CN1845159A - Rapid 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

Quick 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 fast, 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 target and the commander's control plan with low computational complexity and high solvability are that the battlefield commander implements the key issue that commander's control fast must solve to battlefield 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, and 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, constraint condition that therefore must be by reducing commander's controlling models, 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 is implemented to command fast to control as optimization aim by antithesis.

The present invention relates to quick 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 target and the commander's controlling models with low computational complexity and high solvability, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets the fast and low-risk disposition requirement until final acquisition, this method has efficiently, simply, objective, characteristics are widely used and obviously improve its combat capabilities etc., can be widely used in quick commander's control of all battlefield 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 target and the commander's controlling models with low computational complexity and high solvability, 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 quick 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, come this model of rapid solving by reducing constraint condition, 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 quick 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 target and the commander's controlling models with low computational complexity and high solvability to dispose and to transport, and use linear programming, the dual program method of linear programming is found the solution this model, obtain scheme to battlefield 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.

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

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 making the risk of finishing battlefield mechanized infantry deployment and meeting predetermined requirement T.T..

Quick 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 quick commander's control problem of battlefield mechanized infantry's fast and low-risk disposition, it is the analysis of target to quick 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 _jy _j+ S _iy _N+i≤ p _IjBe replaced into D _iy _j+ S _iy _N+i≤ d _IjAnd 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: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

Deployment point demand constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}=D_j,$ (j＝1，…，n)

Assembly place supply constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}\≤S_i,$ (i＝1，…，m)

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

Assembly place i (i=1 ... m) the 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 the spent minimum time: min T=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 deployment point is relevant: $\min Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ j(j＝1，…n)

The overall risk carrying capacity that the battlefield mechanized infantry disposes: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\min Z}_j$

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

The total 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);

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;

S _iFor assembly place i (i=1 ... m) can supply mechanized infantry's quantity (unit: the people);

D _jFor deployment point j (j=1 ... n) need mechanized infantry's quantity (unit: the people);

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 all battlefield mechanized infantries and dispose the risk probability minP of experience, the shortest time T that expends, 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: $\max G=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{D}_j{y}_j+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i{y}_{n+1}$

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

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

Wherein: y _j, y _N+iBe respectively demand and shadow price or the relevant decision variable of opportunity cost of supplying mechanized infantry's constraint condition with former linear programming.

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

Embodiment

Implementation example

In IT-based warfare, the 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 quick 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 quick commander's control problem 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 _jy _j+ S _iy _N+i≤ p _IjBe replaced into D _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product, suppose 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 5 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	Quantity required
							14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point	0.037 0.034 0.025 0.014 0.026 0.024 0.120 0.159 0.112 0.062 0.091 0.126 0.090 0.081	0.013 0.025 0.028 0.015 0.035 0.020 0.098 0.138 0.096 0.037 0.066 0.097 0.068 0.056	0.070 0.083 0.108 0.097 0.082 0.110 0.012 0.051 0.096 0.046 0.017 0.081 0.099 0.020	0.074 0.087 0.112 0.101 0.086 0.100 0.129 0.149 0.025 0.050 0.079 0.086 0.104 0.066	0.044 0.031 0.066 0.058 0.056 0.039 0.105 0.145 0.110 0.059 0.073 0.027 0.011 0.075	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 24.00
Can the deployment amount	250.00	200.00	300.00	400.00	150.00

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

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, 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 assembly place	02 assembly place	03 assembly place	04 assembly place	05 assembly place	People's risk	Risk probability	Passenger-kilometer	Chariot	Expend time in	Shadow price
												14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point	90.00 90.00 70.00	36.00 21.00 40.00 40.00 36.00	60.00 16.00 90.00 24.00	29.00	22.00 18.00	0.468 0.525 2.250 1.860 1.820 0.800 0.720 0.816 0.725 1.332 1.530 0.594 0.198 0.480	0.013 0.025 0.025 0.015 0.026 0.020 0.012 0.051 0.025 0.037 0.017 0.027 0.011 0.020	468.00 525.00 2250.00 1860.00 1820.00 800.00 720.00 816.00 725.00 1332.00 1530.00 594.00 198.00 480.00	3 2 6 9 5 3 4 1 2 3 6 2 2 2	11.14 21.43 21.43 12.26 22.29 17.14 10.29 43.71 21.43 31.71 14.57 23.14 9.43 17.14	0.00 12.00 13.00 2.00 14.00 7.00 0.00 39.00 0.00 24.00 5.00 16.00 0.00 8.00
Add up to	250.00	173.00	190.00	29.00	40.00	14.118	0.051	14118.00	50	43.71 *
												But portion's quantity	250.00	200.00	300.00	400.00	150.00
Surplus after the portion	0.00	27.00	110.00	371.00	110.00
												Shadow price	12.00	13.00	12.00	25.00	11.00

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

By option control command (table 3) is analyzed as can be known; the armored personnel carrier that finishing deployment task needs adds up to 50; time is 43.71 minutes; the armored personnel carrier that 01～05 assembly place needs is respectively 17; 14; 13; 2 and 4; therefore must be to 01; 02 and 03 assembly place implements to lay special stress on protecting; further analyze as can be known; transporting 16 43.71 minutes that the mechanized infantry spent from 03 assembly place to 08 deployment point 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 31.71 minutes the time that whole deployment task is finished; reduction is 27.45%; risk probability is reduced to 0.037; reduction is 27.45%; and for example fruit is adopted the bottleneck that uses the same method and eliminated 31.71 minutes; then can be shortened to 23.14 minutes deployment time; reduction reaches 47.06%; risk probability is reduced to 0.027; reduction is 47.06%, almost only is half of former free and risk probability.

