CN1845141A - Command control method of rapid low risk transport for war field material - Google Patents

Abstract

The invention relates to a quick command control method for quickly low-risk transmitting the materials in the battlefield. Wherein, the commanded object the all battlefield materials; according to the lengths from different concentrate points to different deploy points, the transmission risk probability, the supply amount of provider, the needed amount of demander, and the speed and load of transmission device, the command control mode purposed for transmitting all materials in minimum time or 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-disk transmission. The invention can improve the battle effectiveness, with wider application. The invention also provides relative technique.

Description

Commander's control method of battlefield goods and materials fast and low-risk transportation

Technical field the present invention relates to national defence and association area, is used for the control to battlefield goods and materials fast and low-risk transportation enforcement commander, realizes the low-risk transportation to the battlefield goods and materials.

Background technology is implemented the transportation of low-risk goods and materials between the supply and demand both sides in battlefield commander's control is an important component part of operational commanding control, according to the length of different suppliers to different parties in request goods and materials transportation route, transportation meets with risk probability, the demand of the supply of supplier's goods and materials and party in request's goods and materials, the speed of means of transport and carrying capacity, work out one with realize the supply and demand both sides transport all goods and materials expend time in or meet with the risk minimum be the transportation command control plan of target be the battlefield commander to battlefield goods and materials fast and low-risk transportation implement the key issue that commander's control must solve, the solution of this problem is for increasing substantially fighting capacity, reduce the risk of battlefield goods and materials transportation, expend time in, have crucial meaning.

Mobile operations are most important for the triumph of capturing IT-based warfare, complicated battlefield surroundings may impact the experience risk of goods and materials transportation, thereby reduce the security of transporting supplies, for example commander's control of low-risk goods and materials transportation 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 goods and materials transportation of formulation science.The quality of this plan, not only be related to and implement what of risk that battlefield goods and materials transport point faces and consumption of natural resource, but also be related to some crucial materiels such as can ammunition, fuel oil etc. in time be transported to mechanization combat troop, to guarantee that fighting capacity is unlikely to descend because of the delay that goods and materials transport.

Time seems more important for commander's control of the transportation of the low-risk of battlefield goods and materials and this transportation, therefore must analyze the choose reasonable parameter by antithesis and improve solvability and come battlefield goods and materials fast and low-risk transportation to implement to command with risk in transit and time minimum as optimization aim and control.

The present invention relates to commander's control method of battlefield goods and materials fast and low-risk transportation, relate to military affairs and association area, the object of commander's control is all battlefield goods and materials, this method is according to the length from different suppliers to different parties in request goods and materials transportation route, transportation meets with risk probability, the demand of the supply of supplier's goods and materials and party in request's goods and materials, the speed of means of transport and carrying capacity, structure is to transport all goods and materials and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets battlefield goods and materials fast and low-risk movement 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 goods and materials fast and low-risk transportations, the invention further relates to the technology that realizes this method.

Summary of the invention the present invention is according to the length from different suppliers to different parties in request goods and materials transportation route, transportation meets with risk probability, the demand of the supply of supplier's goods and materials and party in request's goods and materials, the speed of means of transport and carrying capacity, structure is to transport all goods and materials and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, obtain to implement the scheme of commander's control with the transportation to battlefield goods and materials fast and low-risk of two-dimentional form description, and check whether this option control command meets risk and the time demand of finishing whole battlefield goods and materials transport 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, the time bottleneck is adjusted relevant supplier's stock in storage amount and means of transport etc., constantly repeat this and find the solution-check analytic process, meet the option control command of battlefield goods and materials fast and low-risk movement requirement until final acquisition.Therefore, the conception of commander's control of battlefield goods and materials fast and low-risk transportation is proposed, introduce the analytical approach that transportation expends time in and meets with risk probability, set up linear programming and the dual program model of seeking optimum option control command, by finding the solution this model, obtain to implement the scheme of commander's control with the transportation to battlefield goods and materials fast and low-risk of two-dimentional form description, and according to risk and the time requirement of finishing whole goods and materials transportation, by searching risk and the time bottleneck that whole battlefield goods and materials transport task is finished in influence, the unreasonable configuration of supplier's stock in storage amount and means of transport adjusted, continue to optimize and improve this option control command, and the final time requirement that obtains to satisfy battlefield goods and materials fast and low-risk transportation, 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 goods and materials fast and low-risk transportation is:

