraft μ is transferred to the new parking position and the tethering is completed is less than the scheduling time t g , if so, it means that the parking position can be used to ensure the process (μ, ν), the specific process is:

[0107]

[0108] If an idle parking space q can be found for process (μ, ν), then the start time of (μ, ν) is set to the time when aircraft μ is untied from the current parking space p and transferred to parking space q and tied up, that is,

[0109] Set the end time E of (μ,ν) μν =S μν +d μν , update parking space p in time period The state is untethered, that is

[0110] Update parking space q in time period [S μν -tx+1,S μν ] is tethered, that is, T q (S μν -tx+1:S μν )=-2,

[0111] Update parking space q in time period [S μν +1,E μν ] is occupied by aircraft μ, that is, T q (S μν +1:E μν )=μ,

[0112] Add the step (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, end.

[0113] Step 5.3: Determine whether there is a non-idle parking stand that can be used to support the process to be scheduled (μ, ν). If so, first transfer the aircraft on the non-idle parking stand to the nearest idle parking stand, then transfer the aircraft to be scheduled to the non-idle parking stand, set the process to be scheduled to be supported at the idle parking stand, set its start and end time, update the parking stand state variable, and end.

[0114] First, find the parking space at t according to the parking space state variable. g The parking spaces that are not idle at the time and can provide the resources required by the process (μ, ν) and the last time they are occupied by an aircraft are as follows:

[0115]

[0116] Among them, the set UM is used to store g The parking bay number that is not idle at any time and can provide the resources required to guarantee the process (μ, ν).

[0117] Then, the parking stand numbers in the set UM are sorted according to Arrange in order from small to large, and judge whether each parking position in the set UM can be used to guarantee the process (μ, ν). Since each parking position in the set UM is currently occupied by an aircraft, if the aircraft μ to be scheduled is transferred to a parking position in the set UM, the aircraft on the parking position needs to be transferred to other free parking positions first.

[0118] For a non-free parking stand q in the set UM, the aircraft occupying the parking stand is e, and the nearest free parking stand to parking stand q is v, if the following conditions are met:

[0119] 1) The time when aircraft μ is untied from its current parking position p and transferred to parking position q is greater than the time when aircraft e at parking position q is untied, and the time when aircraft μ is transferred to the new parking position and the time when it is tied up is less than the scheduling time t g ;

[0120] 2) The time when aircraft e is untied from its current parking position q and transferred to parking position v is greater than the last time parking position v was occupied by an aircraft, and the time when aircraft e is tied up after transferring to the new parking position is less than the scheduling time t g .

[0121] This means that parking position q can be used to ensure the process (μ, ν). The specific process is:

[0122]

[0123]

[0124] If a non-idle parking space q can be found to guarantee the process (μ, ν), update the parking space q in the time period The state is untethered, that is Let t a represents the time when aircraft e arrives at parking position v, then Update the parking space v in the time period [t a +1,t a +tx] is tethered, that is, T v (t a +1:t a +tx)=-2, update parking space v at t a +tx+1 is occupied by aircraft e, that is, T v (t a +tx+1)=e.

[0125] The start time of (μ, ν) is set to the time when the aircraft μ is untied from the current parking position p and transferred to the parking position q and the tethering is completed, that is, Set the end time E of (μ,ν) μν =S μν +d μν , update parking space p in time period The state is untethered, that is

[0126] Update parking space q in time period [S μν -tx+1,S μν ] is tethered, that is, T q (S μν -tx+1:S μν )=-2,

[0127] Update parking space q in time period [S μν +1,E μν ] is occupied by aircraft μ, that is, T q (S μν +1:E μν )=μ,

[0128] Add the step (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, end step 5.

[0129] If no non-idle parking position can be found to guarantee the process (μ, ν), it means that the process (μ, ν) cannot be executed at the current moment and the process ends.

[0130] Step 6: Let k = k + 1, if k ≤ |D g |, then return to step 4, otherwise, let g=g+1.

[0131] Step 7: If all processes have completed scheduling, output the scheduling plan and end, otherwise return to step 2.

Claims

1. A method for parallel scheduling of aircraft multi-station support operations, characterized in that: The specific steps are: Step 1: For the fleet of n aircraft to be supported, set the phase variable to g=1, initialize the scheduled process set and the ongoing process set, and set the status of all parking positions to idle; Step 2: Let g=g+1. In the current scheduling stage g, count the scheduled process set, the process set being scheduled, and the process set that can be scheduled. Step 3: Assume that the size of the schedulable process set is M, that is, |D g |=M, for the M processes in the schedulable process set, arrange them from high to low priority, and select each process as the process to be scheduled one by one; Step 4: For the kth process to be scheduled (μ, ν), determine whether a parking position can be found to guarantee the process (μ, ν). If so, add the current process (μ, ν) to the ongoing process set A. g In the process (μ, ν), the start and end time of the process (μ, ν) are set, and the parking position state variable is updated; the sequence number k of the process is incremented by 1, and the next process is selected for further judgment; otherwise, the current process (μ, ν) is not processed, the sequence number k of the process is directly incremented by 1, and the next process is selected for further judgment; The specific process of finding the parking position that guarantees the current scheduled process (μ, ν) is: Initialize k = 1; (μ, ν) represents the vth process of the μth aircraft; Step 4.1, determine whether the parking space where the aircraft μ to be scheduled is currently located can be used to support the process (μ, ν) to be scheduled. If so, set the process (μ, ν) to be scheduled to be supported at the current parking space, set its start and end time, update the parking space state variable, and end the search process; otherwise, proceed to step 4.2; Specifically: First, according to the parking position state variables, determine the aircraft μ at time t g The parking position p, Then, determine whether parking position p can guarantee (μ, ν); if so, there are resources r required for the execution of process (μ, ν) μν ∈c p , c p is the set of resource types that can be provided by the pth parking space; then set the start time of (μ, ν) to S μν =t g , the end time is E μν =t g +d μν , d uv represents the duration of the vth process (μ, ν) of the μth aircraft; And add the step (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, update parking space p in time period [t g +1,t g +d μν ] is occupied by aircraft μ, that is, T p (t g +1:t g +d μν )=μ, end; If parking space p cannot be used for (μ, ν) protection, then Finish; Step 4.2, determine whether there is an idle parking space available for the process to be scheduled. If yes, transfer the aircraft to be scheduled to the idle parking space found, set the process to be scheduled to be secured at the idle parking space, set its start and end time, update the parking space state variable, and end the search process; Otherwise, proceed to the next step; Step 4.3, determine whether there is a non-idle parking position A that can be used to support the process to be scheduled. If so, first transfer the aircraft on the non-idle parking position A to the nearest idle parking position B, then transfer the aircraft to be scheduled to the non-idle parking position A, set the process to be scheduled to be supported at the idle parking position A, set its start and end time, update the state variable of parking position A, and end the search process; otherwise, exit directly and end; A non-vacant parking stand is a parking stand currently occupied by other aircraft; Step 5: Determine whether the process number k in the schedulable process set is greater than M. If so, increment the stage variable g by 1, return to step 2, and proceed to the next stage; otherwise, continue to increment k by 1, select the next process and return to step 4 for judgment until all processes are scheduled, and then output the scheduling plan.

