CN1848151A - Fast command control method of battlefield operation aircraft fast and low-risk disposition - Google Patents

Abstract

The present invention relates to a quick command control method for battlefield operational aircraft quick low-danger disposition, belonging to military affairs and related field. The command-controlled object includes all the battlefield operational aircrafts. Said method includes the following steps: constructing command control model, using linear program method and dual program method of linear program to resolve said model, then utilizing two-dimensional tabular form to continuously improve the resolved result so as to obtain the final command control scheme according with the quick low-danger disposition requirements. Said invention also further relates to a technique for implementing said method.

Description

Quick commander's control method of battlefield operational aircraft fast and low-risk disposition

Technical field the present invention relates to national defence and association area, is used for battlefield operational aircraft fast and low-risk disposition is implemented commander's control fast, realizes the fast and low-risk disposition to the battlefield operational aircraft.

It is an important component part of operational commanding control that background technology implements between the assembly place of battlefield operational aircraft and deployment point that quick operational aircraft disposes, length according to operational aircraft flight path from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, speed and contained number of operational aircraft batch, structure is that target and the commander's control plan with low computational complexity and high solvability are that the battlefield commander implements the key issue that commander's control fast must solve to battlefield operational aircraft fast and low-risk disposition dispose all operational aircrafts to expend time in or to meet with the risk minimum, the solution of this problem is for increasing substantially fighting capacity, reduce the risk of disposing operational aircraft, expend time in and, have crucial meaning the demand of consumption of natural resource.

The fast and low-risk disposition ability of battlefield operational aircraft is most important for the triumph of capturing IT-based warfare, but complicated battlefield surroundings may cause adverse effect to the operational aircraft along a certain flight path flight, thereby reduce the security of operational aircraft flight, and the commander of low-risk disposition operational aircraft control is the key that improves mobile operations, and commander's control plan of therefore formulating the deployment operational aircraft of science becomes the matter of utmost importance that must solve.The quality of this plan, not only be related to implement the battlefield operational aircraft dispose the risk that meets with, consumption of natural resource how much, can in time arrive the deployment point but also be related to operational aircraft, to guarantee that fighting capacity is unlikely to descend because of the delay of operational aircraft deployment.

Time seems very important for commander's control that the battlefield operational aircraft is disposed, and constraint condition that therefore must be by reducing commander's controlling models, analyzes that the choose reasonable parameter improves solvability and to dispose risk or to expend time in minimumly to come battlefield operational aircraft fast and low-risk disposition is implemented commander's control fast as optimization aim by antithesis.

The present invention relates to quick commander's control method of battlefield operational aircraft fast and low-risk disposition, relate to military affairs and association area, the object of commander's control is all battlefield operational aircrafts, this method is according to the length of the flight path from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, speed and contained number of operational aircraft batch, structure is target and the commander's controlling models with low computational complexity and high solvability dispose all operational aircrafts to expend time in or to meet with the risk minimum, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition, this method has efficiently, simply, objective, characteristics are widely used and obviously improve its combat capabilities etc., can be widely used in quick commander's control of all battlefield operational aircraft fast and low-risk dispositions, the invention further relates to the technology that realizes this method.

Summary of the invention the present invention is according to the length of the flight path from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, speed and contained number of operational aircraft batch, structure is target and the commander's controlling models with low computational complexity and high solvability dispose all operational aircrafts to expend time in or to meet with the risk minimum, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield operational aircraft fast and low-risk disposition enforcement commander control with two-dimentional form description, and check whether this option control command meets risk and the time demand of finishing whole battlefield operational aircraft deployment task, if do not meet the demands, then by analysis to this two dimension commander control form, and according to shadow price, risk and time bottleneck can be adjusted for the operational aircraft quantity of deployment and the operational aircraft speed of enforcement deployment etc. the relevant episode node, constantly repeat this and find the solution-check analytic process, meet the option control command of fast and low-risk disposition requirement until final acquisition.Therefore, the conception of quick commander's control of battlefield operational aircraft fast and low-risk disposition is proposed, introduce the analytical approach that flight expends time in and meets with risk probability, set up linear programming and the dual program model of seeking optimum option control command, come this model of rapid solving by reducing constraint condition, obtain scheme to battlefield operational aircraft fast and low-risk disposition enforcement commander control with two-dimentional form description, and according to finishing risk and the time requirement that whole operational aircraft is disposed, by searching risk and the time bottleneck that whole battlefield operational aircraft deployment task is finished in influence, the assembly place can be adjusted for the unreasonable configuration of the operational aircraft quantity of disposing with to the operational aircraft speed of implementing to dispose, continue to optimize and improve this option control command, and final risk and the time requirement that obtains to satisfy battlefield operational aircraft fast and low-risk disposition, option control command with two-dimentional form description becomes key character of the present invention.