At first, battlefield goods and materials fast and low-risk transportation problem is defined as by the supplier of goods and materials and the supply and demand system that party in request constituted of goods and materials, the feature of this system can be used the length from different suppliers to different parties in request goods and materials transportation route, transportation meets with risk probability, the demand of the supply of supplier's goods and materials and party in request's goods and materials, the speed and the carrying capacity of means of transport are described, and according to risk that the battlefield goods and materials are transported and time requirement, structure is to transport all goods and materials and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, obtain to implement the scheme of commander's control with the transportation to battlefield goods and materials fast and low-risk of two-dimentional form description, risk and time bottleneck by continuous searching supply and demand system, quantity of inventory to relevant supplier carries out reasonable disposition, adopt methods such as different means of transports, the final time requirement that obtains to satisfy battlefield goods and materials fast and low-risk transportation, the scheme of commander's control is implemented in transportation to the battlefield goods and materials, finishes the commander's control to the transportation of battlefield goods and materials fast and low-risk.

Complicated battlefield surroundings may impact the current risk of goods and materials transportation route, risk can make goods and materials damaged to the transportation of party in request from the supplier, thereby reduce the security of transporting supplies, for goods and materials expend time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of goods and materials transportations, 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 supplier's transporting supplies to different parties in request meets with risk probability or the transportation route of least consume time, the shadow price relevant with different parties in request constraint condition with different suppliers, and transport minimum risk probability that all goods and materials meet with or the minimum time that expends, 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 shadow price, risk and time bottleneck are adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield goods and materials fast and low-risk movement requirement until final acquisition.

Can by quantity from each supplier to each party in request's transporting supplies is described as the zones of different in the two-dimentional form of option control command, size, risk in transit, the quantity of means of transport, transportation that each party in request needs transport power expend time in and relevant shadow price, the situation of change of quantity, surplus material that each supplier supplies goods and materials is with relevant shadow price and transport the priming the pump of all goods and materials 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 goods and materials transportation and the bottleneck of T.T., carry out reasonable disposition, increase the quantity of means of transport and adopt different means such as means of transport by stock in storage again the supplier, eliminate risk and time bottleneck, and repeat this process, until the risk of finishing battlefield goods and materials transportation with meet predetermined requirement T.T..

Commander's control method of the battlefield goods and materials fast and low-risk transportation of the present invention's design is applicable to that all battlefield goods and materials fast and low-risk transportations are key characters of the present invention.

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

$D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into

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

The transportation problem of supposing the battlefield goods and materials can be used by m supply goods and materials node and n demand goods and materials node and exist the network in the path of a transporting supplies to describe between different supply and demand nodes, is x from supplying the goods and materials 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 goods and materials transportation route, risk can make goods and materials damaged to the transportation of party in request from the supplier, thereby reduce the security of transporting supplies, for to transport the commander control that goods and materials risk minimum is a target, this reduction has been equivalent to increase the risk of goods and materials transportations, 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 supplied node from m and transported goods and materials to n demand node, make simultaneously and transport the movement plan that all goods and materials risk minimums, consumed time satisfy pre-provisioning request, and calculate the quantity that each supply node transports the required means of transport of goods and materials, relevant battlefield goods and materials transportation command controlling models and linear programming equation are as follows:

Objective function: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

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

Demand is less than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{il}}\≤D_l,(l=n_e+1,...,n_l)$

Demand is greater than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{is}}\≥D_s,(s=n_l+1,...,n_s)$

Supply equals constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ej}}=S_e,(e=n_s+1,...,m_e)$

Supply is less than constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{lj}}\≤S_l,(l=m_e+1,...,m_l)$

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

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

From supply node i (i=1 ... m) transport goods and materials to demand node j (j=1 ... n) spent time: $T_{\mathrm{ij}}=\frac{d_{\mathrm{ij}}}{C}$

Finish the minimum time that all battlefield goods and materials transport points expend: min T=max{T _Ij}

The maximum transportation relevant with j demand node 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 battlefield goods and materials transportations meet with: min P=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 of battlefield goods and materials transportation: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\min Z}_j$

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

The total goods and materials carrying capacity in battlefield: $Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{Z}_j$

Wherein:

M is the node sum of supply goods and materials;

N is the node sum of demand goods and materials;

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 supply node i (i=1 ... m) with demand node j (j=1 ... n) transportation between meets with risk probability, can be with the function of time t as variable;

d _IjFor supply node i (i=1 ... m) with demand node j (j=1 ... the length of the transportation route n) (unit: kilometer);

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

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

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

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

n _iBe the maximum sequence number less than the constraint condition upper limit relevant with demand node demand;