2. The method for parallel scheduling of aircraft multi-station support operations according to claim 1, characterized in that: In the step 1, the ongoing process set is initialized to the first process set of each aircraft; and the scheduled process set is initialized to an empty set.

3. The method for parallel scheduling of aircraft multi-station support operations according to claim 1, characterized in that: The step 4.2 is specifically as follows: First, according to the parking space state variables, find g The parking stands that are free and can provide the resources required by the process (μ, ν) are numbered and saved in the set EM. At the same time, the last time each parking stand was occupied by an aircraft is found. EM is initially an empty set; Indicates the last time parking stand s was occupied by an aircraft; Then, the parking space numbers in the set EM are sorted according to Arrange in order from small to large, and judge whether each parking position in the set EM can be used to ensure the process (μ, ν); That is, it is determined whether the time when the aircraft μ is untied from the current parking position p and transferred to an empty parking position q in EM is greater than the last time that the parking position is occupied by an aircraft, and whether the time when the aircraft μ is transferred to the new parking position q and the tethering is completed is less than the scheduling time t g If yes, it means that the parking position q can be used to guarantee the process (μ, ν), then the start time of (μ, ν) is set to: the time when the aircraft μ is transferred from the current parking position p to the parking position q and the mooring is completed, that is, End time is E μν =S μν +d μν ; tx represents the time the aircraft is tied up before arriving at the parking stand for operation, and the time it is untied before leaving the parking stand; And update the parking space p in the time period The state is untethered, that is Update parking space q in time period [S μν -tx+1,S μν ] is tethered, that is, T q (S μν -tx+1:S μν )=-2, Update parking space q in time period [S μν +1,E μν ] is occupied by aircraft μ, that is, T q (S μν +1:E μν )=μ, adding the process (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, end.

4. The method for parallel scheduling of aircraft multi-station support operations according to claim 1, characterized in that: The step 4.3 is specifically as follows: First, according to the parking space state variables, we find: g The numbers of the parking stands that are not idle and can provide the resources required for the process (μ, ν) are saved in the set UM, and the last moment when each parking stand was occupied by an aircraft is found; Then, the parking positions in the UM collection are numbered according to Arrange in ascending order, and judge whether each parking position in the set UM can be used to guarantee the process (μ, ν); For a non-free parking stand q in the set UM, the aircraft occupying the parking stand is e, and the nearest free parking stand to parking stand q is v, if the following conditions are met: a) The time when aircraft μ is untied from its current parking position p and transferred to parking position q is greater than the time when aircraft e at parking position q is untied, and the time when aircraft μ is transferred to the new parking position and the time when it is untied is less than the scheduling time t g ; b) The time when aircraft e is untied from its current parking position q and transferred to parking position v is greater than the last time parking position v was occupied by an aircraft, and the time when aircraft e is tied up after transferring to the new parking position is less than the scheduling time t g ; If a non-idle parking space q is found for process (μ, ν), update the parking space q in the time period The state is untethered, that is Let t a represents the time when aircraft e arrives at parking position v, then ΔT pv Indicates the transfer time of the aircraft between the two parking positions p and v; Update the parking space v in the time period [t a +1,t a +tx] is tethered, that is, T v (t a +1:t a +tx)=-2, update parking space v at t a +tx+1 is occupied by aircraft e, that is, T v (t a +tx+1)=e; The start time of (μ, ν) is set to the time when the aircraft μ is untied from the current parking position p and transferred to the parking position q and the tethering is completed, that is, Set the end time E of (μ,ν) μν =S μν +d μν ; Update parking space p in time period The state is untethered, that is Update parking space q in time period [S μν -tx+1,S μν ] is tethered, that is, T q (S μν -tx+1:S μν )=-2, Update parking space q in time period [S μν +1,E μν ] is occupied by aircraft μ, that is, T q (S μν +1:E μν )=μ, adding the process (μ, ν) to A g , that is, A g =A g ∪{(μ,ν)}, end; If no non-idle parking position can be found to guarantee the process (μ, ν), it means that the process (μ, ν) cannot be executed at the current moment and the process ends.

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