The technical scheme of quick commander's control method of battlefield of the present invention operational aircraft fast and low-risk disposition is:

At first, with battlefield operational aircraft fast and low-risk disposition problem definition is by the assembly place of operational aircraft and the assembly deployment system that the deployment point constituted of operational aircraft, the feature of this system can be used the length of the flight path of the operational aircraft deployment from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the demand of deployment point operational aircraft, speed and contained number of operational aircraft batch are described, and according to the risk requirement that the battlefield operational aircraft is disposed, all operational aircrafts expend time in or meet with the risk minimum structure is target and the commander's controlling models with low computational complexity and high solvability to dispose and to transport, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield operational aircraft fast and low-risk disposition enforcement commander control with two-dimentional form description, the risk and the time bottleneck of assembling deployment system by continuous searching, quantity to the operational aircraft of relevant episode node is carried out reasonable disposition, adopt the methods such as operational aircraft of friction speed, final risk and the time requirement that obtains to satisfy battlefield operational aircraft fast and low-risk disposition, battlefield operational aircraft fast and low-risk disposition is implemented the scheme that commander controls, finish commander's control battlefield operational aircraft fast and low-risk disposition.

The quick commander that the battlefield operational aircraft is disposed controls, the computational complexity and the needed computing time of finding the solution commander's linear programming of controlling models and dual program should not exerted an influence to the real-time of commander's control decision, therefore reducing unnecessary constraint condition is the important measures that improve commander's control decision real-time, for computational complexity that reduces commander's controlling models and the solvability that improves commander's controlling models, stipulate that the constraint condition relevant with the deployment point is the constraint condition that equals the deployment point demand, the constraint condition relevant with the assembly place is to be not more than the constraint condition that the assembly place maximum can supply the deployment amount.

Complicated battlefield surroundings may cause adverse effect to the operational aircraft along a certain flight path flight, thereby reduce the security of operational aircraft flight, for expending time in the deployment operational aircraft or meeting with commander's control that the risk minimum is a target, this reduction has been equivalent to increase the risk that operational aircraft flight faces, it can be with the function of time as variable that flight meets with risk probability, also can be and irrelevant constant of time, the flight of different flight paths meets with risk probability can be different.

Find the solution commander's controlling models by the method for finding the solution linear programming and finding the solution the dual program of linear programming, can obtain respectively to meet with risk probability or the flight path of least consume time from the minimum flight that different assembly places deployment operational aircrafts need to different deployment points, with different assembly places and the relevant shadow price of different deployment points constraint condition, the result that will find the solution inserts in a kind of two dimension commander's control form again, according to analysis to this two dimension commander control form, and pass through according to shadow price, risk bottleneck and time bottleneck are adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield operational aircraft fast and low-risk disposition requirement until final acquisition.

Quantity that can be by describing from each assembly place the operational aircraft of disposing each deployment point as the zones of different in the two-dimentional form of option control command, size, the flight that each deployment point need deliver power meet with risk probability, operational aircraft batch, dispose and expend time in and relevant shadow price, each assembly place can dispose operational aircraft quantity, remain operational aircraft quantity situation of change with relevant shadow price and dispose the priming the pump of all operational aircrafts and the minimum time that expends.

If the option control command of trying to achieve can not satisfy predetermined risk and time requirement, then can be by two dimension commander control table, result to former linear programming and dual program analyzes, determine to influence the risk of battlefield operational aircraft deployment and the bottleneck of T.T., carry out reasonable disposition by operational aircraft quantity again to the assembly place, increase the quantity of operational aircraft batch and the means such as operational aircraft that adopt different speed, eliminate risk and time bottleneck, and repeat this process, until making the risk of finishing battlefield operational aircraft deployment and meeting predetermined requirement T.T..

Quick commander's control method of the battlefield operational aircraft fast and low-risk disposition of the present invention's design is applicable to that all battlefield operational aircraft fast and low-risk dispositions are key characters of the present invention.

With to meet with the risk minimum be target being analyzed as follows to quick commander's control problem of battlefield operational aircraft fast and low-risk disposition, it is the analysis of target to quick commander's control problem of battlefield operational aircraft fast and low-risk disposition that this analysis is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition D _jy _j+ S _iy _N+i≤ p _IjBe replaced into D _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product.

Supposing that battlefield operational aircraft fast and low-risk disposition problem can be used by the deployment point of the assembly place of m supply operational aircraft and n demand operational aircraft and between different supply and demand nodes exists the network in the path of a deployment operational aircraft to describe, and is x from assembly place i to the operational aircraft quantity that deployment point j disposes _Ij, it is p that flight meets with risk probability _Ij(t), the length of flight path is d _IjFlight meets with risk probability and is meant that complicated battlefield surroundings may cause adverse effect to the operational aircraft along a certain flight path flight, thereby reduce the security of operational aircraft flight, for expending time in the deployment operational aircraft or meeting with commander's control that the risk minimum is a target, this reduction has been equivalent to increase the risk that operational aircraft flight faces, it can be with the function of time as variable that flight meets with risk probability, also can be and irrelevant constant of time, is expressed as p _Ij, the flight of different flight paths meets with risk probability can be different,

The problem that need to solve be one of design from m assembly place deployment operational aircraft to n deployment point, make the flight of disposing all operational aircrafts meet with risk probability simultaneously and satisfy mapping out the plan of pre-provisioning request for minimum, consumed time, and calculate the quantity that required batch of operational aircraft is disposed in each assembly place, relevant operational aircraft deployment commander's controlling models and linear programming equation are as follows:

Objective function: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

The deployment point is to the constraint condition of operational aircraft demand: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}=D_j,$ (j＝1，…，n)

The assembly place can supply to dispose the constraint condition of operational aircraft amount: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}\≤S_i,$ (i＝1，…，m)

