CN1845144A - Command control method of low risk deployment for war field battle airplane - Google Patents

Abstract

The invention relates to a quick command control method for quickly low-risk deploying operational aircraft on the battlefield. Wherein, the commanded object the all operational aircrafts; according to the flying risk probability from different concentrate points to different deploy points, the deploy amount at the concentrate point, the needed amount at the deploy point, and the number of operational aircraft batch, the command control mode purposed for deploying all operational aircrafts in minimum risk is built; and using linear programming, and the pair rule of linear programming, to solve said mode, and improve the result via the two-dimension table, to obtain the command control method that meeting the demand of quick low-risk deploy. The invention can improve the battle effectiveness, with wider application. The invention also provides relative technique.

Description

Commander's control method of battlefield operational aircraft low-risk disposition

Technical field the present invention relates to national defence and association area, is used for battlefield operational aircraft low-risk disposition is implemented commander's control, realizes the 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, meet with risk probability according to the flight on flight path from different assembly places to different deployment points, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, the quantity of operational aircraft batch, to meet with risk minimums be that commander's control plan of target is that the battlefield commander implements the key issue that commander's control must solve to battlefield operational aircraft low-risk disposition to structure to dispose all operational aircrafts, the solution of this problem is for increasing substantially fighting capacity, reduce to dispose the risk of operational aircraft and, have crucial meaning the demand of consumption of natural resource.

The 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, but also be related to the operational aircraft deployment point of can arriving safe and sound, 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 of battlefield operational aircraft deployment, therefore must analyze the choose reasonable parameter by antithesis and improve solvability and come the control to battlefield operational aircraft low-risk disposition enforcement commander to dispose the risk minimum as optimization aim.

The present invention relates to commander's control method of battlefield operational aircraft low-risk disposition, relate to military affairs and association area, the object of commander's control is all battlefield operational aircrafts, this method meets with risk probability according to the flight on the flight path from different assembly places to different deployment points, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, the quantity of operational aircraft batch, structure is commander's controlling models of target to dispose all operational aircrafts experience risk minimums, 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 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 commander's control of all battlefield operational aircraft low-risk dispositions, the invention further relates to the technology that realizes this method.

Summary of the invention the present invention meets with risk probability according to the flight on the flight path from different assembly places to different deployment points, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, the quantity of operational aircraft batch, structure is commander's controlling models of target to dispose all operational aircrafts experience risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield operational aircraft low-risk disposition enforcement commander control with two-dimentional form description, and check whether this option control command meets the risk 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, the risk bottleneck can be adjusted for the operational aircraft quantity of deployment and the type of the operational aircraft of implementing to dispose etc. the relevant episode node, constantly repeat this and find the solution-check analytic process, meet the option control command of low-risk disposition requirement until final acquisition.Therefore, the conception of commander's control of battlefield operational aircraft low-risk disposition is proposed, introduce the analytical approach that flight 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 low-risk disposition enforcement commander control with two-dimentional form description, and according to finishing the risk requirement that whole operational aircraft is disposed, by searching the risk 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 type of the operational aircraft implementing to dispose, continue to optimize and improve this option control command, and battlefield operational aircraft low-risk disposition requirement is satisfied in final acquisition, option control command with two-dimentional form description becomes key character of the present invention.

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

At first, with battlefield operational aircraft 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, the quantity of operational aircraft batch is described, and according to the risk requirement that the battlefield operational aircraft is disposed, structure is commander's controlling models of target to dispose and to transport all operational aircrafts experience risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield operational aircraft low-risk disposition enforcement commander control with two-dimentional form description, the risk bottleneck of assembling deployment system by continuous searching, quantity to the operational aircraft of relevant episode node is carried out reasonable disposition, adopt dissimilar methods such as operational aircraft, the final requirement that obtains to satisfy battlefield operational aircraft low-risk disposition, battlefield operational aircraft low-risk disposition is implemented the scheme that commander controls, finish commander's control battlefield operational aircraft low-risk disposition.

