CN1845142A - Command control method of airplane rapid deployment in war field battle - Google Patents

Abstract

The invention relates to a quick command control method for quickly deploying operational aircraft on the battlefield. Wherein, the commanded object the all operational aircrafts; according to lengths from different concentrate points to different deploy points, the flying non-baffle probability, the deploy amount at the concentrate point, the needed amount at the deploy point, and the number and number of operational aircraft batch, the command control mode purposed for deploying all operational aircrafts in minimum time 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 time demand of quick deploy. The invention can improve the battle effectiveness, with wider application. The invention also provides relative technique.

Description

Commander's control method that a kind of battlefield operational aircraft is disposed fast

Technical field the present invention relates to national defence and association area, is used for the battlefield operational aircraft is disposed enforcement commander control fast, realizes the quick deployment 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, the without hindrance flight probability of flight path, 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 commander's control plan of target is that the battlefield commander disposes fast the battlefield operational aircraft and implements the key issue that commander's control must solve to dispose all operational aircrafts minimum that expends time in, the solution of this problem is for increasing substantially fighting capacity, minimizing has crucial meaning to disposing the demand of operational aircraft consumption of natural resource.

The quick deployment ability of battlefield operational aircraft is most important for the triumph of capturing IT-based warfare, but complicated battlefield surroundings may impact the traffic capacity of the flight path of disposing operational aircraft, thereby reduce the passage rate of operational aircraft, and commander's control of disposing operational aircraft fast 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 transport resource that consumes 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.Therefore must by antithesis analyze the choose reasonable parameter improve solvability and with deployment time minimum come the battlefield operational aircraft disposed fast as optimization aim and implement commander's control.

The present invention relates to commander's control method that the battlefield operational aircraft is disposed fast, 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, the without hindrance flight probability of flight path, 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 commander's controlling models of target to dispose all operational aircrafts minimum that expends time in, 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 that quick deployment time requires 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 that all battlefield operational aircrafts are disposed fast, 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, the without hindrance flight probability of flight path, 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 commander's controlling models of target to dispose all operational aircrafts minimum that expends time in, and use linear programming, the dual program method of linear programming is found the solution this model, obtain to implement to command the scheme of controlling with two-dimentional form description the battlefield operational aircraft is disposed fast, and check whether this option control command meets 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, the 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 that quick deployment time requires until final acquisition.Therefore, the operational aircraft conception of commander's control of deployment fast in battlefield is proposed, introduce the analytical approach of the without hindrance flight probability of flight path, 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 to implement to command the scheme of controlling with two-dimentional form description the battlefield operational aircraft is disposed fast, and according to finishing the time requirement that whole operational aircraft is disposed, by searching 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 the final time requirement that obtains to satisfy the quick deployment of battlefield operational aircraft, option control command with two-dimentional form description becomes key character of the present invention.

The technical scheme of commander's control method that a kind of battlefield of the present invention operational aircraft is disposed fast is:

At first, operational aircraft quick deployment issue in battlefield is defined as 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, the without hindrance flight probability of flight path, 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 time requirement that the battlefield operational aircraft is disposed, structure is commander's controlling models of target to dispose and to transport all operational aircrafts minimum that expends time in, and use linear programming, the dual program method of linear programming is found the solution this model, obtain to implement to command the scheme of controlling with two-dimentional form description the battlefield operational aircraft is disposed fast, 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, the final time requirement that obtains to satisfy the quick deployment of battlefield operational aircraft, the battlefield operational aircraft is disposed the scheme of implementing commander's control fast, finish commander's control that the battlefield operational aircraft is disposed fast.

Complicated battlefield surroundings may impact the traffic capacity of the flight path of operational aircraft, thereby reduce the passage rate of operational aircraft, for the minimum that expends time in the deployment operational aircraft is commander's control of target, this reduction has been equivalent to increase the length of flight path, flight path length after claiming to increase is equivalent path length, the without hindrance flight probability of flight path is with the function of time as variable, equivalent flight path length then is with the function of the without hindrance flight probability of practical flight path and relevant flight path as variable, when the without hindrance flight probability of flight path is 1, practical flight path and equivalent flight path equal in length, and the without hindrance flight probability of flight path is more little, and then compare equivalent flight path length with the practical flight path just long more.