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

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

Claims (10)

1, the present invention relates to quick 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 target and the commander's controlling models with low computational complexity and high solvability, 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, quick 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, quick 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, quick 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, quick 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 target and the commander's controlling models with low computational complexity and the high solvability objective function that is meant this commander's controlling models is transported all infantries and expended time in or meet with the risk minimum for making.

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

7, quick commander's control method of battlefield according to claim 1 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.

8, quick 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.

9, quick 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 target and the commander's controlling models with low computational complexity and high solvability, and use linear programming, the dual program method of linear programming is found the solution this model and is meant that following is the analysis of target to quick commander's control problem of battlefield mechanized infantry's fast and low-risk disposition with the risk minimum, but it is the analysis of target to quick 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 _iy _j+ S _iy _N+i≤ p _IjBe replaced into D _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product, following mathematical formulae, derivation, result of calculation and application process are applicable to the quick commander's control to all battlefield 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: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

Deployment point demand constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}=D_j,(j=1,\·\·\·,n)$

Assembly place supply constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}\≤S_i,(i=1,\·\·\·,m)$

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

Assembly place i (i=1 ... m) the 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 deployment point is relevant: $\min Z_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}},j(j=1,\·\·\·n)$

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

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

The total 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);

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;

S _iFor assembly place i (i=1 ... m) can supply mechanized infantry's quantity (unit: the people);

D _jFor deployment point j (j=1 ... n) need mechanized infantry's quantity (unit: the people);

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 all battlefield mechanized infantries and dispose the risk probability minP of experience, the shortest time T that expends, 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: $\max G=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{D}_j{y}_j+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i{y}_{n+i}$

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

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

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

10, quick commander's control method of battlefield according to claim 1 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 target and the commander's controlling models with low computational complexity and high solvability, 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 making the risk of finishing battlefield mechanized infantry deployment and meeting predetermined requirement T.T., this process can with following be that target is described the example of quick commander's control problem of battlefield mechanized infantry's fast and low-risk disposition with the risk minimum, it is the instance analysis of target to quick 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 _jy _j+ S _iy _N+i≤ p _IjBe replaced into d _jy _j+ S _iy _N+i≤ d _IjAnd similarly analyze and get final product, but the mathematical formulae described in example, result of calculation, various form and application process are applicable to the quick commander's control to all battlefield 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 5 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 Quantity required 14 deployment points, 13 deployment points, 12 deployment points, 11 deployment points, 10 deployment points, 09 deployment point, 08 deployment point, 07 deployment point, 06 deployment point, 05 deployment point, 04 deployment point, 03 deployment point, 02 deployment point, 01 deployment point 0.037 0.034 0.025 0.014 0.026 0.024 0.120 0.159 0.112 0.062 0.091 0.126 0.090 0.081 0.013 0.025 0.028 0.015 0.035 0.020 0.098 0.138 0.096 0.037 0.066 0.097 0.068 0.056 0.070 0.083 0.108 0.097 0.082 0.110 0.012 0.051 0.096 0.046 0.017 0.081 0.099 0.020 0.074 0.087 0.112 0.101 0.086 0.100 0.129 0.149 0.025 0.050 0.079 0.086 0.104 0.066 0.044 0.031 0.066 0.058 0.056 0.039 0.105 0.145 0.110 0.059 0.073 0.027 0.011 0.075 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 24.00 Can the deployment amount 250.00 200.00 300.00 400.00 150.00

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 Quantity required 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 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 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 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 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 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 22.00 18.00 14 deployment points 81.00 56.00 20.00 66.00 75.00 24.00 Can the deployment amount 250.00 200.00 300.00 400.00 150.00

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

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

By option control command (table 3) is analyzed as can be known; the armored personnel carrier that finishing deployment task needs adds up to 50; time is 43.71 minutes; the armored personnel carrier that 01～05 assembly place needs is respectively 17; 14; 13; 2 and 4; therefore must be to 01; 02 and 03 assembly place implements to lay special stress on protecting; further analyze as can be known; transporting 16 43.71 minutes that the mechanized infantry spent from 03 assembly place to 08 deployment point 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 31.71 minutes the time that whole deployment task is finished; reduction is 27.45%; risk probability is reduced to 0.037; reduction is 27.45%; and for example fruit is adopted the bottleneck that uses the same method and eliminated 31.71 minutes; then can be shortened to 23.14 minutes deployment time; reduction reaches 47.06%; risk probability is reduced to 0.027; reduction is 47.06%; almost only be half of former free and risk probability

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

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