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 meeting with commander's control that the risk minimum is a target to dispose operational aircraft, 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 to meet with the flight path of risk probability respectively 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, the risk bottleneck is adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield operational aircraft 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 with relevant shadow price, each assembly place can dispose operational aircraft quantity, remain the situation of change and relevant shadow price and the priming the pump of disposing all operational aircrafts of operational aircraft quantity.

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

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

The case study of commander's control of battlefield operational aircraft low-risk disposition is as follows.

Supposing that battlefield operational aircraft 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), 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 meeting with commander's control that the risk minimum is a target to dispose operational aircraft, 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 be minimum mapping out the plan, 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 that equals of operational aircraft demand: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ie}}=D_e,$ (e＝1，…，n _e)

The deployment point to the operational aircraft demand less than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{il}}\≤D_l,$ (l＝n _e+1，…，n _l)

The deployment point to the operational aircraft demand greater than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{is}}\≥D_s,$ (s＝n _l+1，…，n _s)

The assembly place can supply to dispose the constraint condition that equals of operational aircraft amount: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ej}}=S_e,$ (e＝n _s+1，…，m _e)

The assembly place can for dispose the operational aircraft amount less than constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{lj}}\≤S_l,$ (l＝m _e+1，…，m _l)

The assembly place can for dispose the operational aircraft amount greater than constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{sj}}\≥S_s,$ (s＝m _l+1，…，m _s)

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

The classification of the amount relevant with the deployment point Demand Constraint: $D_v=\left\{\begin{array}{c}{D}_e,(1\≤v\≤n_e)\\ D_l,(n_e+1\≤v\≤n_l)\\ D_s,(n_l+1\≤v\≤n_s)\end{array}\right.$

Can supply to dispose the classification of the relevant amount of constraint with the assembly place: $S_u=\left\{\begin{array}{c}{S}_e,(n_s+1\≤u\≤m_e)\\ S_l,(m_e+1\≤u\≤m_l)\\ S_s,(m_l+1\≤u\≤m_s)\end{array}\right.$

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

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: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\min Z_j$

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;

E is the sequence number that equals the amount of equaling of constraint condition;

L is the sequence number less than the constraint condition upper limit;

S is the sequence number greater than the constraint condition lower limit;

n _eMaximum sequence number for the equal amount that equal constraint condition relevant with the deployment point demand;

n _lBe the maximum sequence number less than the constraint condition upper limit relevant with the deployment point demand;

n _sBe the maximum sequence number greater than constraint condition lower limit relevant with the deployment point demand;

D _eFor with the deployment point need the relevant amount of the quantity of operational aircraft (e=1 ..., n _e) (unit: frame);

D _lFor needing the relevant upper limit (l=n of operational aircraft quantity with the deployment point _e+ 1 ..., n _l) (unit: frame);

D _sFor needing the relevant lower limit (s=n of operational aircraft quantity with the deployment point _l+ 1 ..., n _s) (unit: frame);

m _eMaximum sequence number for the equal amount that equal constraint condition relevant with assembly place deployment amount;

m _lBe the maximum sequence number less than the constraint condition upper limit relevant with assembly place deployment amount;

m _sBe the maximum sequence number greater than constraint condition lower limit relevant with assembly place deployment amount;

S _eFor disposing the relevant amount (e=n of quantity of operational aircraft with the assembly place _s+ 1 ..., m _e) (unit: frame);

S _lFor disposing the relevant upper limit (l=m of operational aircraft quantity with the assembly place _e+ 1 ..., m _l) (unit: frame);

S _sFor disposing the relevant lower limit (s=m of operational aircraft quantity with the assembly place _l+ 1 ..., m _s) (unit: frame);

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;

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, the last risk carrying capacity minZ that can calculate each deployment point again _j, maximum flight meets with risk probability p _jFinish the flight experience risk probability minP that all battlefield operational aircrafts are disposed, thereby realize commander's control to battlefield operational aircraft 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:

