CN1845158A - Command control method of rapid low risk deployment for war field mechanization infantry - Google Patents

Abstract

The invention relates to a quick command control method for quickly low-risk deploying mechanization infantry on the battlefield. Wherein, the commanded object the all mechanization infantries; according to the lengths from different concentrate points to different deploy points, the transmission risk probability, the deploy amount at the concentrate point, the needed amount at the deploy point, and the load of transmission device, the command control mode purposed for transmitting all infantries in lowest 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 mechanized infantry's fast and low-risk disposition

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

Background technology is implemented low-risk mechanized infantry transportation between battlefield mechanized infantry's assembly place and deployment point commander's control is an important component part of operational commanding control, length according to mechanized infantry's transportation route from different assembly places to different deployment points, transportation meets with risk probability, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the speed of means of transport and carrying capacity, structure is to transport all infantries and expend time in or the risk minimum is that commander's control plan of target is that the battlefield commander implements the key issue that commander's control must solve to battlefield mechanized infantry's fast and low-risk disposition, the solution of this problem is for increasing substantially fighting capacity, reduce the risk of disposing the mechanized infantry, expend time in and, have crucial meaning the demand of the means of transport of disposing the mechanized infantry.

Mobile operations are most important for the triumph of capturing IT-based warfare, complicated battlefield surroundings may impact the current risk of mechanized infantry's transportation route, risk can make the mechanized infantry lost to the transportation of deployment point from the assembly place, for example low-risk disposition mechanized infantry's commander control is the key that improves mobile operations between combat division or trip and the subordinate, and wherein the matter of utmost importance that must solve is commander's control plan of the deployment mechanized infantry of formulation science.The quality of this plan, not only be related to implement the battlefield mechanized infantry dispose the risk that meets with, consumption transport resource how much, can in time arrive the deployment point but also be related to the mechanized infantry, to guarantee that fighting capacity is unlikely to descend because of the delay that the mechanized infantry transports.

For the battlefield mechanized infantry dispose and commander's control of this deployments the time seem more important, therefore must analyze that the choose reasonable parameter improves solvability and to dispose risk or to expend time in minimumly to come battlefield mechanized infantry's fast and low-risk disposition implemented to command to control by antithesis as optimization aim.

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

Summary of the invention the present invention is according to the length of the mechanized infantry's transportation route from different assembly places to different deployment points, transportation meets with risk probability, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the speed of means of transport and carrying capacity, structure is to transport all infantries and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield mechanized infantry's fast and low-risk disposition enforcement commander control with two-dimentional form description, and check whether this option control command meets risk and the time demand of finishing whole battlefield mechanized infantry's deployment task, if do not meet the demands, then by analysis to this two dimension commander control form, and according to shadow price, risk and time bottleneck can be adjusted for the mechanized infantry's quantity of deployment and the means of transport of enforcement deployment etc. the relevant episode node, constantly repeat this and find the solution-check analytic process, meet the option control command of battlefield mechanized infantry's fast and low-risk disposition risk and time requirement until final acquisition.Therefore, the conception of commander's control of battlefield mechanized infantry's fast and low-risk disposition is proposed, introduce the analytical approach that transportation expends time in and meets with risk probability, set up linear programming and the dual program model of seeking optimum option control command, by finding the solution this model, obtain scheme to battlefield mechanized infantry's fast and low-risk disposition enforcement commander control with two-dimentional form description, and according to finishing risk and the time requirement that whole mechanized infantry disposes, by searching risk and the time bottleneck that whole battlefield mechanized infantry's deployment task is finished in influence, the assembly place can be adjusted for the unreasonable configuration of mechanized infantry's quantity of disposing with to the means of transport of implementing to dispose, continue to optimize and improve this option control command, and battlefield mechanized infantry's fast and 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 mechanized infantry's fast and low-risk disposition is:

At first, the supply and demand system that battlefield mechanized infantry's fast and low-risk disposition problem definition is constituted for the party in request (deployment point) by mechanized infantry's supplier (assembly place) and mechanized infantry, the feature of this system can be used the length of the transportation route of disposing from different suppliers to the different mechanized infantries of party in request, transportation meets with risk probability, supplier mechanized infantry's supply and the mechanized infantry's of party in request demand, the speed and the carrying capacity of means of transport are described, and according to the risk requirement that the battlefield mechanized infantry is disposed, all mechanized infantries' structure expend time in or the risk minimum is commander's controlling models of target to dispose and to transport, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield mechanized infantry's fast and low-risk disposition enforcement commander control with two-dimentional form description, risk and time bottleneck by continuous searching supply and demand system, quantity to relevant supplier's mechanized infantry is carried out reasonable disposition, adopt methods such as different means of transports, final risk and the time requirement that obtains to satisfy battlefield mechanized infantry's fast and low-risk disposition, battlefield mechanized infantry's fast and low-risk disposition is implemented the scheme that commander controls, finish commander's control battlefield mechanized infantry's fast and low-risk disposition.

Complicated battlefield surroundings may impact the current risk of mechanized infantry's transportation route, risk can make the mechanized infantry lost to the transportation of deployment point from the assembly place, thereby reduce Transport Machinery infantry's security, for the mechanized infantry expends time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of mechanized infantry's transportation, it can be with the function of time as variable that transportation meets with risk probability, also can be and irrelevant constant of time, the transportation in different 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, the minimum transportation that can obtain respectively from different assembly place Transport Machinery infantries to different deployment points meets with risk probability or the transportation route of least consume time, with different assembly places and the relevant shadow price of different deployment points constraint condition, the result that will find the solution inserts in a kind of two dimension commander's control form again, according to analysis to this two dimension commander control form, and pass through according to shadow price, risk and time bottleneck are adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield mechanized infantry's fast and low-risk disposition requirement until final acquisition.

Can by each deployment point Transport Machinery infantry's quantity is described as the zones of different in the two-dimentional form of option control command from each assembly place, size, risk in transit, the quantity of means of transport, transportation that each deployment point needs transport power expend time in and relevant shadow price, each assembly place can dispose the mechanized infantry quantity, remain mechanized infantry's quantity situation of change with relevant shadow price and transport all mechanized infantries' priming the pump and the minimum time that expends.

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

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

With risk minimum being analyzed as follows that be target to commander's control problem of battlefield mechanized infantry's fast and low-risk disposition, it is the analysis of target to commander's control problem of battlefield mechanized infantry's fast and low-risk disposition that this analysis is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition

$D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}$ And similarly analyze and get final product.

Supposing that battlefield mechanized infantry's fast and low-risk disposition problem can be used by m supply mechanized infantry's assembly place and n demand mechanized infantry's deployment point and between different supply and demand nodes exists the network in a Transport Machinery infantry's path to describe, and is x from supplying mechanized infantry's quantity that node i transports to demand node j _Ij, it is p that transportation meets with risk probability _Ij(t), the length of transportation route is d _IjTransportation meets with risk probability and is meant that complicated battlefield surroundings may impact the current risk of mechanized infantry's transportation route, risk can make the mechanized infantry lost to the transportation of party in request from the supplier, thereby reduce Transport Machinery infantry's security, for the mechanized infantry expends time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of mechanized infantry's transportation, it can be with the function of time as variable that transportation meets with risk probability, also can be and irrelevant constant of time, be expressed as p _Ij, the transportation in different paths meets with risk probability can be different.

The problem that need to solve is that one of design is transported the mechanized infantry to n deployment point from m assembly place, make the movement plan of transporting all mechanized infantry's risk minimums, the satisfied requirement of being scheduled to of consumed time simultaneously, and calculate the quantity that the required means of transport of mechanized infantry is transported in each assembly place, it is as follows that relevant mechanized infantry disposes commander controlling models and linear programming equation:

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 demand equals constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ie}}=D_e,$ (e＝1，…，n _e)

The deployment point demand is 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 demand is 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 supply equals constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ej}}=S_e,$ (e＝n _s+1，…，m _e)

The assembly place supply is 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 is in large supply in 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: $D_v=\left\{\begin{array}{c}{D}_e,(1\≤v\≤n_e)\\ D_l,(n_e+1\≤v\≤n_l)\\ D_s,(n_l+1\≤v\≤n_s)\end{array}\right.$

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

Assembly place i (i=1 ... m) the means of transport quantity V of Xu Yaoing _i:

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

Finish all mechanized infantries and dispose spent minimum time: minT=max{T _Ij}

The maximum transportation 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 all mechanical infantries and dispose the risk probability of experience: minP=max{p _j, j (j=1 ... n)

With j the risk carrying capacity that the demand node 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 mechanized infantry disposes: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\min Z_j$

With j the goods and materials carrying capacity that the demand node is relevant: $Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ j(j＝1，…n)

The total mechanized infantry's carrying capacity in battlefield: $Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{Z}_j$

Wherein:

M is supply mechanized infantry's assembly place sum;

N is demand mechanized infantry's a deployment point sum;

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) transportation between meets with risk probability, can be with the function of time t as variable;

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

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 mechanized infantry's quantity (e=1 ..., n _e) (unit: the people);

D _lFor needing the relevant upper limit (l=n of mechanized infantry's quantity with the deployment point _e+ 1 ..., n _l) (unit: the people);

D _sFor needing the relevant lower limit (s=n of mechanized infantry's quantity with the deployment point _l+ 1 ..., n _s) (unit: the people);

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

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

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

S _eFor supplying mechanized infantry's the relevant amount (e=n of quantity with the assembly place _s+ 1 ..., m _e) (unit: the people);

S _lFor supplying mechanized infantry's quantity the relevant upper limit (l=m with the assembly place _e+ 1 ..., m _l) (unit: the people);

S _sFor supplying mechanized infantry's quantity relevant lower limit (s=m with the assembly place _l+ 1 ..., m _s) (unit: the people);

V _iFor the supply mechanized infantry assembly place i (i=1 ... m) transport the means of transport quantity that the mechanized infantry needs;

L transports mechanized infantry's ability (unit: the people) for each means of transport;

C transports mechanized infantry's speed (unit: kilometer/hour) for each means of transport;

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 mechanized infantry's quantity x that each assembly place must be transported to the related deployment point _Ij, the p of associated pathway _Ij,, can calculate the means of transport quantity V that each assembly place needs again according to the dead weight capacity L of means of transport _i, transport at last mechanized infantry's speed C and the longest path between assembly place and deployment point according to means of transport, can calculate the risk carrying capacity minZ of each deployment point again _j, maximum transportation meets with risk probability p _jFinish risk probability minP, the shortest time T that expends that whole mechanized infantry's deployment task meets with, thereby realize commander's control to battlefield mechanized infantry's fast and low-risk disposition, for constraint condition rationally being set, improving solvability, utilizing above-mentioned linear programming model better, the dual linear programming model that provides this model is as follows:

Objective function:

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

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;

$y_{m_e\left(i\right)}=y_u(n_s+1\≤u\≤m_e),y_{m_i\left(i\right)}=y_u(m_e+1\≤u\≤m_l),y_{m_s\left(i\right)}=y_u(m_l+1\≤u\≤m_s)$ 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 shadow price or the relevant decision variable of opportunity cost with the demand of former linear programming and supply mechanized infantry 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 mechanized infantry's of mechanization combat division deployment ability is an important component part of its fighting capacity, to huge battlefield mechanized infantry's deployment and the demand of transporting power and time, make commander's control of implementing battlefield mechanized infantry deployment become vital task, the implementation example of commander's control of battlefield mechanized infantry's fast and low-risk disposition that with the risk minimum is target is as follows, it is the implementation example analysis of target to commander's control of battlefield mechanized infantry's fast and low-risk disposition that this implementation example is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}$ And similarly analyze and get final product, suppose that certain mechanization combat division must be that 16 people, average speed per hour are 70 kilometers armored personnel carrier with dead weight capacity, transport the mechanized infantry of specified amount to 14 deployment points from 6 assembly places, transportation experience risk probability and portion's amount of asking are as shown in table 1 between assembly place and the deployment point.

Table 1: transportation meets with risk probability, portion's amount of asking (unit: probability, people) between mechanized division 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

The length of transportation route and portion ask as shown in table 2 between assembly place and the deployment point.