Condition of Non-Negative Constrains: x _Ij〉=0, (i=1 ..., m; J=1 ..., n)

Assembly place i (i=1 ... m) quantity of the operational aircraft of need disposing batch

From assembly place i (i=1 ... m) dispose operational aircraft to deployment point j (j=1 ... n) spent time: $T_{\mathrm{ij}}=\frac{d_{\mathrm{ij}}}{C}$

Finish all operational aircrafts and dispose spent minimum time: minT=max{T _Ij}

The maximum flight relevant with j deployment point meets with risk probability: $p_j=\underset{p_{\mathrm{ij}}\∈P_{\mathrm{op}}}{\max }\left\{p_{\mathrm{ij}}\right\},$ j(j＝1，…n)

Finish flight experience risk probability: the minP=max{p that all operational aircrafts are disposed _j, j (j=1 ... n)

With j the risk carrying capacity that the deployment point is relevant: ${\min Z}_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ j(j＝1，…n)

The overall risk carrying capacity that the battlefield operational aircraft is disposed: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\min Z}_j$

With j the operational aircraft carrying capacity that the deployment point is relevant: $Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ j(j＝1，…n)

The total operational aircraft carrying capacity in battlefield: $Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{Z}_j$

Wherein:

M is for disposing the assembly place sum of operational aircraft;

N is the deployment point sum of demand operational aircraft;

P _OpBe commander's controlling models p by associated pathway when obtaining optimum solution _IjThe set of forming;

The value of objective function was called the risk carrying capacity when minZ obtained optimum solution for commander's controlling models, and this value is the smaller the better;

p _IjFor assembly place i (i=1 ... m) with deployment point j (j=1 ... n) flight between meets with risk probability, can be with the function of time t as variable;

d _IjFor assembly place i (i=1 ... m) with deployment point j (j=1 ... the length of the flight path n) (unit: kilometer);

V _iFor the assembly place i that disposes operational aircraft (i=1 ... m) dispose batch quantity that operational aircraft needs;

L is the ability (unit: frame) of each batch deployment operational aircraft;

C is the speed (unit: kilometer/hour) of each batch deployment operational aircraft;

S _iFor assembly place i (i=1 ... m) quantity (unit: frame) of the operational aircraft that can dispose;

D _jFor deployment point j (j=1 ... n) need the quantity (unit: frame) of operational aircraft;

Above-mentioned model shows: objective function be equivalent to ask probability-weighted and, on the basis of trying to achieve risk carrying capacity minZ value by linear programming, can calculate each assembly place must be to the operational aircraft quantity x of related deployment point deployment _Ij, the p of associated pathway _Ij, count L according to the contained operational aircraft frame of each batch again, can calculate the operational aircraft batch V that need dispose each assembly place _i,, can calculate the risk carrying capacity minZ of each deployment point again at last according to the speed C and the longest path between assembly place and deployment point of each batch deployment operational aircraft _j, maximum flight meets with risk probability p _jFinish flight experience risk probability minP, the shortest time T that expends that all battlefield operational aircrafts are disposed, thereby realize commander's control to battlefield operational aircraft fast and low-risk disposition, for constraint condition rationally being set, improving solvability, utilizing above-mentioned linear programming model better, the dual linear programming model that provides this model is as follows:

Objective function: $\max G=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{D}_j{y}_j+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i{y}_{n+i}$

Constraint condition: D _jy _j+ S _iy _N+i≤ p _Ij, (i=1 ..., m; J=1 ..., n)

Condition of Non-Negative Constrains: y _j, y _N+i〉=0, (i=1 ..., m; J=1 ..., n)

Wherein: y _j, y _N+iBe respectively with the demand of former linear programming and dispose the shadow price or the relevant decision variable of opportunity cost of operational aircraft constraint condition,

Since primal linear programming solves be with deployment point j and assembly place i (i=1 ..., m; J=1 ..., the resource optimal utilization problem that constraint condition n) is relevant, thus dual program solve then be estimate to make deployment point j and assembly place i (i=1 ..., m; J=1 ..., constraint condition n) satisfies the cost problem that must pay, promptly uses the valency problem, and shadow price y _jAnd y _N+iReflection make just deployment point j and assembly place i (i=1 ..., m; J=1, n) constraint condition satisfies the cost that must pay, by making the target function value relevant minimize (or maximization) with cost, shadow price can be used for each constraint condition of comparison and carry out equivalence analysis to the contribution of target function value or to this contribution influence, shadow price is big more, show that this constraint condition is big more to the influence of the priming the pump delivery power of option control command, but it is also just difficult more to satisfy this condition, therefore, introducing shadow price just can be by comparing shadow price and realistic objective functional value, and can variation that study former linear programming constraint condition make objective function obtain gain.

Embodiment

Implementation example

In IT-based warfare, the deployment ability of operational aircraft is an important component part of fighting capacity, huge battlefield operational aircraft is disposed ability and the demand of time, make commander's control of implementing battlefield operational aircraft deployment become vital task, to meet with the risk minimum is that the implementation example of quick commander's control problem of battlefield operational aircraft fast and low-risk disposition of target is as follows, it is the implementation example analysis of target to quick commander's control problem of battlefield operational aircraft fast and low-risk disposition that this implementation example is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition D _jy _j+ S _iy _N+i≤ p _IjBe replaced into D _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product, suppose with 16, average speed per hour to be that 70 kilometers operational aircraft is as an operational aircraft batch, dispose the operational aircraft of specified amounts to 14 deployment points from 5 assembly places, between assembly place and the deployment point flight meet with risk probability, assembly place operational aircraft can the deployment amount and the deployment point as shown in table 1 to the demand of operational aircraft.