$\max G=\underset{v=1}{\overset{n_e}{\mathrm{\Σ}}}{D}_v{y}_v+\underset{v=n_e+1}{\overset{n_l}{\mathrm{\Σ}}}{D}_v{y}_v+\underset{v=n_l+1}{\overset{n_s}{\mathrm{\Σ}}}{D}_v{y}_v+\underset{u=n_s+1}{\overset{m_e}{\mathrm{\Σ}}}{S}_u{y}_u+\underset{u=m_e+1}{\overset{m_l}{\mathrm{\Σ}}}{S}_u{y}_u+\underset{u=m_l+1}{\overset{m_s}{\mathrm{\Σ}}}{S}_u{y}_u$

Constraint condition: $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}(i=1,\·\·\·,m;j=1,\·\·\·,n)$

Condition of Non-Negative Constrains: $y_{m_l\left(i\right)},y_{n_l\left(j\right)}\≤0(i=1,\·\·\·,m;j=1,\·\·\·,n)$

Non-positive constraint condition: $y_{m_s\left(i\right)},y_{n_s\left(j\right)}\≥0(i=1,\·\·\·,m;j=1,\·\·\·,n)$

Wherein:

$y_{n_e\left(j\right)}=y_v(1\≤v{\≤n}_e),y_{n_l\left(j\right)}=y_v(n_e+1\≤v{\≤n}_l),y_{n_s\left(j\right)}=y_v(n_l+1\≤v{\≤n}_s)$ Under the variable relevant with j

Mark sequence number transforming function transformation function;

$y_{m_e\left(i\right)}=y_u(n_s+1\≤u\≤m_e),y_{m_l\left(i\right)}=y_u(m_e+1\≤u\≤m_l),y_{m_s\left(i\right)}=y_u(m_l+1\≤u\≤m_s)$ Be the variable subscript sequence number transforming function transformation function relevant with i;

y _v, y _u(v=1 ..., n _sU=n _s+ 1 ..., m _s) be 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 _vAnd y _uReflection 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, the implication of a certain constraint condition shadow price is when the constant of its pairing constraint condition right-hand member increases a unit, the numerical value that former problem objective function optimal value increases, 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, the difficulty that satisfies this condition is big more, therefore, by comparing shadow price and realistic objective functional value, can the variation that can 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, and the demand to huge battlefield operational aircraft deployment ability makes commander's control of implementing battlefield operational aircraft deployment become vital task.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 6 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 bound of 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	06 assembly place	The demand upper limit	The demand lower limit
									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	0.060 0.019 0.056 0.030 0.048 0.065 0.075 0.030 0.069 0.070 0.026 0.065 0.072 0.044	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 30.00 35.00 28.00	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 80.00 20.00 25.00 22.00
But portion's upper limit	100.00	200.00	300.00	400.00	150.00	350.00
									But subordinate's limit	100.00	60.00	40.00	10.00	10.00	20.00

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 2, 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

Table 2: minimum flight meets with risk probability and disposes option control command (unit: frame, frame risk, probability, batch)

	01 collection point	02 collection point	03 collection point	04 collection point	05 collection point	06 collection point	The frame risk	Risk probability	Batch	Upper limit shadow valency	Lower limit shadow valency
												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	30.00 70.00	36.00 60.00 64.00 40.00	60.00 36.00 80.00 22.00	29.00	20.00 25.00	21.00 66.00 16.00	0.468 0.399 2.430 2.940 1.820 0.800 0.720 0.480 0.725 1.656 1.360 0.540 0.275 0.440	0.013 0.019 0.028 0.030 0.026 0.020 0.012 0.030 0.025 0.046 0.017 0.027 0.011 0.020	3 2 6 9 5 3 4 1 2 3 5 2 2 2	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00
Add up to	100.00	200.00	198.00	29.00	45.00	103.00	15.053	0.046*	49

