CN1845157A - Command control method of 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 low-risk disposition

Technical field the present invention relates to national defence and association area, is used for battlefield mechanized infantry's low-risk disposition is implemented commander's control, realizes the 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, meet with risk probability according to the transportation on mechanized infantry's transportation route from different assembly places to different deployment points, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the carrying capacity of means of transport, structure 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 low-risk disposition to transport all infantry's risk minimums, the solution of this problem is for increasing substantially fighting capacity, reduce to dispose mechanized infantry's risk 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.

Time seems more important for commander's control of battlefield mechanized infantry deployment and this deployment, therefore must analyze the choose reasonable parameter by antithesis and improve solvability and come the control to battlefield mechanized infantry's low-risk disposition enforcement commander to dispose the risk minimum as optimization aim.

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

Summary of the invention the present invention meets with risk probability according to the transportation on the mechanized infantry's transportation route from different assembly places to different deployment points, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the carrying capacity of means of transport, structure is commander's controlling models of target to transport all infantry's risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield mechanized infantry's low-risk disposition enforcement commander control with two-dimentional form description, and check whether this option control command meets the risk demand of finishing whole battlefield 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, the risk 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 that battlefield mechanized infantry's low-risk disposition risk requires until final acquisition.Therefore, the conception of commander's control of battlefield mechanized infantry's low-risk disposition is proposed, introduce the analytical approach that transportation 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 low-risk disposition enforcement commander control with two-dimentional form description, and according to finishing the risk requirement that whole mechanized infantry disposes, by searching the risk 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 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 low-risk disposition is:

At first, the supply and demand system that battlefield mechanized infantry's 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 transportation that the feature of this system can be used on mechanized infantry's transportation route from different assembly places to different deployment points meets with risk probability, supplier mechanized infantry's supply and the mechanized infantry's of party in request demand, the carrying capacity of means of transport is described, and according to the risk requirement that the battlefield mechanized infantry is disposed, structure is commander's controlling models of target to dispose and to transport all mechanized infantry's risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield mechanized infantry's low-risk disposition enforcement commander control with two-dimentional form description, risk 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, battlefield mechanized infantry's low-risk disposition requirement is satisfied in final acquisition, battlefield mechanized infantry's low-risk disposition is implemented the scheme that commander controls, finish commander's control battlefield mechanized infantry's 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 to transport the commander control that mechanized infantry's risk minimum is a target, 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, can obtain respectively to dispose and transport the mechanized infantry to the minimum risk of the different parties in request shadow price relevant with different parties in request constraint condition with different suppliers from different suppliers, 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 risk bottleneck is adjusted correlation parameter, constantly find the solution and update, can finally obtain to meet the option control command of battlefield mechanized infantry's low-risk disposition requirement.

Can be by to describe from each assembly place the quantity and the relevant shadow price of each deployment point Transport Machinery infantry's quantity, size that each deployment point needs transport power, risk in transit, means of transport as the zones of different in the two-dimentional form of option control command, mechanized infantry's quantity, the situation of change and relevant shadow price and the priming the pump that transports all mechanized infantries of residue mechanized infantry quantity can be disposed in each assembly place.

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

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

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

Supposing that battlefield mechanized infantry's 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), 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 party in request from the supplier, thereby reduce Transport Machinery infantry's security, for to transport the commander control that mechanized infantry's risk minimum is a target, 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 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:

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

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;

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;

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, the last risk carrying capacity minZ that can calculate each deployment point again _j, maximum transportation meets with risk probability p _jFinish the risk probability minP that whole mechanized infantry's deployment task meets with, thereby realize commander's control,, provide the dual linear rule of this model for constraint condition rationally being set, improving solvability, utilizing above-mentioned linear programming model better to battlefield mechanized infantry's low-risk disposition

It is as follows to draw model:

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, huge battlefield mechanized infantry is disposed the demand of ability, make commander's control of implementing battlefield mechanized infantry deployment become vital task, 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

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, it is as shown in table 2 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

Table 2: mechanization combat division minimum risk is disposed option control command (unit: people, people's risk, probability)

	01 collection point	02 collection point	03 collection point	04 collection point	05 collection point	06 collection point	People's risk	Risk probability	The chariot number	Upper limit shadow valency	Lower limit shadow valency
												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	29.00		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	0.013 0.019 0.028 0.030 0.026 0.020 0.012 0.030 0.025 0.046 0.017	3 2 6 9 5 3 4 1 2 3 5	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00