Table 1: flight meets with risk probability, portion's amount of asking (unit: probability, frame) between assembly place and the deployment point

01 assembly place

02 assembly place

03 assembly place

04 assembly place

05 assembly place

Quantity required

14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point	0.037 0.034 0.025 0.014 0.026 0.024 0.120 0.159 0.112 0.062 0.091 0.126 0.090 0.081	0.013 0.025 0.028 0.015 0.035 0.020 0.098 0.138 0.096 0.037 0.066 0.097 0.068 0.056	0.070 0.083 0.108 0.097 0.082 0.110 0.012 0.051 0.096 0.046 0.017 0.081 0.099 0.020	0.074 0.087 0.112 0.101 0.086 0.100 0.129 0.149 0.025 0.050 0.079 0.086 0.104 0.066	0.044 0.031 0.066 0.058 0.056 0.039 0.105 0.145 0.110 0.059 0.073 0.027 0.011 0.075	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 24.00
							Can the deployment amount	250.00	200.00	300.00	400.00	150.00

Between assembly place and the deployment point length of flight path, assembly place operational aircraft can the deployment amount and the deployment point as shown in table 2 to the demand of operational aircraft.

Table 2: flight path length, portion's amount of asking (unit: kilometer, frame) between assembly place and the deployment point

	01 assembly place	02 assembly place	03 assembly place	04 assembly place	05 assembly place	Quantity required
							14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point	37.00 34.00 25.00 14.00 26.00 24.00 120.00 159.00 112.00 62.00 91.00 126.00 90.00 81.00	13.00 25.00 28.00 15.00 35.00 20.00 98.00 138.00 96.00 37.00 66.00 97.00 68.00 56.00	70.00 83.00 108.00 97.00 82.00 110.00 12.00 51.00 96.00 46.00 17.00 81.00 99.00 20.00	74.00 87.00 112.00 101.00 86.00 100.00 129.00 149.00 25.00 50.00 79.00 86.00 104.00 66.00	44.00 31.00 66.00 58.00 56.00 39.00 105.00 145.00 110.00 59.00 73.00 27.00 11.00 75.00	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 24.00
Can the deployment amount	250.00	200.00	300.00	400.00	150.00

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, the option control command of the minimum risk operational aircraft that calculates by simplex algorithm deployment is as shown in table 3, and wherein the frame risk is the risk carrying capacity minZ of deployment point _j, risk probability is that the maximum flight of deployment point meets with risk probability p _j, the frame kilometer is the operational aircraft carrying capacity Z of deployment point _j

Table 3: minimum flight meets with risk probability and disposes option control command (unit: frame, frame risk, probability, frame kilometer, batch, minute)

	01 assembly place	02 assembly place	03 assembly place	04 assembly place	05 assembly place	The frame risk	Risk probability	The frame kilometer	Batch	Expend time in	Shadow price
												01 deployment point		36.00				0.468	0.013	468.00	3	11.14	0.00

14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point	90.00 90.00 70.00	21.00 40.00 40.00 36.00	60.00 16.00 90.00 24.00	29.00	22.00 18.00	0.525 2.250 1.860 1.820 0.800 0.720 0.816 0.725 1.332 1.530 0.594 0.198 0.480	0.025 0.025 0.015 0.026 0.020 0.012 0.051 0.025 0.037 0.017 0.027 0.011 0.020	525.00 2250.00 1860.00 1820.00 800.00 720.00 816.00 725.00 1332.00 1530.00 594.00 198.00 480.00	2 6 9 5 3 4 1 2 3 6 2 2 2	21.43 21.43 12.26 22.29 17.14 10.29 43.71 21.43 31.71 14.57 23.14 9.43 17.14	12.00 13.00 2.00 14.00 7.00 0.00 39.00 0.00 24.00 5.00 16.00 0.00 8.00
												Add up to	250.00	173.00	190.00	29.00	40.00	14.118	0.051	14118.00	50	43.71 *
But portion's quantity	250.00	200.00	300.00	400.00	150.00
												Surplus after the portion	0.00	27.00	110.00	371.00	110.00
Shadow price	12.00	13.00	12.00	25.00	11.00

* finishing the minimum time that deployment task expends is 43.71 minutes

By option control command (table 3) is analyzed as can be known; finish operational aircraft that deployment task needs and batch add up to 50; time is 43.71 minutes; the operational aircraft that 01～05 assembly place needs batch is respectively 17; 14; 13; 2 and 4; therefore must be to 01; 02 and 03 assembly place implements to lay special stress on protecting; further analyze as can be known; disposing 16 43.71 minutes that operational aircraft spent from 03 assembly place to 08 deployment point is bottlenecks that the whole deployment task of restriction is finished sooner; this deployment also is simultaneously to reduce to finish the bottleneck that the flight of disposing in all battlefields meets with risk probability; if with speed faster operational aircraft finish this part deployment; then can be shortened to 31.71 minutes the time that whole deployment task is finished; reduction is 27.45%; risk probability is reduced to 0.037; reduction is 27.45%; and for example fruit is adopted the bottleneck that uses the same method and eliminated 31.71 minutes; then can be shortened to 23.14 minutes deployment time; reduction reaches 47.06%; risk probability is reduced to 0.027; reduction is 47.06%, almost only is half of former free and risk probability.