But portion's quantity	100.00	200.00	300.00	400.00	150.00	350.00
												Surplus after the portion	0.00	0.00	102.00	371.00	105.00	247.00
Upper limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00
												Lower limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00

* the flight of finishing deployment task meets with risk probability

By option control command (table 2) is analyzed as can be known; finish operational aircraft that deployment task needs and batch add up to 49; it is 0.046 that flight meets with risk probability; the operational aircraft that 01～06 assembly place needs batch is respectively 11; 16; 14; 2; 4 and 12; therefore must be to 02; 03 and 06 assembly place implements to lay special stress on protecting; further analyze as can be known; meeting with risk probability 0.046 from 03 assembly place to the flight of 36 operational aircrafts of 10 deployment points deployment is to reduce to finish the bottleneck that the risk probability that meets with is disposed in all battlefields; finish this part deployment if meet with the operational aircraft of risk probability with lower flight; then risk probability can be reduced to 0.030 from 0.046; reduction is 34.78%.

From to demand constraint condition D _v(v=1,18) 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, relevant constraint condition does not constitute influence to target function value, the easiest to be satisfied, promptly this resource is not in short supply, if increase this resource again the optimal value of objective function is further reduced, again for example, in order to satisfy constraint condition D ₁₀, the risk of disposing operational aircraft to 10 deployment points is 0.046, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult satisfied, can be by D with similar method _vThe complexity that satisfies, from difficulty to easy ordering: D ₁₀, D ₈, D ₁₆, D ₅, D ₃, D ₉..., to deployment amount constraint condition Su (u=19 ..., 29) analysis of shadow price as can be known, their shadow price is 0, therefore, in specific span, changes S _uValue target function value is not constituted influence, must be pointed out that shadow price is not changeless, can be along with D _vAnd S _uVariation and change, make the resource that does not constitute influence originally become influential resource, by analysis to shadow price, can adjust constraint condition targetedly, reach the purpose that reduces risk, because shadow price is the result who obtains, only in its valid interval under specific constraint condition, price just has relative stability

From finish the work the back each assembly place residue operational aircraft amount as can be seen, the operational aircraft of 02 assembly place exhausts, obviously on the low side, and the operational aircraft amount of 04 assembly place is obviously bigger than normal, and according to the antithesis analysis, the shadow price of their constraint condition is 0, this statement of facts: if there is more operational aircraft 02 assembly place, there is operational aircraft still less 04 assembly place, just may obtain better to map out the plan, so adjust the upper limit S of constraint condition targetedly ₂₅Be increased to 400 from 200, make S simultaneously ₂₇Reduce to 200 from 400, the improvement project that the minimum of obtaining is disposed is as shown in table 3,

Table 3: minimum flight meets with risk probability and disposes the improvement project of option control command (unit: frame, frame risk, probability, batch)

	01 collection point	02 collection point	03 collection point	04 collection point	05 collection point	06 collection point	The frame risk	Risk probability	Batch	Upper limit shadow valency	Lower limit shadow valency
												01 deployment point		36.00					0.468	0.013	3	13.00	13.00

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	30.00 70.00	60.00 130.00 40.00 36.00	60.00 80.00 22	29.00	20.00 25.00	21.00 16.00	0.399 2.430 1.950 1.820 0.800 0.720 0.480 0.725 1.332 1.360 0.540 0.275 0.440	0.019 0.028 0.015 0.026 0.020 0.012 0.030 0.025 0.037 0.017 0.027 0.011 0.020	2 6 9 5 3 4 1 2 3 5 2 2 2	19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00	19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00
												Add up to	100.00	302.00	162.00	29.00	45.00	37.00	13.739	0.037 *	49
But portion's quantity	100.00	400.00	300.00	200.00	150.00	350.00
												Surplus after the portion	0.00	98.00	138.00	171.00	105.00	313.00
Upper limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00
												Lower limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00

* the flight of finishing deployment task meets with risk probability

Analysis by his-and-hers watches 3 as can be known, the risk of finishing deployment task is 0.037, amount of decrease is 19.57%, the overall risk carrying capacity is reduced to 13.739 risks, amount of decrease is 8.73%, antithesis the analysis showed that: shadow price is without any variation, but the scheme after improving is better, therefore, can also carry out reasonable configuration to the operational aircraft of each assembly place with said method, realization can be disposed the Optimal Management of operational aircraft quantity.