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

D _eFor with the demand node need the relevant amount of the quantity of goods and materials (e=1 ..., n _e) (unit: ton);

D _lFor needing the relevant upper limit (l=n of goods and materials quantity with the demand node _e+ 1 ..., n _l) (unit: ton);

D _sFor needing the relevant lower limit (s=n of goods and materials quantity with the demand node _i+ 1 ..., n _s) (unit: ton);

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

m _lFor with supply node supply relevant maximum sequence number less than the constraint condition upper limit;

m _sFor with supply node supply relevant maximum sequence number greater than the constraint condition lower limit;

S _eFor supplying the relevant amount (e=n of quantity of goods and materials with the supply node _s+ 1 ..., m _e) (unit: ton);

S _lFor supplying goods and materials quantity the relevant upper limit (l=m with the supply node _e+ 1 ..., m _l) (unit: ton);

S _sFor supplying goods and materials quantity relevant lower limit (s=m with the supply node _l+ 1 ..., m _s) (unit: ton);

V _iFor the supply goods and materials node i (i=1 ... m) transport the means of transport quantity that goods and materials need;

L transports the ability (unit: ton) of goods and materials for each means of transport;

C transports the speed (unit: kilometer/hour) of goods and materials for each means of transport;

Above-mentioned model shows: objective function be equivalent to ask probability-weighted and, on the basis of trying to achieve risk carrying capacity min Z value by linear programming, can calculate each and supply the goods and materials quantity x that node must transport to the related needs node _Ij, the p of associated pathway _Ij,, can calculate the means of transport quantity V that each supply node needs again according to the dead weight capacity L of means of transport _i, transport at last the speed C and the longest path between the supply and demand node of goods and materials according to means of transport, can calculate the risk carrying capacity minZ of each demand node again _j, maximum transportation meets with risk probability p _jFinish risk probability min P, the shortest time T that expends that all battlefield goods and materials transportations meet with, thereby realize commander's control to the transportation of battlefield goods and materials fast and low-risk, 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: $y_{m_i\left(i\right)},y_{n_i\left(j\right)}\≤0(i=1,...,m;j=1,...,n)$

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

Wherein:

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

Mark sequence number transforming function transformation function;

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

Variable subscript sequence number transforming function transformation function; y _v, y _u(v=1 ..., n _sU=n _s+ 1 ..., m _s) be respectively the relevant decision variable of shadow price with the demand of former linear programming and supply goods and materials constraint condition;

Since primal linear programming solves be with demand node j and supply node i (i=1 ..., m; J=1 ..., n) the relevant resource optimal utilization problem of constraint condition, thus dual program solve be potential demand node j and supply node i (i=1 ..., m; J=1 ..., n) constraint condition satisfies the cost problem that must pay, promptly uses the valency problem, and shadow price y _vAnd y _uThe node of the demand just j of reflection and supply node 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 battlefield movement capacity of mechanization combat division is an important component part of its fighting capacity, to huge battlefield goods and materials low-risk transporting power and the demand of time, the commander's control that makes enforcement battlefield goods and materials low-risk transport becomes vital task, the implementation example of commander's control problem of battlefield goods and materials fast and low-risk transportation that with the risk minimum is target is as follows, it is the implementation example analysis of target to commander's control problem of battlefield goods and materials fast and low-risk transportation that this implementation example is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}$ And similarly analyze and get final product, suppose that certain mechanization combat division must be that 16 tons, average speed per hour are 70 kilometers truck with dead weight capacity, transport the materiel of specified amount to 14 demand points from 6 supply centre, transportation experience risk probability and supply and demand amount are as shown in table 1 between the supply and demand point.

Table 1: transportation meets with risk probability, supply and demand amount (unit: probability, ton) between the mechanization combat division supply and demand point

	01 supply centre	02 supply centre	03 supply centre	04 supply centre	05 supply centre	06 supply centre	The demand upper limit	The demand lower limit
									01 demand point	0.037	0.013	0.070	0.074	0.044	0.060	36.00	36.00

02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points	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	0.025 0.028 0.015 0.035 0.020 0.098 0.138 0.096 0.037 0.066 0.097 0.068 0.056	0.083 0.108 0.097 0.082 0.110 0.012 0.051 0.096 0.046 0.017 0.081 0.099 0.020	0.087 0.112 0.101 0.086 0.100 0.129 0.149 0.025 0.050 0.079 0.086 0.104 0.066	0.031 0.066 0.058 0.056 0.039 0.105 0.145 0.110 0.059 0.073 0.027 0.011 0.075	0.019 0.056 0.030 0.048 0.065 0.075 0.030 0.069 0.070 0.026 0.065 0.072 0.044	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	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
									Can keep supplying limit	100.00	200.00	300.00	400.00	150.00	350.00
Can supply lower limit	100.00	60.00	40.00	10.00	10.00	20.00

The length of transportation route and supply and demand amount are as shown in table 2 between the supply and demand point.