Table 2: transportation route length, portion's amount of asking (unit: kilometer, people) between mechanization combat division 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, it is as shown in table 3 to calculate mechanization combat division minimum risk transportation command controlling schemes by simplex algorithm, and wherein people's risk is the risk carrying capacity min Z of deployment point _j, risk probability is that the maximum transportation of deployment point meets with risk probability p _j, passenger-kilometer is mechanized infantry's carrying capacity Z of deployment point _j

Table 3: mechanization combat division minimum risk is disposed option control command (unit: people, people's risk, probability, passenger-kilometer,, minute)

	01 collection point	02 collection point	03 collection point	04 collection point	05 collection point	06 collection point	People's risk	Risk probability	Passenger-kilometer	The chariot number	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	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 0017 0.027 0.011 0.020	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	15.053	0.046	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 needs

By option control command (table 3) is analyzed as can be known; the armored personnel carrier that finishing deployment task needs adds up to 49; time is 39.43 minutes; the armored personnel carrier that 01～06 assembly place needs 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; transporting 36 39.43 minutes that the mechanized infantry spent from 03 assembly place to 10 deployment points is bottlenecks that the whole deployment task of restriction is finished sooner; this transports also is simultaneously to reduce to finish the bottleneck that the risk probability that meets with is disposed in all battlefields; if finish this part mechanized infantry's transportation with helicopter; then can be shortened to 25.71 minutes the time of finishing whole deployment task; reduction is 34.80%; risk probability is reduced to 0.030 from 0.046, and 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 transporting the mechanized infantry to 10 deployment points is 0.046,39.43 minutes consuming time, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult to satisfy, 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 supply 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, carrying capacity and deployment time, because shadow price is the result who obtains under specific constraint condition, only in its valid interval, price just has relative stability.

Measure as can be seen from the residue mechanized infantry of each assembly place, back of finishing the work, the mechanized infantry who disposes of 02 assembly place exhausts, obviously on the low side, and that the mechanized infantry who disposes of 04 assembly place measures is obviously bigger than normal, according to the antithesis analysis, the shadow price of their constraint condition is 0, this statement of facts: can dispose the mechanized infantry if 02 assembly place has more, there is disposed mechanized infantry 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 mechanization combat division minimum risk of obtaining is disposed is as shown in table 4.

Table 4: the improvement project (unit: people, people's risk, probability, passenger-kilometer,, minute) that mechanization combat division minimum risk is disposed

	01 collection point	02 collection point	03 collection point	04 collection point	05 collection point	06 collection point	People's risk	Risk probability	Passenger-kilometer	The chariot number	Need the time	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 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	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	13.739	0.037	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 4 as can be known, the risk of finishing deployment task is 0.037, amount of decrease is 19.57%, the time that needs shortens to 31.71 minutes, amount of decrease is 19.58%, the overall risk carrying capacity is reduced to 13.739 people's risks, amount of decrease is 8.73%, total carrying capacity is reduced to 13739 ton kilometres, 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 mechanized infantry who disposes of each assembly place, the Optimal Management of mechanized infantry's amount that realization can be disposed with said method.

Claims (9)

1, the present invention relates to commander's control method of battlefield mechanized infantry's fast and low-risk disposition, relate to military affairs and association area, the object of commander's control is all battlefield mechanized infantries, this method is according to the length of the mechanized infantry's transportation route from different assembly places to different deployment points, transportation meets with risk probability, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the speed of means of transport and carrying capacity, structure is to transport all infantries and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, meet the option control command of fast and low-risk disposition requirement until final acquisition, this scheme is applicable to commander's control of all battlefield mechanized infantries' fast and low-risk disposition.

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

3, commander's control method of battlefield according to claim 1 mechanized infantry's fast and low-risk disposition, it is characterized in that described this method according to length, the transportation of mechanized infantry's transportation route from different assembly places to different deployment points meet with risk probability, assembly place infantry can the deployment amount and the deployment point speed of infantry's demand, means of transport and carrying capacity are meant by these parameters can set up the supply and demand system that a battlefield mechanized infantry disposes, obtain on this basis the battlefield mechanized infantry is disposed the method for implementing commander's control.