Claims (9)

1, the present invention relates to commander's control method of battlefield operational aircraft low-risk disposition, relate to military affairs and association area, the object of commander's control is all battlefield operational aircrafts, this method meets with risk probability according to the flight on the flight path from different assembly places to different deployment points, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, the quantity of operational aircraft batch, structure is commander's controlling models of target to dispose all operational aircrafts experience risk minimums, 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 low-risk disposition requirement until final acquisition, this scheme is applicable to commander's control of the low-risk disposition of all battlefield operational aircrafts.

2, commander's control method of battlefield according to claim 1 operational aircraft 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 make probability-weighted that all flights meet with risks for minimum, can be for the scheme of implementing.

3, commander's control method of battlefield according to claim 1 operational aircraft low-risk disposition, it is characterized in that described this method according to the flight on 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 quantity of the demand of operational aircraft, operational aircraft batch is meant by these parameters can sets 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, commander's control method of battlefield according to claim 1 operational aircraft 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 meeting with commander's control that the risk minimum is a target to dispose operational aircraft, 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, commander's control method of battlefield according to claim 1 operational aircraft low-risk disposition is characterized in that to meet with risk minimums be that the target of commander's controlling models of target objective function of being meant this commander controlling models is for making all operational aircrafts experience risk minimums of deployment to described structure to dispose all operational aircrafts.

6, commander's control method of battlefield according to claim 1 operational aircraft 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 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 to meet with the flight path of risk probability respectively 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, the risk bottleneck is adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield operational aircraft low-risk disposition requirement until final acquisition.

7, commander's control method of battlefield according to claim 1 operational aircraft 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 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 with relevant shadow price, the quantity of operational aircraft can be disposed in each assembly place, the situation of change and relevant shadow price and the priming the pump of disposing all operational aircrafts of residue operational aircraft quantity.

8, commander's control method of battlefield according to claim 1 operational aircraft low-risk disposition, it is characterized in that described this method meets with risk probability according to the flight on the flight path from different assembly places to different deployment points, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, the quantity of operational aircraft batch, structure is commander's controlling models of target to dispose all operational aircrafts experience risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model and is meant the following case study that the commander of battlefield operational aircraft low-risk disposition is controlled, but following mathematical formulae, derivation, result of calculation and application process are applicable to the commander's control to all battlefield operational aircraft low-risk dispositions

Supposing that battlefield operational aircraft 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), 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 meeting with commander's control that the risk minimum is a target to dispose operational aircraft, 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 be minimum mapping out the plan, 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 that equals of operational aircraft demand: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ie}}=D_e,$ (e＝1，…，n _e)

The deployment point to the operational aircraft demand less than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{il}}\≤D_l,$ (l＝n _e+1，…，n _l)

The deployment point to the operational aircraft demand greater than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{is}}\≥D_s,$ (s＝n _l+1，…，n _s)

The assembly place can supply to dispose the constraint condition that equals of operational aircraft amount: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ej}}=S_e,$ (e＝n _s+1，…，m _e)

The assembly place can for dispose the operational aircraft amount less than constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{lj}}\≤S_l,$ (l＝m _e+1，…，m _l)

The assembly place can for dispose the operational aircraft amount greater than constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{sj}}\≥S_s,$ (s＝m _l+1，…，m _s)

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

The classification of the amount relevant with the deployment point Demand Constraint: $D_v=\left\{\begin{array}{c}{D}_e,(1\≤v\≤n_e)\\ D_l,(n_e+1\≤v\≤n_l)\\ D_s,(n_l+1\≤v\≤n_s)\end{array}\right.$