Table 2: transportation route length, supply and demand amount (unit: kilometer, ton) between the mechanization combat division supply and demand point

	01 supply centre	02 supply centre	03 supply centre	04 supply centre	05 supply centre	06 supply centre	The demand upper limit	The demand lower limit
									01 demand point, 02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points	37.00 34.00 25.00 14.00 26.00 24.00 120.00 159.00 112.00 62.00 91.00 126.00 90.00 81.00	13.00 25.00 28.00 15.00 35.00 20.00 98.00 138.00 96.00 37.00 66.00 97.00 68.00 56.00	70.00 83.00 108.00 97.00 82.00 110.00 12.00 51.00 96.00 46.00 17.00 81.00 99.00 20.00	74.00 87.00 112.00 101.00 86.00 100.00 129.00 149.00 25.00 50.00 79.00 86.00 104.00 66.00	44.00 31.00 66.00 58.00 56.00 39.00 105.00 145.00 110.00 59.00 73.00 27.00 11.00 75.00	60.00 19.00 56.00 30.00 48.00 65.00 75.00 30.00 69.00 70.00 26.00 65.00 72.00 44.00	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 30.00 35.00 28.00	36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 80.00 20.00 25.00 22.00
Can keep supplying limit	100.00	200.00	300.00	400.00	150.00	350.00
									Can supply lower limit	100.00	60.00	40.00	10.00	10.00	20.00

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, it is as shown in table 3 to calculate mechanization combat division minimum risk transportation command controlling schemes by simplex algorithm, and wherein the ton risk is the risk carrying capacity min Z of demand node _j, risk probability is that the maximum transportation of demand node meets with risk probability p _j, ton kilometre is the goods and materials carrying capacity Z of demand node _j

Table 3: mechanization combat division minimum risk transportation command controlling schemes (unit: ton, ton risk, probability, ton kilometre,, minute)

	01 for point	02 for point	03 for point	04 for point	05 for point	06 for point	The ton risk	Risk probability	Ton kilometre	The truck number	Need the time	Upper limit shadow valency	Lower limit shadow valency
														01 demand point		36.00					0.468	0.013	468.00	3	11.14	13.00	13.00

02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points	30.00 70.00	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	0.399 2.430 2.940 1.820 0.800 0.720 0.480 0.725 1.656 1.360 0.540 0.275 0.440	0.019 0.028 0.030 0.026 0.020 0.012 0.030 0.025 0.046 0.017 0.027 0.011 0.020	399.00 2430.00 2940.00 1820.00 800.00 720.00 480.00 725.00 1656.00 1360.00 540.00 275.00 440.00	2 6 9 5 3 4 1 2 3 5 2 2 2	16.29 24.00 25.71 22.29 17.14 10.29 25.71 21.43 39.43 14.57 23.14 9.43 17.14	19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00	19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00
														Add up to	100.00	200.00	198.00	29.00	45.00	103.00	15.053	0.046	15053.00	49	39.43 *
Quantity available	100.00	200.00	300.00	400.00	150.00	350.00
														For the back surplus	0.00	0.00	102.00	371.00	105.00	247.00
Upper limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00
														Lower limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00

* finish the minimum time that transport task needs

By option control command (table 3) is analyzed as can be known; the truck that finishing transport task needs adds up to 49; time is 39.43 minutes; the truck that 01～06 supply centre needs is respectively 11; 16; 14; 2; 4 and 12; therefore must be to 02; 03 and 06 supply centre implements to lay special stress on protecting; further analyze as can be known; transporting 36 tons of 39.43 minutes that goods and materials spent from 03 supply centre to 10 demand points is bottlenecks that the whole transport task of restriction is finished sooner; this transports also is simultaneously the bottleneck that reduces the risk probability of finishing all battlefield goods and materials transportation experiences; if finish the transportation of this part goods and materials with helicopter; then can be shortened to 25.71 minutes the time of finishing whole transport task; reduction is 34.80%; risk probability is reduced to 0.030 from 0.046, and reduction is 34.78%.