Usually, the target of the objective function of commander's controlling models is for making all operational aircrafts of deployment minimum that expends time in, but when the without hindrance flight probability of the flight path in all paths was 1, the target of the objective function of this commander's controlling models also was minimum for the carrying capacity that all operational aircrafts of deployment are needed simultaneously.

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 dispose the minimum time that operational aircraft needs to different deployment points from different assembly places, 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, by analysis to this form, and according to shadow price, the time bottleneck is adjusted correlation parameter, constantly find the solution and update, can finally obtain to meet the option control command of the quick deployment time requirement of battlefield operational aircraft.

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, the size that each deployment point need deliver power, operational aircraft batch, dispose the minimum time and relevant shadow price that expend, the situation of change of quantity, residue operational aircraft quantity that operational aircraft can be disposed in each assembly place is with relevant shadow price and dispose the minimum time that all operational aircrafts expend.

If the option control command of trying to achieve can not satisfy the preset time 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 T.T., means such as operational aircraft by the quantity of the operational aircraft of assembly place being carried out reasonable disposition, increasing operational aircraft batch and adopt friction speed again, eliminate the time bottleneck, and repeat this process, until making the predetermined requirement that meets T.T. of finishing battlefield operational aircraft deployment.

Commander's control method that the battlefield operational aircraft of the present invention's design is disposed fast is applicable to that it is key character of the present invention that all battlefield operational aircrafts are disposed fast.

The case study of commander's control that the battlefield operational aircraft is disposed fast is as follows.

Supposing that operational aircraft quick deployment issue in battlefield 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, the without hindrance flight probability of flight path is p _Ij(t), the physical length of flight path is r _Ij, the equivalent length of flight path is d _IjThe without hindrance flight probability of flight path is meant that complicated battlefield surroundings may impact the traffic capacity of operational aircraft flight path, thereby reduce the passage rate of operational aircraft, for the minimum that expends time in the deployment operational aircraft is commander's control of target, this reduction has been equivalent to increase the length of flight path, flight path length after claiming to increase is equivalent path length, the without hindrance flight probability of flight path is with the function of time as variable, equivalent flight path length then is with the function of the without hindrance flight probability of practical flight path and relevant flight path as variable, when the without hindrance flight probability of flight path is 1, practical flight path and equivalent flight path equal in length.

The problem that need to solve be one of design from m assembly place deployment operational aircraft to n deployment point, make the carrying capacity and the consumed time of disposing all operational aircraft costs be minimum mapping out the plan simultaneously, 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: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

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: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{1l}\≤D_l,(l=n_e+1,...,n_l)$

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: $S_u=\left\{\begin{array}{c}{S}_e,(n_s+1\≤u\≤m_e)\\ S_l,(m_e+1\≤u\≤m_l)\\ S_s,(m_l+1\≤u\≤m_s)\end{array}\right.$

The equivalent length of flight path is: d _Ij=f (r _Ij, p _Ij(t)), (0＜p _Ij(t)≤1; 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 the spent minimum time: min T=max{T _Ij}

Wherein:

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

N is the deployment point sum of demand operational aircraft;

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

p _Ij(t) be assembly place i (i=1 ... m) with deployment point j (j=1 ... n) the without hindrance flight probability of the flight path between is with the function of time t as variable;

d _IjFor assembly place i (i=1 ... m) with deployment point j (j=1 ... the equivalent length of the flight path n) (unit: kilometer), work as p _Ij(t)=1 o'clock, r _IjWith d _IjEquate;

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;

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

Above-mentioned model shows: try to achieve by linear programming on the basis of min Z value, can calculate each assembly place must be to the operational aircraft quantity x of related deployment point deployment _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 _iLast speed C and the longest path between assembly place and deployment point according to each batch deployment operational aircraft, can calculate again and finish the spent shortest time T of whole operational aircraft deployment task, thereby realize that the commander that the battlefield operational aircraft is disposed fast controls, 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: $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}(i=1,...,m;1,...,n)$

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;

$y_{m_e\left(i\right)}=y_u(n_s+1\≤u\≤m_e),$ $y_{m_l\left(i\right)}=y_u(m_e+1\≤u\≤m_l),$ $y_{m_s\left(i\right)}=y_u(m_l+1\≤u\≤m_s)$ For relevant with i

Variable subscript sequence number transforming function transformation function; 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 minimum 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 huge battlefield operational aircraft is disposed ability and the demand of time, 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 amount to 14 deployment points from 6 assembly places, 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 1 to the bound of the demand of operational aircraft, make the without hindrance flight Probability p of all flight paths here _Ij(t) be 1, d _Ij=r _Ij/ p _Ij(t), therefore practical flight path and equivalent flight path equal in length, the i.e. r between different assembly places and deployment point _IjWith d _IjEquate.