4, commander's control method of battlefield according to claim 1 mechanized infantry's fast and low-risk disposition, it is characterized in that described transportation meets with risk probability and is meant that complicated battlefield surroundings may impact the current risk of mechanized infantry's transportation route, risk can make the mechanized infantry lost to the transportation of deployment point from the assembly place, thereby reduce Transport Machinery infantry's security, for the mechanized infantry expends time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of mechanized infantry's transportation, it can be with the function of time as variable that transportation meets with risk probability, also can be and irrelevant constant of time, the transportation in different paths meets with risk probability can be different.

5, commander's control method of battlefield according to claim 1 mechanized infantry's fast and low-risk disposition is characterized in that described structure is to transport all infantries and expend time in or the risk minimum is that the target of commander's controlling models of target objective function of being meant this commander's controlling models is transported all mechanized infantries and expended time in or meet with the risk minimum for making.

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

7, commander's control method of battlefield according to claim 1 mechanized infantry's fast and low-risk disposition, it is characterized in that described and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition is meant can be by describing from each assembly place as the zones of different in the two-dimentional form of option control command to each deployment point Transport Machinery infantry's quantity, each deployment point needs the size of transport power, risk in transit, the quantity of means of transport, transportation expends time in and relevant shadow price, and mechanized infantry's quantity can be disposed in each assembly place, the situation of change of residue mechanized infantry quantity is with relevant shadow price and transport all mechanized infantries' priming the pump and the minimum time that expends.

8, commander's control method of battlefield according to claim 1 mechanized infantry's fast and low-risk disposition, it is characterized in that the length of described this method according to mechanized infantry's transportation route from different assembly places to different deployment points, transportation meets with risk probability, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the speed of means of transport and carrying capacity, structure is to transport all infantries and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model and is meant that following is the analysis of target to commander's control problem of battlefield mechanized infantry's fast and low-risk disposition with the risk minimum, but it is the analysis of target to commander's control problem of battlefield mechanized infantry's fast and low-risk disposition that this analysis is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}$ And similarly analyze and get final product, following mathematical formulae, derivation, result of calculation and application process are applicable to the commander's control to all battlefield mechanized infantry's fast and low-risk dispositions,

Supposing that battlefield mechanized infantry's fast and low-risk disposition problem can be used by m supply mechanized infantry's assembly place and n demand mechanized infantry's deployment point and between different supply and demand nodes exists the network in a Transport Machinery infantry's path to describe, and is x from supplying mechanized infantry's quantity that node i transports to demand node j _Ij, it is p that transportation meets with risk probability _Ij(t), the length of transportation route is d _IjTransportation meets with risk probability and is meant that complicated battlefield surroundings may impact the current risk of mechanized infantry's transportation route, risk can make the mechanized infantry lost to the transportation of party in request from the supplier, thereby reduce Transport Machinery infantry's security, for the mechanized infantry expends time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of mechanized infantry's transportation, it can be with the function of time as variable that transportation meets with risk probability, also can be and irrelevant constant of time, be expressed as p _Ij, the transportation in different paths meets with risk probability can be different,

The problem that need to solve is that one of design is transported the mechanized infantry to n deployment point from m assembly place, make the movement plan of transporting all mechanized infantry's risk minimums, the satisfied requirement of being scheduled to of consumed time simultaneously, and calculate the quantity that the required means of transport of mechanized infantry is transported in each assembly place, it is as follows that relevant mechanized infantry disposes commander controlling models and linear programming equation:

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 demand equals constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ie}}=D_e,(e=1,\·\·\·,n_e)$

The deployment point demand is 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 demand is 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 supply equals constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ej}}=S_e,(e=n_s+1,\·\·\·,m_e)$

The assembly place supply is 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 is in large supply in 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: $D_v=\left\{\begin{array}{c}{D}_e,(1\≤v\≤n_e)\\ D_l,(n_e+1\≤v\≤n_l)\\ D_s,(n_l+1\≤v\≤n_s)\end{array}\right.$

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

Assembly place i (i=1 ... m) the means of transport quantity of Xu Yaoing

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

Finish all mechanized infantries and dispose spent minimum time: minT=max{T _Ij}

The maximum transportation 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 risk probability that all mechanized infantries dispose experience: minP=max{p _j, j (j=1 ... n)

With j the risk carrying capacity that the demand node 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 mechanized infantry disposes: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\min Z_j$

With j the goods and materials carrying capacity that the demand node is relevant: $Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},j(j=1,\·\·\·n)$