From to demand constraint condition D _v(v=1 ..., 18) analysis of shadow price as can be known, the size of price has reflected that truly the related constraint condition is full.Complexity, 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 increasing this resource can not make the optimal value of objective function further reduce more yet, again for example, in order to satisfy constraint condition D ₁₀, the risk of transporting goods and materials to 10 demand points is 0.046,39.43 minutes consuming time, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult to satisfy, can be by D with similar method _vThe complexity that satisfies, from difficulty to easy ordering: D ₁₀, D ₈, D ₁₆, D ₅, D ₃, D ₉..., to supply constraint condition S _u(u=19 ..., 29) analysis of shadow price as can be known, their shadow price is 0, therefore, in specific span, the value that changes Su does not constitute influence to target function value, must be pointed out that shadow price is not changeless, can be along with D _vAnd S _uVariation and change, make the resource that does not constitute influence originally become influential resource, by analysis to shadow price, can adjust constraint condition targetedly, reach the purpose that reduces risk, carrying capacity and haulage time, because shadow price is the result who obtains under specific constraint condition, only in its valid interval, price just has relative stability.

From finish the work the back each supply centre tank farm stock as can be seen, the stock in storage of 02 supply centre exhausts, obviously on the low side, and the stock in storage amount of 04 supply centre is obviously bigger than normal, and according to the antithesis analysis, the shadow price of their constraint condition is 0, this statement of facts: if there are more goods and materials 02 supply centre, there are goods and materials still less 04 supply centre, just may obtain better movement 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 of the mechanization combat division minimum risk transportation of obtaining is as shown in table 4.

Table 4: the improvement project of mechanization combat division minimum risk transportation (unit: ton, ton risk, probability, ton kilometre,, minute)

	01 for point	02 for point	03 for point	04 for point	05 for point	06 for point	The ton risk	Risk probability	Ton kilometre	The truck number	Need the time	Upper limit shadow valency	Lower limit shadow valency
														01 demand point, 02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points	30.00 70.00	36.00 60.00 130.00 40.00 36.00	60.00 80.00 22	29.00	20.00 25.00	21.00 16.00	0.468 0.399 2.430 1.950 1.820 0.800 0.720 0.480 0.725 1.332 1.360 0.540 0.275 0.440	0.013 0.019 0.028 0.015 0.026 0.020 0.012 0.030 0.025 0.037 0.017 0.027 0.011 0.020	468.00 399.00 2430.00 1950.00 1820.00 800.00 720.00 480.00 725.00 1332.00 1360.00 540.00 275.00 440.00	3 2 6 9 5 3 4 1 2 3 5 2 2 2	11.14 16.29 24.00 12.86 22.29 17.14 10.29 25.71 21.43 31.71 14.57 23.14 9.43 17.14	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00	13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00
Add up to	100.00	302.00	162.00	29.00	45.00	37.00	13.739	0.037	13739.00	49	31.71 *
														Quantity available	100.00	400.00	300.00	200.00	150.00	350.00
For the back surplus	0.00	98.00	138.00	171.00	105.00	313.00
														Upper limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00
Lower limit shadow valency	0.00	0.00	0.00	0.00	0.00	0.00

* finish the minimum time that transport task needs

Analysis by his-and-hers watches 4 as can be known, the risk of finishing transport task is 0.037, amount of decrease is 19.57%, the time that needs shortens to 31.71 minutes, amount of decrease is 19.58%, the overall risk carrying capacity is reduced to 13.739 tons of risks, amount of decrease is 8.73%, total carrying capacity is reduced to 13739 ton kilometres, amount of decrease is 8.73%, antithesis the analysis showed that: shadow price is without any variation, but the scheme after improving is better, therefore, can also carry out reasonable configuration to the goods and materials of each supply centre, realize the Optimal Management of tank farm stock with said method.

Claims (8)

1, the present invention relates to commander's control method of battlefield goods and materials fast and low-risk transportation, relate to military affairs and association area, the object of commander's control is all battlefield goods and materials, this method is according to the length from different suppliers to different parties in request goods and materials transportation route, transportation meets with risk probability, the demand of the supply of supplier's goods and materials and party in request's goods and materials, the speed of means of transport and carrying capacity, structure is to transport all goods and materials and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, meet the option control command of battlefield goods and materials fast and low-risk movement requirement until final acquisition, this scheme is applicable to commander's control of all battlefield goods and materials fast and low-risks transportations.