Can supply to dispose the classification of the relevant amount of constraint with the assembly place: $S_u=\left\{\begin{array}{c}{S}_e,(n_s+1\≤u\≤m_e)\\ S_l,(m_e+1\≤u\≤m_l)\\ S_s,(m_l+1\≤u\≤m_s)\end{array}\right.$

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

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 the flight experience risk probability that all operational aircrafts are disposed: min P=max{p _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: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\min Z_j$

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 min Z 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;

E is the sequence number that equals the amount of equaling of constraint condition;

L is the sequence number less than the constraint condition upper limit;

S is the sequence number greater than the constraint condition lower limit;

n _eMaximum sequence number for the equal amount that equal constraint condition relevant with the deployment point demand;

n _lBe the maximum sequence number less than the constraint condition upper limit relevant with the deployment point demand;

n _sBe the maximum sequence number greater than constraint condition lower limit relevant with the deployment point demand;

D _eFor with the deployment point need the relevant amount of the quantity of operational aircraft (e=1 ..., n _e) (unit: frame);

D _lFor needing the relevant upper limit (l=n of operational aircraft quantity with the deployment point _e+ 1 ..., n _l) (unit: frame);

D _sFor needing the relevant lower limit (s=n of operational aircraft quantity with the deployment point _l+ 1 ..., n _s) (unit: frame);

m _eMaximum sequence number for the equal amount that equal constraint condition relevant with assembly place deployment amount;

m _lBe the maximum sequence number less than the constraint condition upper limit relevant with assembly place deployment amount;

m _sBe the maximum sequence number greater than constraint condition lower limit relevant with assembly place deployment amount;

S _eFor disposing the relevant amount (e=n of quantity of operational aircraft with the assembly place _s+ 1 ..., m _e) (unit: frame);

S _lFor disposing the relevant upper limit (l=m of operational aircraft quantity with the assembly place _e+ 1 ..., m _l) (unit: frame);

S _sFor disposing the relevant lower limit (s=m of operational aircraft quantity with the assembly place _l+ 1 ..., m _s) (unit: frame);

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;

Above-mentioned model shows: objective function be equivalent to ask probability-weighted and, on the basis of trying to achieve risk carrying capacity min Z 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, the last risk carrying capacity min Z that can calculate each deployment point again _j, maximum flight meets with risk probability p _jFinish the flight experience risk probability min P that all battlefield operational aircrafts are disposed, thereby realize commander's control to battlefield operational aircraft 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: $\max G=\underset{v=1}{\overset{n_e}{\mathrm{\Σ}}}{D}_v{y}_v+\underset{v=n_e+1}{\overset{n_l}{\mathrm{\Σ}}}{D}_v{y}_v+\underset{v=n_l+1}{\overset{n_s}{\mathrm{\Σ}}}{D}_v{y}_v+\underset{u=n_s+1}{\overset{m_e}{\mathrm{\Σ}}}{S}_u{y}_u+\underset{u=m_e+1}{\overset{m_l}{\mathrm{\Σ}}}{S}_u{y}_u+\underset{u=m_l+1}{\overset{m_s}{\mathrm{\Σ}}}{S}_u{y}_u$

Constraint condition: $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}(i=1,\·\·\·,m;j=1,\·\·\·,n)$

Condition of Non-Negative Constrains: $y_{m_l\left(i\right)},y_{n_l\left(j\right)}\≤0(i=1,\·\·\·,m;j=1,\·\·\·,n)$

Non-positive constraint condition: $y_{m_s\left(i\right)},y_{n_s\left(j\right)}\≥0(i=1,\·\·\·,m;j=1,\·\·\·,n)$