The total mechanized infantry's carrying capacity in battlefield: $Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{Z}_j$

Wherein:

M is supply mechanized infantry's assembly place sum;

N is demand mechanized infantry's a deployment point sum;

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) transportation between meets with risk probability, can be with the function of time t as variable;

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

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 mechanized infantry's quantity (e=1 ..., n _e) (unit: the people);

D _lFor needing the relevant upper limit (l=n of mechanized infantry's quantity with the deployment point _e+ 1 ..., n _l) (unit: the people);

D _sFor needing the relevant lower limit (s=n of mechanized infantry's quantity with the deployment point _l+ 1 ..., n _s) (unit: the people);

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

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

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

S _eFor supplying mechanized infantry's the relevant amount (e=n of quantity with the assembly place _s+ 1 ..., m _e) (unit: the people);

S _lFor supplying mechanized infantry's quantity the relevant upper limit (l=m with the assembly place _e+ 1 ..., m) (unit: the people);

S _sFor supplying mechanized infantry's quantity relevant lower limit (s=m with the assembly place _l+ 1 ..., m _s) (unit: the people);

V _iFor the supply mechanized infantry assembly place i (i=1 ... m) transport the means of transport quantity that the mechanized infantry needs;

L transports mechanized infantry's ability (unit: the people) for each means of transport;

C transports mechanized infantry's speed (unit: kilometer/hour) for each means of transport;

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 mechanized infantry's quantity x that each assembly place must be transported to the related deployment point _Ij, the p of associated pathway _Ij,, can calculate the means of transport quantity V that each assembly place needs again according to the dead weight capacity L of means of transport _i, transport at last mechanized infantry's speed C and the longest path between assembly place and deployment point according to means of transport, can calculate the risk carrying capacity minZ of each deployment point again _j, maximum transportation meets with risk probability p _jFinish risk probability minP, the shortest time T that expends that whole mechanized infantry's deployment task meets with, thereby realize commander's control to battlefield mechanized infantry's fast and low-risk disposition, for constraint condition rationally being set, improving solvability, utilizing above-mentioned linear programming model better, the dual linear programming model that provides this model is as follows:

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

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 shadow price or the relevant decision variable of opportunity cost with the demand of former linear programming and supply mechanized infantry 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 mechanized infantry's fast and low-risk disposition, it is characterized in that the length of described this method according to mechanized infantry's transportation route from different assembly places to different deployment points, transportation meets with risk probability, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the speed of means of transport and carrying capacity, structure is to transport all infantries and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition is meant if the option control command of trying to achieve can not satisfy predetermined risk and time requirement, then can be by two dimension commander control table, result to former linear programming and dual program analyzes, determine to influence the risk of battlefield mechanized infantry deployment and the bottleneck of T.T., carry out reasonable disposition by mechanized infantry's quantity again to the assembly place, increase the quantity of means of transport and adopt different means such as means of transport, eliminate risk and time bottleneck, and repeat this process, until finishing the risk that the battlefield mechanized infantry disposes and meeting predetermined requirement T.T., this process can with following be that target is described the example of commander's control problem of battlefield mechanized infantry's fast and low-risk disposition with the risk minimum, it is the instance analysis of target to commander's control problem of battlefield mechanized infantry's fast and low-risk disposition that this example is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}$ And similarly analyze and get final product, but the mathematical formulae described in example, result of calculation, various form and application process are applicable to the commander's control to all battlefield mechanized infantry's fast and low-risk dispositions,

Suppose that certain mechanization combat division must be that 16 people, average speed per hour are 70 kilometers armored personnel carrier with dead weight capacity, transport the mechanized infantry of specified amount to 14 deployment points from 6 assembly places, transportation experience risk probability and portion's amount of asking are as shown in table 1 between assembly place and the deployment point

Table 1: transportation meets with risk probability, portion's amount of asking (unit: probability, people) between mechanized division 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

The length of transportation route and portion ask as shown in table 2 between assembly place and the deployment point,