2, commander's control method of battlefield goods and materials fast and low-risk transportation according to claim 1, the object that it is characterized in that described commander's control is meant the object of all battlefield goods and materials as commander's control for all battlefield goods and materials, described commander's control is meant according to the actual demand of battlefield to goods and materials, design is transported to different parties in request with the battlefield goods and materials from different suppliers, and all transportations are expended time in or the probability-weighted that meets with risk for minimum, can be for the scheme of implementing.

3, commander's control method of battlefield goods and materials fast and low-risk transportation according to claim 1, it is characterized in that described this method is meant the supply and demand system that can set up a battlefield goods and materials transportation by these parameters according to supply and the demand of party in request's goods and materials, the speed and the carrying capacity of means of transport that the length from different suppliers to different parties in request goods and materials transportation route, transportation meet with risk probability, supplier's goods and materials, obtains the battlefield goods and materials are transported the method for implementing commander's control on this basis.

4, commander's control method of battlefield according to claim 1 goods and materials fast and low-risk transportation, it is characterized in that described transportation meets with risk probability and is meant that complicated battlefield surroundings may impact the current risk of goods and materials transportation route, risk can make goods and materials damaged to the transportation of party in request from the supplier, thereby reduce the security of transporting supplies, for goods and materials expend time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of goods and materials transportations, 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 goods and materials fast and low-risk transportation, 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 battlefield goods and materials fast and low-risk movement 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 supplier's transporting supplies to different parties in request meets with risk probability or the transportation route of least consume time, the shadow price relevant with different parties in request constraint condition with different suppliers, and transport minimum risk probability that all goods and materials meet with or the minimum time that expends, 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 shadow price, risk and time bottleneck are adjusted correlation parameter, constantly find the solution and update, meet the option control command of battlefield goods and materials fast and low-risk movement requirement until final acquisition.

6, commander's control method of battlefield according to claim 1 goods and materials fast and low-risk transportation, 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 battlefield goods and materials fast and low-risk movement requirement until final acquisition is meant can be by describing the quantity from each supplier to each party in request's transporting supplies as the zones of different in the two-dimentional form of option control command, each party in request needs the size of transport power, risk in transit, the quantity of means of transport, transportation expends time in and relevant shadow price, and each supplier supplies the quantity of goods and materials, the situation of change of surplus material is with relevant shadow price and transport the priming the pump of all goods and materials and the minimum time that expends.

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

The transportation problem of supposing the battlefield goods and materials can be used by m supply goods and materials node and n demand goods and materials node and exist the network in the path of a transporting supplies to describe between different supply and demand nodes, is x from supplying the goods and materials 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 goods and materials transportation route, risk can make goods and materials damaged to the transportation of party in request from the supplier, thereby reduce the security of transporting supplies, for goods and materials expend time in or the risk minimum is commander's control of target to transport, this reduction has been equivalent to increase the risk of goods and materials transportations, 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 supplied node from m and transported goods and materials to n demand node, make simultaneously and transport the movement plan that all goods and materials risk minimums, consumed time satisfy pre-provisioning request, and calculate the quantity that each supply node transports the required means of transport of goods and materials, relevant battlefield goods and materials transportation command controlling models and linear programming equation are as follows:

Objective function: $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$

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

Demand is less than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{il}}\≤D_l,$ (l＝n _e+1，…，n _l)

Demand is greater than constraint condition: $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{is}}\≥D_s,$ (s＝n _l+1，…，n _s)

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

Supply is less than constraint condition: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{lj}}\≤S_l,$ (l＝m _e+1，…，m _l)

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

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

From supply node i (i=1 ... m) transport goods and materials to demand node j (j=1 ... n) spent time: $T_{\mathrm{ij}}=\frac{d_{\mathrm{ij}}}{C}$

Finish the minimum time that all battlefield goods and materials transport points expend: min T=max{T _Ij}

The maximum transportation relevant with j demand node 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 battlefield goods and materials transportations meet with: min P=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 of battlefield goods and materials transportation: $\min Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\min Z}_j$

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

The total goods and materials carrying capacity in battlefield: $Z=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{Z}_j$

Wherein:

M is the node sum of supply goods and materials;

N is the node sum of demand goods and materials;

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 supply node i (i=1 ... m) with demand node j (j=1 ... n) transportation between meets with risk probability, can be with the function of time t as variable;

d _IjFor supply node i (i=1 ... m) with demand node j (j=1 ... the length of the transportation route n) (unit: kilometer);

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

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

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

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

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

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

D _eFor with the demand node need the relevant amount of the quantity of goods and materials (e=1 ..., n _e) (unit: ton);

D _lFor needing the relevant upper limit (l=n of goods and materials quantity with the demand node _e+ 1 ..., n _l) (unit: ton);