From to demand constraint condition D _j(j=1,14) analysis of shadow price as can be known, the size of price has truly reflected the complexity that the related constraint condition satisfies, shadow price is 0 to be meant in specific span, and relevant constraint condition does not constitute influence to target function value, the easiliest satisfies, again for example, in order to satisfy constraint condition D ₈, the risk of disposing operational aircraft to 08 deployment point is 0.051,43.71 minutes consuming time, the shadow price of this constraint condition is a maximal value 39, illustrates that this condition is the most difficult to satisfy, can be by D with similar method _jThe complexity that satisfies, from difficulty to easy ordering: D ₈, D ₁₀, D ₁₂, D ₅..., to deployment amount constraint condition S _i(i=1 ..., 5) analysis of shadow price as can be known, S _iThe complexity that satisfies, from difficulty to easy ordering: S ₄, S ₂, S ₁, S ₃, S ₅, i.e. constraint condition S ₄The most difficult satisfied.

In addition, from the residue operational aircraft amount of each assembly place, back of finishing the work as can be seen, the surplus of 01 assembly place and 02 assembly place is obviously on the low side, and particularly the operational aircraft that can dispose of 01 assembly place exhausts, this statement of facts:, add S if there is more operational aircraft 01 assembly place ₁Constraint condition more easily satisfies, and just may obtain better to map out the plan, and therefore, can also carry out reasonable configuration to the operational aircraft of each assembly place with said method, and realization can be disposed the Optimal Management of operational aircraft quantity.

Claims (10)

1, the present invention relates to quick commander's control method of battlefield operational aircraft fast and low-risk disposition, relate to military affairs and association area, the object of commander's control is all battlefield operational aircrafts, this method is according to the length of the flight path from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, speed and contained number of operational aircraft batch, structure is target and the commander's controlling models with low computational complexity and high solvability dispose all operational aircrafts to expend time in or to meet with the risk minimum, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, meet the option control command of fast and low-risk disposition requirement until final acquisition, this scheme is applicable to commander's control of the fast and low-risk disposition of all battlefield operational aircrafts.

2, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, the object that it is characterized in that described commander's control is meant the object of all battlefield operational aircrafts as commander's control for all battlefield operational aircrafts, described commander's control is meant according to the actual demand of battlefield to operational aircraft, design is deployed to different deployment points with the battlefield operational aircraft from different assembly places, and all flights are expended time in or the probability-weighted that meets with risk for minimum, can be for the scheme of implementing.

3, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that described this method according to length, the flight of flight path from different assembly places to different deployment points meet with risk probability, assembly place operational aircraft can the deployment amount and the deployment point speed of the demand of operational aircraft, operational aircraft batch and contained number are meant by these parameters can set up the supply and demand system that a battlefield operational aircraft is disposed, obtain on this basis the battlefield operational aircraft is disposed the method for implementing commander's control.

4, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that described flight meets with risk probability and is meant that complicated battlefield surroundings may cause adverse effect to the operational aircraft along a certain flight path flight, thereby reduce the security of operational aircraft flight, for expending time in the deployment operational aircraft or meeting with commander's control that the risk minimum is a target, this reduction has been equivalent to increase the risk that operational aircraft flight faces, it can be with the function of time as variable that flight meets with risk probability, also can be and irrelevant constant of time, the flight of different flight paths meets with risk probability can be different.

5, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition is characterized in that described structure is that the target of target and the commander's controlling models with low computational complexity and the high solvability objective function that is meant this commander's controlling models is disposed all operational aircrafts and expended time in or meet with the risk minimum for making to dispose all operational aircrafts and expend time in or to meet with the risk minimum.

6, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that described structure is that target and the commander's controlling models with low computational complexity and high solvability are meant for computational complexity that reduces this commander's controlling models and the solvability that improves this commander's controlling models dispose all operational aircrafts to expend time in or to meet with the risk minimum, stipulates that the constraint condition relevant with the deployment point is the constraint condition that equals deployment point deployment amount, the constraint condition relevant with the assembly place is to be not more than the constraint condition that the assembly place maximum can the deployment amount.

7, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that described and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition is meant by the method for finding the solution linear programming and finding the solution the dual program of linear programming finds the solution commander's controlling models, can obtain respectively to meet with risk probability or the flight path of least consume time from the minimum flight that different assembly places deployment operational aircrafts need to different deployment points, with different assembly places and the relevant shadow price of different deployment points constraint condition, the result that will find the solution inserts in a kind of two dimension commander's control form again, according to analysis to this two dimension commander control form, and pass through according to shadow price, risk bottleneck and time bottleneck are adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield operational aircraft fast and low-risk disposition requirement until final acquisition.

8, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that described and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition is meant can be by describing the quantity of the operational aircraft of disposing to each deployment point from each assembly place as the zones of different in the two-dimentional form of option control command, each deployment point need deliver the size of power, flight meets with risk probability, operational aircraft batch, deployment expends time in and relevant shadow price, and the quantity of operational aircraft can be disposed in each assembly place, the situation of change of residue operational aircraft quantity is with relevant shadow price and dispose the priming the pump of all operational aircrafts and the minimum time that expends.

9, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that the length of described this method according to flight path from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, speed and contained number of operational aircraft batch, structure is target and the commander's controlling models with low computational complexity and high solvability dispose all operational aircrafts to expend time in or to meet with the risk minimum, and use linear programming, the dual program method of linear programming is found the solution this model and is meant that following is the analysis of target to quick commander's control problem of battlefield operational aircraft fast and low-risk disposition to meet with the risk minimum, but it is the analysis of target to quick commander's control problem of battlefield operational aircraft fast and low-risk disposition that this analysis is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition D _jy _j+ S _iy _N+i≤ p _IjBe replaced into D _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product, following mathematical formulae, derivation, result of calculation and application process are applicable to the quick commander's control to all battlefield operational aircraft fast and low-risk dispositions,

Supposing that battlefield operational aircraft fast and low-risk disposition problem can be used by the deployment point of the assembly place of m supply operational aircraft and n demand operational aircraft and between different supply and demand nodes exists the network in the path of a deployment operational aircraft to describe, and is x from assembly place i to the operational aircraft quantity that deployment point j disposes _Ij, it is p that flight meets with risk probability _Ij(t), the length of flight path is d _IjFlight meets with risk probability and is meant that complicated battlefield surroundings may cause adverse effect to the operational aircraft along a certain flight path flight, thereby reduce the security of operational aircraft flight, for expending time in the deployment operational aircraft or meeting with commander's control that the risk minimum is a target, this reduction has been equivalent to increase the risk that operational aircraft flight faces, it can be with the function of time as variable that flight meets with risk probability, also can be and irrelevant constant of time, is expressed as p _Ij, the flight of different flight paths meets with risk probability can be different,

The problem that need to solve be one of design from m assembly place deployment operational aircraft to n deployment point, make the flight of disposing all operational aircrafts meet with risk probability simultaneously and satisfy mapping out the plan of pre-provisioning request for minimum, consumed time, and calculate the quantity that required batch of operational aircraft is disposed in each assembly place, relevant operational aircraft deployment commander's controlling models and linear programming equation are as follows:

Objective function: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

The deployment point is to the constraint condition of operational aircraft demand: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}=D_j,(j=1,\·\·\·,n)$

The assembly place can supply to dispose the constraint condition of operational aircraft amount: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}\≤S_i,(i=1,\·\·\·,m)$

Condition of Non-Negative Constrains: x _Ij〉=0, (i=1 ..., m; J=1 ..., n)

Assembly place i (i=1 ... m) the quantity V of the operational aircraft of need disposing batch _i:

From assembly place i (i=1 ... m) dispose operational aircraft to deployment point j (j=1 ... n) spent time: $T_{\mathrm{ij}}=\frac{d_{\mathrm{ij}}}{C}$

Finish all operational aircrafts and dispose spent minimum time: minT=max{T _Ij}

The maximum flight relevant with j deployment point meets with risk probability: $p_j=\underset{p_{\mathrm{ij}}\∈P_{\mathrm{op}}}{\max }\left\{p_{\mathrm{ij}}\right\},j(j=1,\·\·\·n)$

Finish flight experience risk probability: the minP=max{p that all operational aircrafts are disposed _j, j (j=1 ... n)

With j the risk carrying capacity that the deployment point is relevant: $\min Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}},j(j=1,\·\·\·n)$

The overall risk carrying capacity that the battlefield operational aircraft is disposed: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\min Z_j$

With j the operational aircraft carrying capacity that the deployment point is relevant: $Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},j(j=1,\·\·\·n)$

The total operational aircraft carrying capacity in battlefield: $Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{Z}_j$

Wherein:

M is for disposing the assembly place sum of operational aircraft;

N is the deployment point sum of demand operational aircraft;

P _OpBe commander's controlling models p by associated pathway when obtaining optimum solution _IjThe set of forming;

The value of objective function was called the risk carrying capacity when minZ obtained optimum solution for commander's controlling models, and this value is the smaller the better;

p _IjFor assembly place i (i=1 ... m) with deployment point j (j=1 ... n) flight between meets with risk probability, can be with the function of time t as variable;

d _IjFor assembly place i (i=1 ... m) with deployment point j (j=1 ... the length of the flight path n) (unit: kilometer);

V _iFor the assembly place i that disposes operational aircraft (i=1 ... m) dispose batch quantity that operational aircraft needs;

L is the ability (unit: frame) of each batch deployment operational aircraft;

C is the speed (unit: kilometer/hour) of each batch deployment operational aircraft;

S _iFor assembly place i (i=1 ... m) quantity (unit: frame) of the operational aircraft that can dispose;

D _jFor deployment point j (j=1 ... n) need the quantity (unit: frame) of operational aircraft;