Table 2: transportation route length, portion's amount of asking (unit: kilometer, people) between mechanization combat division 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 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 13.00 25.00 28.00 15.00 35.00 20.00 98.00 138.00 96.00 70.00 83.00 108.00 97.00 82.00 110.00 12.00 51.00 96.00 74.00 87.00 112.00 101.00 86.00 100.00 129.00 149.00 25.00 44.00 31.00 66.00 58.00 56.00 39.00 105.00 145.00 110.00 60.00 19.00 56.00 30.00 48.00 65.00 75.00 30.00 69.00 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points 62.00 91.00 126.00 90.00 81.00 37.00 66.00 97.00 68.00 56.00 46.00 17.00 81.00 99.00 20.00 50.00 79.00 86.00 104.00 66.00 59.00 73.00 27.00 11.00 75.00 70.00 26.00 65.00 72.00 44.00 36.00 90.00 30.00 35.00 28.00 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, it is as shown in table 3 to calculate mechanization combat division minimum risk transportation command controlling schemes by simplex algorithm, and wherein people's risk is the risk carrying capacity minZ of deployment point _j, risk probability is that the maximum transportation of deployment point meets with risk probability p _j, passenger-kilometer is mechanized infantry's carrying capacity Z of deployment point _j,

Table 3: mechanization combat division minimum risk is disposed option control command (unit: people, people's risk, probability, passenger-kilometer,, minute) 01 collection point 02 collection point 03 collection point 04 collection point 05 collection point 06 collection point People's risk Risk probability Passenger-kilometer The chariot number 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 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 0.020 468.00 399.00 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 15.053 0.046 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 needs

By option control command (table 3) is analyzed as can be known; the armored personnel carrier that finishing deployment task needs adds up to 49; time is 39.43 minutes; the armored personnel carrier that 01～06 assembly place needs 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; transporting 36 39.43 minutes that the mechanized infantry spent from 03 assembly place to 10 deployment points is bottlenecks that the whole deployment task of restriction is finished sooner; this transports also is simultaneously to reduce to finish the bottleneck that the risk probability that meets with is disposed in all battlefields; if finish this part mechanized infantry's transportation with helicopter; then can be shortened to 25.71 minutes the time of finishing whole deployment task; reduction is 34.80%; risk probability is 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 transporting the mechanized infantry to 10 deployment points is 0.046,39.43 minutes consuming time, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult to satisfy, 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 supply 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, carrying capacity and deployment time, because shadow price is the result who obtains, only in its valid interval under specific constraint condition, price just has relative stability

Measure as can be seen from the residue mechanized infantry of each assembly place, back of finishing the work, the mechanized infantry who disposes of 02 assembly place exhausts, obviously on the low side, and that the mechanized infantry who disposes of 04 assembly place measures is obviously bigger than normal, according to the antithesis analysis, the shadow price of their constraint condition is 0, this statement of facts: can dispose the mechanized infantry if 02 assembly place has more, there is disposed mechanized infantry 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 mechanization combat division minimum risk of obtaining is disposed is as shown in table 4,

Table 4: the improvement project (unit: people, people's risk, probability, passenger-kilometer,, minute) that mechanization combat division minimum risk is disposed 01 collection point 02 collection point 03 collection point 04 collection point 05 collection point 06 collection point People's risk Risk probability Passenger-kilometer The chariot number Need the time Upper limit shadow valency Lower limit shadow valency 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 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 0.013 0.019 0.028 0.015 0.026 0.020 0.012 0.030 0.025 0.037 0.017 0.027 0.011 468.00 399.00 2430.00 1950.00 1820.00 800.00 720.00 480.00 725.00 1332.00 1360.00 540.00 275.00 3 2 6 9 5 3 4 1 2 3 5 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 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 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 14 deployment points 22 0.440 0.020 440.00 2 17.14 0.00 20.00 Add up to 100.00 302.00 162.00 29.00 45.00 37.00 13.739 0.037 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 4 as can be known, the risk of finishing deployment task is 0.037, amount of decrease is 19.57%, the time that needs shortens to 31.71 minutes, amount of decrease is 19.58%, the overall risk carrying capacity is reduced to 13.739 people's risks, amount of decrease is 8.73%, total carrying capacity is reduced to 13739 ton kilometres, 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 mechanized infantry who disposes of each assembly place, the Optimal Management of mechanized infantry's amount that realization can be disposed with said method.