D _sFor needing the relevant lower limit (s=n of goods and materials quantity with the demand node _l+ 1 ..., n _s) (unit: ton);

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

m _lFor with supply node supply relevant maximum sequence number less than the constraint condition upper limit;

m _sFor with supply node supply relevant maximum sequence number greater than the constraint condition lower limit;

S _eFor supplying the relevant amount (e=n of quantity of goods and materials with the supply node _s+ 1 ..., m _e) (unit: ton);

S _lFor supplying goods and materials quantity the relevant upper limit (l=m with the supply node _e+ 1 ..., m _l) (unit: ton);

S _sFor supplying goods and materials quantity relevant lower limit (s=m with the supply node _l+ 1 ..., m _s) (unit: ton);

V _iFor the supply goods and materials node i (i=1 ... m) transport the means of transport quantity that goods and materials need;

L transports the ability (unit: ton) of goods and materials for each means of transport;

C transports the speed (unit: kilometer/hour) of goods and materials for each means of transport;

Above-mentioned model shows: objective function be equivalent to ask probability-weighted and, on the basis of trying to achieve risk carrying capacity min Z value by linear programming, can calculate each and supply the goods and materials quantity x that node must transport to the related needs node _Ij, the p of associated pathway _Ij,, can calculate the means of transport quantity V that each supply node needs again according to the dead weight capacity L of means of transport _i, transport at last the speed C and the longest path between the supply and demand node of goods and materials according to means of transport, can calculate the risk carrying capacity min Z of each demand node again _j, maximum transportation meets with risk probability p _jFinish risk probability min P, the shortest time T that expends that all battlefield goods and materials transportations meet with, thereby realize commander's control to the transportation of battlefield goods and materials fast and low-risk, 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:

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

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;

$y_{m_e\left(i\right)}=y_u(n_s\≤u\≤m_e),y_{m_l\left(i\right)}=y_u(m_e+1\≤u\≤m_l),y_{m_s\left(l\right)}=y_u(m_l+1\≤u\≤m_s)$ 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 the relevant decision variable of shadow price with the demand of former linear programming and supply goods and materials constraint condition;

Since primal linear programming solves be with demand node j and supply node i (i=1 ..., m; J=1 ..., n) the relevant resource optimal utilization problem of constraint condition, thus dual program solve be potential demand node j and supply node i (i=1 ..., m; J=1 ..., n) constraint condition satisfies the cost problem that must pay, promptly uses the valency problem, and the node of the demand just j of shadow price yv and yu reflection and supply node 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.

8, commander's control method of battlefield according to claim 1 goods and materials fast and low-risk transportation, it is characterized in that described this method is according to the length from different suppliers to different parties in request goods and materials transportation route, transportation meets with risk probability, the demand of the supply of supplier's goods and materials and party in request's goods and materials, the speed of means of transport and carrying capacity, structure is to transport all goods and materials and expend time in or the risk minimum is commander's controlling models of target, and use linear programming, the dual program method of linear programming is found the solution this model, by two-dimentional form solving result is updated again, the option control command that meets battlefield goods and materials fast and low-risk movement 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 goods and materials transportation and the bottleneck of T.T., carry out reasonable disposition by stock in storage again to the supplier, 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 the risk of finishing the transportation of battlefield goods and materials with meet predetermined requirement T.T., this process can be target with the risk minimum describe the example of commander's control problem of battlefield goods and materials fast and low-risk transportation with following, it is the instance analysis of target to commander's control problem of battlefield goods and materials fast and low-risk transportation that this example is equally applicable to the minimum that expends time in, and only need objective function this moment $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{p}_{\mathrm{ij}}{x}_{\mathrm{ij}}$ Be replaced into $\min Z=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{x}_{\mathrm{ij}},$ With constraint condition $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤p_{\mathrm{ij}}$ Be replaced into $D_e{y}_{n_e\left(j\right)}+D_l{y}_{n_l\left(j\right)}+D_s{y}_{n_s\left(j\right)}+S_e{y}_{m_e\left(i\right)}+S_l{y}_{m_l\left(i\right)}+S_s{y}_{m_s\left(i\right)}\≤d_{\mathrm{ij}}$ And similarly analyze and get final product, but the mathematical formulae described in example, result of calculation, various form and application process are applicable to the commander's control to all battlefield goods and materials fast and low-risk transportations,