Above-mentioned model shows: objective function be equivalent to ask probability-weighted and, on the basis of trying to achieve risk carrying capacity minZ value by linear programming, can calculate each assembly place must be to the operational aircraft quantity x of related deployment point deployment _Ij, the p of associated pathway _Ij, count L according to the contained operational aircraft frame of each batch again, can calculate the operational aircraft batch V that need dispose each assembly place _i,, can calculate the risk carrying capacity minZ of each deployment point again at last according to the speed C and the longest path between assembly place and deployment point of each batch deployment operational aircraft _j, maximum flight meets with risk probability p _jFinish flight experience risk probability minP, the shortest time T that expends that all battlefield operational aircrafts are disposed, thereby realize commander's control to battlefield operational aircraft fast and low-risk disposition, for constraint condition rationally being set, improving solvability, utilizing above-mentioned linear programming model better, the dual linear programming model that provides this model is as follows:

Objective function: $\max G=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{D}_j{y}_j+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i{y}_{n+i}$

Constraint condition: D _jy _j+ S _iy _N+i≤ p _Ij, (i=1 ..., m; J=1 ..., n)

Condition of Non-Negative Constrains: y _j, y _N+i〉=0, (i=1 ..., m; J=1 ..., n)

Wherein: y _j, y _N+iBe respectively with the demand of former linear programming and dispose the shadow price or the relevant decision variable of opportunity cost of operational aircraft constraint condition,

Since primal linear programming solves be with deployment point j and assembly place i (i=1 ..., m; J=1 ..., the resource optimal utilization problem that constraint condition n) is relevant, thus dual program solve then be estimate to make deployment point j and assembly place i (i=1 ..., m; J=1 ..., constraint condition n) satisfies the cost problem that must pay, promptly uses the valency problem, and shadow price y _jAnd y _N+iReflection make just deployment point j and assembly place i (i=1 ..., m; J=1, n) constraint condition satisfies the cost that must pay, by making the target function value relevant minimize (or maximization) with cost, shadow price can be used for each constraint condition of comparison and carry out equivalence analysis to the contribution of target function value or to this contribution influence, shadow price is big more, show that this constraint condition is big more to the influence of the priming the pump delivery power of option control command, but it is also just difficult more to satisfy this condition, therefore, introducing shadow price just can be by comparing shadow price and realistic objective functional value, and can variation that study former linear programming constraint condition make objective function obtain gain.

10, quick commander's control method of battlefield according to claim 1 operational aircraft fast and low-risk disposition, it is characterized in that the length of described this method according to flight path from different assembly places to different deployment points, flight meets with risk probability, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, speed and contained number of operational aircraft batch, structure is target and the commander's controlling models with low computational complexity and high solvability dispose all operational aircrafts to expend time in or to meet with the risk minimum, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition is meant if the option control command of trying to achieve can not satisfy predetermined risk and time requirement, then can be by two dimension commander control table, result to former linear programming and dual program analyzes, determine to influence the risk of battlefield operational aircraft deployment and the bottleneck of T.T., carry out reasonable disposition by operational aircraft quantity again to the assembly place, increase the quantity of operational aircraft batch and the means such as operational aircraft that adopt different speed, eliminate risk and time bottleneck, and repeat this process, until making the risk of finishing battlefield operational aircraft deployment and meeting predetermined requirement T.T., this process can with following be that target is described the example of quick commander's control problem of battlefield operational aircraft fast and low-risk disposition to meet with the risk minimum, it is the instance analysis of target to quick commander's control problem of battlefield operational aircraft fast and low-risk disposition that this example is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition D _jy _j+ S _iy _N+i≤ p _IjBe replaced into D _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product, but the mathematical formulae described in example, result of calculation, various form and application process are applicable to the quick commander's control to all battlefield operational aircraft fast and low-risk dispositions,

Suppose with 16, average speed per hour to be that 70 kilometers operational aircraft is as an operational aircraft batch, dispose the operational aircraft of specified amount to 14 deployment points from 5 assembly places, between assembly place and the deployment point flight meet with risk probability, assembly place operational aircraft can the deployment amount and the deployment point as shown in table 1 to the demand of operational aircraft

Table 1: flight meets with risk probability, portion's amount of asking (unit: probability, frame) between assembly place and the deployment point 01 assembly place 02 assembly place 03 assembly place 04 assembly place 05 assembly place Quantity required 14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point 0.037 0.034 0.025 0.014 0.026 0.024 0.120 0.159 0.112 0.062 0.091 0.126 0.090 0.081 0.013 0.025 0.028 0.015 0.035 0.020 0.098 0.138 0.096 0.037 0.066 0.097 0.068 0.056 0.070 0.083 0.108 0.097 0.082 0.110 0.012 0.051 0.096 0.046 0.017 0.081 0.099 0.020 0.074 0.087 0.112 0.101 0.086 0.100 0.129 0.149 0.025 0.050 0.079 0.086 0.104 0.066 0.044 0.031 0.066 0.058 0.056 0.039 0.105 0.145 0.110 0.059 0.073 0.027 0.011 0.075 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 24.00 Can the deployment amount 250.00 200.00 300.00 400.00 150.00

Between assembly place and the deployment point length of flight path, assembly place operational aircraft can the deployment amount and the deployment point as shown in table 2 to the demand of operational aircraft,