Wherein: $y_{n_e\left(j\right)}=y_v(1\≤v\≤n_e),y_{n_l\left(j\right)}=y_v(n_e+1\≤v\≤n_l),y_{n_s\left(j\right)}=y_v(n_l+1\≤v\≤n_s)$ Be the variable subscript sequence number transforming function transformation function relevant with j; $y_{m_e\left(i\right)}=y_u(n_s+1\≤u\≤m_e),y_{m_l\left(i\right)}=y_u(m_e+1\≤u\≤m_l),y_{m_s\left(i\right)}=y_u(m_l+1\≤u\≤m_s)$ Be the variable subscript sequence number transforming function transformation function relevant with i;

y _v, y _u(v=1 ..., n _sU=n _s+ 1 ..., m _s) be 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 _vAnd y _uReflection 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, the implication of a certain constraint condition shadow price is when the constant of its pairing constraint condition right-hand member increases a unit, the numerical value that former problem objective function optimal value increases, 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, the difficulty that satisfies this condition is big more, therefore, by comparing shadow price and realistic objective functional value, can the variation that can study former linear programming constraint condition make objective function obtain gain.

9, commander's control method of battlefield according to claim 1 operational aircraft low-risk disposition, it is characterized in that described this method meets with risk probability according to the flight on the flight path from different assembly places to different deployment points, the assembly place operational aircraft can the deployment amount and the deployment point to the demand of operational aircraft, the quantity of operational aircraft batch, structure is commander's controlling models of target to dispose all operational aircrafts experience risk minimums, 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 low-risk disposition requirement until final acquisition is meant if the option control command of trying to achieve can not satisfy predetermined risk requirement, then can be by two dimension commander control table, result to former linear programming and dual program analyzes, determine to influence the bottleneck that the battlefield operational aircraft is disposed risk, carry out reasonable disposition by operational aircraft quantity again to the assembly place, increase the quantity of operational aircraft batch and adopt dissimilar means such as operational aircraft, eliminate the risk bottleneck, and repeat this process, until making the risk of finishing battlefield operational aircraft deployment meet predetermined requirement, this process can be described with following example, but the mathematical formulae described in example, result of calculation, various forms and application process are applicable to the commander's control to all battlefield operational aircraft 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 6 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 bound of 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 06 assembly place The demand upper limit The demand lower limit 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 0.060 0.019 0.056 0.030 0.048 0.065 0.075 0.030 0.069 0.070 0.026 0.065 0.072 0.044 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 30.00 35.00 28.00 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 80.00 20.00 25.00 22.00 But portion's upper limit 100.00 200.00 300.00 400.00 150.00 350.00 But subordinate's limit 100.00 60.00 40.00 10.00 10.00 20.00

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 2, and wherein the frame risk is the risk carrying capacity min Z of deployment point _j, risk probability is that the maximum flight of deployment point meets with risk probability p _j,

Table 2: minimum flight meets with risk probability and disposes option control command (unit: frame, frame risk, probability, batch) 01 collection point 02 collection point 03 collection point 04 collection point 05 collection point 06 collection point The frame risk Risk probability Batch Upper limit shadow valency Lower limit shadow valency 03 deployment point, 02 deployment point, 01 deployment point 30.00 36.00 60.00 21.00 0.468 0.399 2.430 0.013 0.019 0.028 3 2 6 13.00 19.00 25.00 13.00 19.00 25.00 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 70.00 64.00 40.00 60.00 36.00 80.00 22.00 29.00 20.00 25.00 66.00 16.00 2.940 1.820 0.800 0.720 0.480 0.725 1.656 1.360 0.540 0.275 0.440 0.030 0.026 0.020 0.012 0.030 0.025 0.046 0.017 0.027 0.011 0.020 9 5 3 4 1 2 3 5 2 2 2 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00 Add up to 100.00 200.00 198.00 29.00 45.00 103.00 15.053 0.046 ^* 49 But portion's quantity 100.00 200.00 300.00 400.00 150.00 350.00 Surplus after the portion 0.00 0.00 102.00 371.00 105.00 247.00 Upper limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00 Lower limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00