Table 1: 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	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	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	60.00 19.00 56.00 30.00 48.00 65.00 75.00 30.00 69.00 70.00 26.00 65.00 72.00 44.00	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 time operational aircraft that calculates by simplex algorithm deployment is as shown in table 2.

Table 2: minimum time is disposed option control command (unit: frame, frame kilometer, batch, minute)

	01 assembly place	02 assembly place	03 assembly place	04 assembly place	05 assembly place	06 assembly place	The frame kilometer	Batch quantity	Expend time in	Upper limit shadow valency	Lower limit shadow valency
												04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point	30.00	36.00 60.00 64.00				21.00 66.00	468.00 399.00 2430.00 2940.00	3 2 6 9	11.14 16.29 24.00 25.71	13.00 19.00 25.00 14.00	13.00 19.00 25.00 14.00

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	70.00	40.00	60.00 36.00 80.00 22.00	29.00	20.00 25.00	16.00	1820.00 800.00 720.00 480.00 725.00 1656.00 1360.00 540.00 275.00 440.00	5 3 4 1 2 3 5 2 2 2	22.29 17.14 10.29 25.71 21.43 39.43 14.57 23.14 9.43 17.14	26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00	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	15053.00	49	39.43 *
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

* finish the minimum time that deployment task expends

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; time is 39.43 minutes; 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; disposing 36 39.43 minutes that operational aircraft spent from 03 assembly place to 10 deployment points is bottlenecks that the whole deployment task of restriction is finished sooner; if with speed faster operational aircraft finish this part deployment; then can be shortened to 25.71 minutes the time of finishing whole deployment task, reduction is 34.80%.

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, dispose 39.43 minutes consuming time of operational aircraft to 10 deployment points, 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 and reduce carrying capacity and the purpose of flight time, because shadow price is the result who obtains under specific constraint condition, only in its valid interval, 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 time of obtaining is disposed is as shown in table 3.

Table 3: minimum time is disposed the improvement project (unit: frame, frame kilometer, batch, minute) of commander's control

	01 assembly place	02 assembly place	03 assembly place	04 assembly place	05 assembly place	06 assembly place	The frame kilometer	Batch quantity	Expend time in	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	468.00 399.00 2430.00 1950.00 1820.00 800.00 720.00 480.00 725.00 1332.00 1360.00 540.00 275.00 440.00	3 2 6 9 5 3 4 1 2 3 5 2 2 2	11.14 16.29 24.00 12.86 22.29 17.14 10.29 25.71 21.43 31.71 14.57 23.14 9.43 17.14	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	13739.00	49	31.71 *
												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

* finish the minimum time that deployment task needs

Analysis by his-and-hers watches 3 as can be known, the time that finishing deployment task needs shortens to 31.71 minutes, amount of decrease is 19.58%, total carrying capacity is reduced to 13739 kilometers, and amount of decrease is 8.73%, and 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 that the battlefield operational aircraft is disposed fast, 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, the without hindrance flight probability of flight path, 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 commander's controlling models of target to dispose all operational aircrafts minimum that expends time in, 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 that quick deployment time requires until final acquisition, this scheme is applicable to commander's control of the quick deployment of all battlefield operational aircrafts.

2, the quick commander's control method of disposing of battlefield operational aircraft according to claim 1, 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 the total flight time that needs or total carrying capacity for minimum, can be for the scheme of implementing.