14 deployment points, 13 deployment points, 12 deployment points			22.00		20.00 25.00		0.540 0.275 0.440	0.027 0.011 0.020	2 2 2	0.00 0.00 0.00	27.00 11.00 20.00
												Add up to	100.00	200.00	198.00	29.00	45.00	103.00	15.053	0.046 *	49
But portion's quantity	100.00	200.00	300.00	400.00	150.00	350.00
												Surplus after the portion	0.00	0.00	102.00	371.00	105.00	247.00
Upper limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00
												Lower limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00

* finish the risk probability of deployment task

By option control command (table 2) is analyzed as can be known; the armored personnel carrier that finishing deployment task needs adds up to 49; risk probability is 0.046; 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; the risk probability 0.046 that transports 36 mechanized infantries to 10 deployment points from 03 assembly place is to reduce to finish all battlefields and dispose the bottleneck that meets with risk probabilities; if finish this part mechanized infantry's transportation with more low-risk helicopter; then the risk probability of finishing whole deployment task can be reduced to 0.030 from 0.046, reduction is 34.78%.

From to demand constraint condition D _v(v=1,18) analysis of shadow price as can be known, the size of price has truly reflected the complexity that the related constraint condition satisfies, shadow price is 0 to be meant in specific span, relevant constraint condition does not constitute influence to target function value, the easiest to be satisfied, promptly this resource is not in short supply, if increase this resource again the optimal value of objective function is further reduced, again for example, in order to satisfy constraint condition D ₁₀, the risk of transporting the mechanized infantry to 10 deployment points is 0.046, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult satisfied, can be by D with similar method _vThe complexity that satisfies, from difficulty to easy ordering: D ₁₀, D ₈, D ₁₆, D ₅, D ₃, D ₉..., to 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 _v, and S _uVariation and change, make the resource that does not constitute influence originally become influential resource, by analysis to shadow price, can adjust constraint condition targetedly, reach the purpose that reduces risk, because shadow price is the result who obtains 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 3.

Table 3: the improvement project that mechanization combat division minimum risk is disposed (unit: people, people's risk, probability)

	01 collection point	02 collection point	03 collection point	04 collection point	05 collection point	06 collection point	People's risk	Risk probability	The chariot number	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	0.168 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	3 2 5 6 9 5 3 4 1 2 3 5 2 2 2	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00
Add up to	100.00	302.00	162.00	29.00	45.00	37.00	13.739	0.037 *	49
												But portion's quantity	100.00	400.00	300.00	200.00	150.00	350.00
Surplus after the portion	0.00	98.00	138.00	171.00	105.00	313.00
												Upper limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00
Lower limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00

* finish the risk probability of deployment task

Analysis by his-and-hers watches 3 as can be known, the risk of finishing deployment task is 0.037, amount of decrease is 19.57%, the overall risk carrying capacity is reduced to 13.739 people's risks, amount of decrease is 8.73%, antithesis the analysis showed that: shadow price is without any variation, but the scheme after improving is better, therefore, can also carry out reasonable configuration to the 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 low-risk disposition, relate to military affairs and association area, the object of commander's control is all battlefield mechanized infantries, this method meets with risk probability according to the transportation on the mechanized infantry's transportation route from different assembly places to different deployment points, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the carrying capacity of means of transport, structure is commander's controlling models of target to transport all infantry's risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, meet the option control command of low-risk disposition requirement until final acquisition, this scheme is applicable to commander's control of all battlefield mechanized infantries' low-risk disposition.

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

3, commander's control method of battlefield according to claim 1 mechanized infantry's low-risk disposition, it is characterized in that described this method according to the transportation on 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 carrying capacity of infantry's demand, means of transport is meant by these parameters can sets 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 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 to transport the commander control that mechanized infantry's risk minimum is a target, 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 low-risk disposition 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 transported all mechanized infantries and met with the risk minimum for making to transport all infantry's risk minimums.

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

7, commander's control method of battlefield according to claim 1 mechanized infantry's low-risk disposition, it is characterized in that described and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the low-risk disposition requirement until final acquisition is meant can be by describing 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 can be disposed mechanized infantry's quantity with relevant shadow price, each assembly place, the situation of change and relevant shadow price and the priming the pump that transports all mechanized infantries of residue mechanized infantry quantity.