* the flight of finishing deployment task meets with risk probability

By option control command (table 2) is analyzed as can be known; finish operational aircraft that deployment task needs and batch add up to 49; it is 0.046 that flight meets with risk probability; the operational aircraft that 01～06 assembly place needs batch is respectively 11; 16; 14; 2; 4 and 12; therefore must be to 02; 03 and 06 assembly place implements to lay special stress on protecting; further analyze as can be known; meeting with risk probability 0.046 from 03 assembly place to the flight of 36 operational aircrafts of 10 deployment points deployment is to reduce to finish the bottleneck that the risk probability that meets with is disposed in all battlefields; finish this part deployment if meet with the operational aircraft of risk probability with lower flight; then risk probability can be reduced to 0.030 from 0.046; reduction is 34.78%

From to demand constraint condition D _v(v=1,18) 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, relevant constraint condition does not constitute influence to target function value, the easiest to be satisfied, promptly this resource is not in short supply, if increase this resource again the optimal value of objective function is further reduced, again for example, in order to satisfy constraint condition D ₁₀, the risk of disposing operational aircraft to 10 deployment points is 0.046, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult satisfied, can be by D with similar method _vThe complexity that satisfies, from difficulty to easy ordering: D ₁₀, D ₈, D ₁₆, D ₅, D ₃, D ₉..., to deployment amount constraint condition S _u(u=19 ..., 29) analysis of shadow price as can be known, their shadow price is 0, therefore, in specific span, changes S _uValue target function value is not constituted influence, must be pointed out that shadow price is not changeless, can be along with D _vAnd S _uVariation and change, make the resource that does not constitute influence originally become influential resource, by analysis to shadow price, can adjust constraint condition targetedly, reach the purpose that reduces risk, because shadow price is the result who obtains, only in its valid interval under specific constraint condition, price just has relative stability

From finish the work the back each assembly place residue operational aircraft amount as can be seen, the operational aircraft of 02 assembly place exhausts, obviously on the low side, and the operational aircraft amount of 04 assembly place is obviously bigger than normal, and according to the antithesis analysis, the shadow price of their constraint condition is 0, this statement of facts: if there is more operational aircraft 02 assembly place, there is operational aircraft still less 04 assembly place, just may obtain better to map out the plan, so adjust the upper limit S of constraint condition targetedly ₂₅Be increased to 400 from 200, make S simultaneously ₂₇Reduce to 200 from 400, the improvement project that the minimum of obtaining is disposed is as shown in table 3,

Table 3: minimum flight meets with risk probability and disposes the improvement project of option control command (unit: frame, frame risk, probability, batch) 01 collection point 02 collection point 03 collection point 04 collection point 05 collection point 06 collection point The frame risk Risk probability Batch Upper limit shadow valency Lower limit shadow valency 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 30.00 70.00 36.00 60.00 130.00 40.00 36.00 60.00 80.00 22 29.00 20.00 25.00 21.00 16.00 0.468 0.399 2.430 1.950 1.820 0.800 0.720 0.480 0.725 1.332 1.360 0.540 0.275 0.440 0.013 00019 0.028 0.015 0.026 0.020 0.012 0.030 0.025 0.037 0.017 0.027 0.011 0.020 3 2 6 9 5 3 4 1 2 3 5 2 2 2 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00 Add up to 100.00 302.00 162.00 29.00 45.00 37.00 13.739 0.037 ^* 49 But portion's quantity 100.00 400.00 300.00 200.00 150.00 350.00 Surplus after the portion 0.00 98.00 138.00 171.00 105.00 313.00 Upper limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00 Lower limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00

* the flight of finishing deployment task meets with risk probability

Analysis by his-and-hers watches 3 as can be known, the risk of finishing deployment task is 0.037, amount of decrease is 19.57%, the overall risk carrying capacity is reduced to 13.739 risks, amount of decrease is 8.73%, antithesis the analysis showed that: shadow price is without any variation, but the scheme after improving is better, therefore, can also carry out reasonable configuration to the operational aircraft of each assembly place with said method, realization can be disposed the Optimal Management of operational aircraft quantity.