3, the quick commander's control method of disposing of battlefield operational aircraft according to claim 1, it is characterized in that described this method according to the without hindrance flight probability of length, flight path of flight path, assembly place operational aircraft from different assembly places to different deployment points 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, commander's control method that battlefield according to claim 1 operational aircraft is disposed fast, it is characterized in that the without hindrance flight probability of described flight path is meant that complicated battlefield surroundings may impact the traffic capacity of the flight path of operational aircraft, thereby reduce the passage rate of operational aircraft, for the minimum that expends time in the deployment operational aircraft is commander's control of target, this reduction has been equivalent to increase the length of flight path, flight path length after claiming to increase is equivalent path length, the without hindrance flight probability of flight path is with the function of time as variable, equivalent flight path length then is with the function of the without hindrance flight probability of practical flight path and relevant flight path as variable, when the without hindrance flight probability of flight path is 1, practical flight path and equivalent flight path equal in length.

5, the quick commander's control method of disposing of battlefield operational aircraft according to claim 1, it is characterized in that described structure is that the target of commander's controlling models of target objective function of being meant this commander's controlling models is disposed all operational aircrafts minimum that expends time in for making to dispose all operational aircrafts minimum that expends time in, but when the without hindrance flight probability of the flight path in all paths was 1, the target of the objective function of this commander's controlling models also was minimum for the carrying capacity that all operational aircrafts of deployment are needed simultaneously.

6, commander's control method that battlefield according to claim 1 operational aircraft is disposed fast, 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, meeting option control command that quick deployment time requires until final acquisition is meant by the method for finding the solution linear programming and finding the solution the dual program of linear programming and finds the solution commander's controlling models, can obtain respectively to dispose the minimum time that operational aircraft needs to different deployment points from different assembly places, 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 time bottleneck is adjusted correlation parameter, constantly find the solution and update, meet the option control command of the quick deployment time requirement of battlefield operational aircraft until final acquisition.

7, commander's control method that battlefield according to claim 1 operational aircraft is disposed fast, 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, meeting until final acquisition that option control command that quick deployment time requires 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, operational aircraft batch, the minimum time that deployment expends can be disposed the quantity of operational aircraft with relevant shadow price, each assembly place, the situation of change of residue operational aircraft quantity is with relevant shadow price and dispose the minimum time that all operational aircrafts expend.

8, commander's control method that battlefield according to claim 1 operational aircraft is disposed fast, it is characterized in that the length of described this method according to flight path from different assembly places to different deployment points, the without hindrance flight probability of flight path, 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 commander's controlling models of target to dispose all operational aircrafts minimum that expends time in, and use linear programming, the dual program method of linear programming is found the solution the case study that this model is meant that the following commander that the battlefield operational aircraft is disposed fast controls, but following mathematical formulae, derivation, result of calculation and application process are applicable to commander's control that all battlefield operational aircrafts are disposed fast

Supposing that operational aircraft quick deployment issue in battlefield 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, the without hindrance flight probability of flight path is p _Ij(t), the physical length of flight path is r _Ij, the equivalent length of flight path is d _IjThe without hindrance flight probability of flight path is meant that complicated battlefield surroundings may impact the traffic capacity of operational aircraft flight path, thereby reduce the passage rate of operational aircraft, for the minimum that expends time in the deployment operational aircraft is commander's control of target, this reduction has been equivalent to increase the length of flight path, flight path length after claiming to increase is equivalent path length, the without hindrance flight probability of flight path is with the function of time as variable, equivalent flight path length then is with the function of the without hindrance flight probability of practical flight path and relevant flight path as variable, when the without hindrance flight probability of flight path is 1, practical flight path and equivalent flight path equal in length

The problem that need to solve be one of design from m assembly place deployment operational aircraft to n deployment point, make the carrying capacity and the consumed time of disposing all operational aircraft costs be minimum mapping out the plan simultaneously, 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: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

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: $S_u=\left\{\begin{array}{c}{S}_e,(n_s+1\≤u\≤m_e)\\ S_l,(m_e+1\≤u\≤m_l)\\ S_s,(m_l+1\≤u\≤m_s)\end{array}\right.$

The equivalent length of flight path is: d _Ij=f (r _Ij, p _Ij(t)), (0＜p _Ij(t)≤1; 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 the spent minimum time: min T=max{T _Ij}

Wherein:

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

N is the deployment point sum of demand operational aircraft;

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

p _Ij(t) be assembly place i (i=1 ... m) with deployment point j (j=1 ... n) the without hindrance flight probability of the flight path between is with the function of time t as variable;

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

p _Ij(t)=1 o'clock, r _IjWith d _IjEquate;