Table 2: flight path length, portion's amount of asking (unit: kilometer, frame) between assembly place and the deployment point 01 assembly place 02 assembly place 03 assembly place 04 assembly place 05 assembly place Quantity required 14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point 37.00 34.00 25.00 14.00 26.00 24.00 120.00 159.00 112.00 62.00 91.00 126.00 90.00 81.00 13.00 25.00 28.00 15.00 35.00 20.00 98.00 138.00 96.00 37.00 66.00 97.00 68.00 56.00 70.00 83.00 108.00 97.00 82.00 110.00 12.00 51.00 96.00 46.00 17.00 81.00 99.00 20.00 74.00 87.00 112.00 101.00 86.00 100.00 129.00 149.00 25.00 50.00 79.00 86.00 104.00 66.00 44.00 31.00 66.00 58.00 56.00 39.00 105.00 145.00 110.00 59.00 73.00 27.00 11.00 75.00 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 24.00 Can the deployment amount 250.00 200.00 300.00 400.00 150.00

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, the option control command of the minimum risk operational aircraft that calculates by simplex algorithm deployment is as shown in table 3, and wherein the frame risk is the risk carrying capacity minZ of deployment point _j, risk probability is that the maximum flight of deployment point meets with risk probability p _j, the frame kilometer is the operational aircraft carrying capacity Z of deployment point _j,

Table 3: minimum flight meets with risk probability and disposes option control command (unit: frame, frame risk, probability, frame kilometer, batch, minute) 01 assembly place 02 assembly place 03 assembly place 04 assembly place 05 assembly place The frame risk Risk probability The frame kilometer Batch Expend time in Shadow price 14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point 90.00 90.00 70.00 36.00 21.00 40.00 40.00 36.00 60.00 16.00 90.00 24.00 29.00 22.00 18.00 0.468 0.525 2.250 1.860 1.820 0.800 0.720 0.816 0.725 1.332 1.530 0.594 0.198 0.480 0.013 0.025 0.025 0.015 0.026 0.020 0.012 0.051 0.025 0.037 0.017 0.027 0.011 0.020 468.00 525.00 2250.00 1860.00 1820.00 800.00 720.00 816.00 725.00 1332.00 1530.00 594.00 198.00 480.00 3 2 6 9 5 3 4 1 2 3 6 2 2 2 11.14 21.43 21.43 12.26 22.29 17.14 10.29 43.71 21.43 31.71 14.57 23.14 9.43 17.14 0.00 12.00 13.00 2.00 14.00 7.00 0.00 39.00 0.00 24.00 5.00 16.00 0.00 8.00 Add up to 250.00 173.00 190.00 29.00 40.00 14.118 0.051 14118.00 50 43.71 ^* But portion's quantity 250.00 200.00 300.00 400.00 150.00 Surplus after the portion 0.00 27.00 110.00 371.00 110.00 Shadow price 12.00 13.00 12.00 25.00 11.00

* finishing the minimum time that deployment task expends is 43.71 minutes

By option control command (table 3) is analyzed as can be known; finish operational aircraft that deployment task needs and batch add up to 50; time is 43.71 minutes; the operational aircraft that 01～05 assembly place needs batch is respectively 17; 14; 13; 2 and 4; therefore must be to 01; 02 and 03 assembly place implements to lay special stress on protecting; further analyze as can be known; disposing 16 43.71 minutes that operational aircraft spent from 03 assembly place to 08 deployment point is bottlenecks that the whole deployment task of restriction is finished sooner; this deployment also is simultaneously to reduce to finish the bottleneck that the flight of disposing in all battlefields meets with risk probability; if with speed faster operational aircraft finish this part deployment; then can be shortened to 31.71 minutes the time that whole deployment task is finished; reduction is 27.45%; risk probability is reduced to 0.037; reduction is 27.45%; and for example fruit is adopted the bottleneck that uses the same method and eliminated 31.71 minutes; then can be shortened to 23.14 minutes deployment time; reduction reaches 47.06%; risk probability is reduced to 0.027; reduction is 47.06%; almost only be half of former free and risk probability

From to demand constraint condition D _j(j=1,14) analysis of shadow price as can be known, the size of price has truly reflected the complexity that the related constraint condition satisfies, shadow price is 0 to be meant in specific span, and relevant constraint condition does not constitute influence to target function value, the easiliest satisfies, again for example, in order to satisfy constraint condition D ₈, the risk of disposing operational aircraft to 08 deployment point is 0.051,43.71 minutes consuming time, the shadow price of this constraint condition is a maximal value 39, illustrates that this condition is the most difficult to satisfy, can be by D with similar method _jThe complexity that satisfies, from difficulty to easy ordering: D ₈, D ₁₀, D ₁₂, D ₅..., to deployment amount constraint condition S _i(i=1 ..., 5) analysis of shadow price as can be known, S _iThe complexity that satisfies, from difficulty to easy ordering: S ₄, S ₂, S ₁, S ₃, S ₅, i.e. constraint condition S ₄It is the most difficult satisfied,

In addition, from the residue operational aircraft amount of each assembly place, back of finishing the work as can be seen, the surplus of 01 assembly place and 02 assembly place is obviously on the low side, and particularly the operational aircraft that can dispose of 01 assembly place exhausts, this statement of facts:, add S if there is more operational aircraft 01 assembly place ₁Constraint condition more easily satisfies, and just may obtain better to map out the plan, and therefore, can also carry out reasonable configuration to the operational aircraft of each assembly place with said method, and realization can be disposed the Optimal Management of operational aircraft quantity.