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

Supposing that battlefield mechanized infantry's 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), 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 party in request from the supplier, thereby reduce Transport Machinery infantry's security, for to transport the commander control that mechanized infantry's risk minimum is a target, 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 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

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

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;

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;

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, the last risk carrying capacity minZ that can calculate each deployment point again _j, maximum transportation meets with risk probability p _jFinish the risk probability minP that whole mechanized infantry's deployment task meets with, thereby realize commander's control to battlefield mechanized infantry's 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 low-risk disposition, it is characterized in that described this method meets with risk probability according to the transportation on the mechanized infantry's transportation route from different assembly places to different deployment points, the assembly place infantry can the deployment amount and the deployment point to infantry's demand, the carrying capacity of means of transport, structure is commander's controlling models of target to transport all infantry's risk minimums, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the low-risk disposition requirement until final acquisition is meant if the option control command of trying to achieve can not satisfy predetermined risk requirement, then can be by two dimension commander control table, result to former linear programming and dual program analyzes, determine to influence the risk bottleneck that the battlefield mechanized infantry disposes, 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 the risk bottleneck, and repeat this process, meet predetermined requirement until the risk of finishing battlefield mechanized infantry 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 the commander's control to all battlefield mechanized infantry's 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

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, it is as shown in table 2 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,

Table 2: mechanization combat division minimum risk is disposed option control command (unit: people, people's risk, probability) 01 collection point 02 collection point 03 collection point 04 collection point 05 collection point 06 collection point People's risk Risk probability The chariot number Upper limit shadow valency Lower limit shadow valency 14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point 30.00 70.00 36.00 60.00 64.00 40.00 60.00 36.00 80.00 22.00 29.00 20.00 25.00 21.00 66.00 16.00 0.468 0.399 2.430 2.940 1.820 0.800 0.720 0.480 0.725 1.656 1.360 0.540 0.275 0.440 0.013 0.019 0.028 0.030 0.026 0.020 0.012 0.030 0.025 0.046 0.017 0.027 0.011 0.020 3 2 6 9 5 3 4 1 2 3 5 2 2 2 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00 Add up to 100.00 200.00 198.00 29.00 45.00 103.00 15.053 0.046 ^* 49 But portion's quantity 100.00 200.00 300.00 400.00 150.00 350.00 Surplus after the portion 0.00 0.00 102.00 371.00 105.00 247.00 Upper limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00 Lower limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00

* finish the risk probability of deployment task

By option control command (table 2) is analyzed as can be known; the armored personnel carrier that finishing deployment task needs adds up to 49; risk probability is 0.046; 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; the risk probability 0.046 that transports 36 mechanized infantries to 10 deployment points from 03 assembly place is to reduce to finish all battlefields and dispose the bottleneck that meets with risk probabilities; if finish this part mechanized infantry's transportation with more low-risk helicopter; then the risk probability of finishing whole deployment task can be reduced to 0.030 from 0.046; reduction is 34.78%

From to demand constraint condition D _v(v=1,18) analysis of shadow price as can be known, the size of price has truly reflected the complexity that the related constraint condition satisfies, shadow price is 0 to be meant in specific span, relevant constraint condition does not constitute influence to target function value, the easiest to be satisfied, promptly this resource is not in short supply, if increase this resource again the optimal value of objective function is further reduced, again for example, in order to satisfy constraint condition D ₁₀, the risk of transporting the mechanized infantry to 10 deployment points is 0.046, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult satisfied, can be by D with similar method _vThe complexity that satisfies, from difficulty to easy ordering: D ₁₀, D ₈, D ₁₆, D ₅, D ₃, D ₉..., to 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 D _uVariation and change, make the resource that does not constitute influence originally become influential resource, by analysis to shadow price, can adjust constraint condition targetedly, reach the purpose that reduces risk, because shadow price is the result who obtains, only in its valid interval under specific constraint condition, price just has relative stability

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 3,

Table 3: the improvement project that mechanization combat division minimum risk is disposed (unit: people, people's risk, probability) 01 collection point 02 collection point 03 collection point 04 collection point 05 collection point 06 collection point People's risk Risk probability The chariot number 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 3 2 6 9 5 3 4 1 2 3 5 2 2 2 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00 Add up to 100.00 302.00 162.00 29.00 45.00 37.00 13.739 0.037 ^* 49 But portion's quantity 100.00 400.00 300.00 200.00 150.00 350.00 Surplus after the portion 0.00 98.00 138.00 171.00 105.00 313.00 Upper limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00 Lower limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00

* finish the risk probability of deployment task

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