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 _lFor 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;

Above-mentioned model shows: try to achieve by linear programming on the basis of min Z value, can calculate each assembly place must be to the operational aircraft quantity x of related deployment point deployment _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 _iLast speed C and the longest path between assembly place and deployment point according to each batch deployment operational aircraft, can calculate again and finish the spent shortest time T of whole operational aircraft deployment task, thereby realize that the commander that the battlefield operational aircraft is disposed fast controls, 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: $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}(i=1,\·\·\·,m;j=1,\·\·\·,n)$

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;

$y_{m_e\left(i\right)}=y_u(n_s+1\≤u\≤m_e),y_{m_l\left(j\right)}=y_u(m_e+1\≤u\≤m_l),y_{m_s\left(i\right)}=y_u(m_l+1\≤u\≤m_s)$ 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 minimum 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 that battlefield according to claim 1 operational aircraft is disposed fast, it is characterized in that the length of described this method according to flight path from different assembly places to different deployment points, the without hindrance flight probability of flight path, 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 commander's controlling models of target to dispose all operational aircrafts minimum that expends time in, 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 quick deployment time requirement until final acquisition is meant if the option control command of trying to achieve can not satisfy the preset time 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 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 the time bottleneck, and repeat this process, until making the predetermined requirement that meets T.T. of finishing battlefield operational aircraft deployment, 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 commander's control that all battlefield operational aircrafts are disposed fast

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 length of flight path, 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, make the without hindrance flight Probability p of all flight paths here _Ij(t) be 1, d _Ij=r _Ij/ p _Ij(t), therefore practical flight path and equivalent flight path equal in length, the i.e. r between different assembly places and deployment point _IjWith d _IjEquate,

Table 1: 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 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 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 60.00 19.00 56.00 30.00 48.00 65.00 75.00 30.00 69.00 70.00 26.00 65.00 72.00 44.00 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 time operational aircraft that calculates by simplex algorithm deployment is as shown in table 2,

Table 2: minimum time is disposed option control command (unit: frame, frame kilometer, batch, minute) 01 assembly place 02 assembly place 03 assembly place 04 assembly place 05 assembly place 06 assembly place The frame kilometer Batch quantity Expend time in 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 16.00 468.00 399.00 2430.00 2940.00 1820.00 800.00 720.00 480.00 725.00 1656.00 1360.00 540.00 275.00 440.00 3 2 6 9 5 3 4 1 2 3 5 2 2 2 11.14 16.29 24.00 25.71 22.29 17.14 10.29 25.71 21.43 39.43 14.57 23.14 9.43 17.14 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 15053.00 49 39.43 ^* 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

* finish the minimum time that deployment task expends

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; time is 39.43 minutes; 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; disposing 36 39.43 minutes that operational aircraft spent from 03 assembly place to 10 deployment points is bottlenecks that the whole deployment task of restriction is finished sooner; if with speed faster operational aircraft finish this part deployment; then can be shortened to 25.71 minutes the time of finishing whole deployment task; reduction is 34.80%

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, dispose 39.43 minutes consuming time of operational aircraft to 10 deployment points, 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 and reduce carrying capacity and the purpose of flight time, because shadow price is the result who obtains under specific constraint condition, only in its valid interval, 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 time of obtaining is disposed is as shown in table 3,

Table 3: minimum time is disposed the improvement project (unit: frame, frame kilometer, batch, minute) of commander's control 01 assembly place 02 assembly place 03 assembly place 04 assembly place 05 assembly place 06 assembly place The frame kilometer Batch quantity Expend time in 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 16.00 468.00 399.00 2430.00 1950.00 1820.00 800.00 720.00 480.00 725.00 1332.00 1360.00 540.00 275.00 440.00 3 2 6 9 5 3 4 1 2 3 5 2 2 2 11.14 16.29 24.00 12.86 22.29 17.14 10.29 25.71 21.43 31.71 14.57 23.14 9.43 17.14 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 13739.00 49 31.71 ^* 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

* finish the minimum time that deployment task needs

Analysis by his-and-hers watches 3 as can be known, the time that finishing deployment task needs shortens to 31.71 minutes, amount of decrease is 19.58%, total carrying capacity is reduced to 13739 kilometers, and amount of decrease is 8.73%, and 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.