Suppose that certain mechanization combat division must be that 16 tons, average speed per hour are 70 kilometers truck with dead weight capacity, transport the materiel of specified amount from 6 supply centre to 14 demand points, between the supply and demand point transportation meet with risk probability and the supply and demand amount as shown in table 1,

Table 1: transportation meets with risk probability, supply and demand amount (unit: probability, ton) between the mechanization combat division supply and demand point 01 supply centre 02 supply centre 03 supply centre 04 supply centre 05 supply centre 06 supply centre The demand upper limit The demand lower limit 01 demand point, 02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points 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 Can keep supplying limit 100.00 200.00 300.00 400.00 150.00 350.00 Can supply lower limit 100.00 60.00 40.00 10.00 10.00 20.00

The length of transportation route and supply and demand amount are as shown in table 2 between the supply and demand point,

Table 2: transportation route length, supply and demand amount (unit: kilometer, ton) between the mechanization combat division supply and demand point 01 supply centre 02 supply centre 03 supply centre 04 supply centre 05 supply centre 06 supply centre The demand upper limit The demand lower limit 01 demand point, 02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points 37.00 34.00 25.00 14.00 26.00 24.00 120.00 159.00 112.00 62.00 91.00 126.00 90.00 81.00 13.00 25.00 28.00 15.00 35.00 20.00 98.00 138.00 96.00 37.00 66.00 97.00 68.00 56.00 70.00 83.00 108.00 97.00 82.00 110.00 12.00 51.00 96.00 46.00 17.00 81.00 99.00 20.00 74.00 87.00 112.00 101.00 86.00 100.00 129.00 149.00 25.00 50.00 79.00 86.00 104.00 66.00 44.00 31.00 66.00 58.00 56.00 39.00 105.00 145.00 110.00 59.00 73.00 27.00 11.00 75.00 60.00 19.00 56.00 30.00 48.00 65.00 75.00 30.00 69.00 70.00 26.00 65.00 72.00 44.00 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 90.00 30.00 35.00 28.00 36.00 21.00 90.00 130.00 70.00 40.00 60.00 16.00 29.00 36.00 80.00 20.00 25.00 22.00 Can keep supplying limit 100.00 200.00 300.00 400.00 150.00 350.00 Can supply lower limit 100.00 60.00 40.00 10.00 10.00 20.00

According to above-mentioned linear programming and commander controlling models and relevant dual linear programming model, it is as shown in table 3 to calculate mechanization combat division minimum risk transportation command controlling schemes by simplex algorithm, and wherein the ton risk is the risk carrying capacity min Z of demand node _j, risk probability is that the maximum transportation of demand node meets with risk probability p _j, ton kilometre is the goods and materials carrying capacity Z of demand node _j,

Table 3: mechanization combat division minimum risk transportation command controlling schemes (unit: ton, ton risk, probability, ton kilometre,, minute) 01 for point 02 for point 03 for point 04 for point 05 for point 06 for point The ton risk Risk probability Ton kilometre The truck number Need the time Upper limit shadow valency Lower limit shadow valency 01 demand point, 02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points 30.00 70.00 36.00 60.00 64.00 40.00 60.00 36.00 80.00 22.00 29.00 20.00 25.00 21.00 66.00 16.00 0.468 0.399 2.430 2.940 1.820 0.800 0.720 0.480 0.725 1.656 1.360 0.540 0.275 0.440 0.013 0.019 0.028 0.030 0.026 0.020 0.012 0.030 0.025 0.046 0.017 0.027 0.011 0.020 468.00 399.00 2430.00 2940.00 1820.00 800.00 720.00 480.00 725.00 1656.00 1360.00 540.00 275.00 440.00 3 2 6 9 5 3 4 1 2 3 5 2 2 2 11.14 16.29 24.00 25.71 22.29 17.14 10.29 25.71 21.43 39.43 14.57 23.14 9.43 17.14 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00 Add up to 100.00 200.00 198.00 29.00 45.00 103.00 15.053 0.046 15053.00 49 39.43 ^* Quantity available 100.00 200.00 300.00 400.00 150.00 350.00 For the back surplus 0.00 0.00 102.00 371.00 105.00 247.00 Upper limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00 Lower limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00

* finish the minimum time that transport task needs

By option control command (table 3) is analyzed as can be known; the truck that finishing transport task needs adds up to 49; time is 39.43 minutes; the truck that 01～06 supply centre needs is respectively 11; 16; 14; 2; 4 and 12; therefore must be to 02; 03 and 06 supply centre implements to lay special stress on protecting; further analyze as can be known; transporting 36 tons of 39.43 minutes that goods and materials spent from 03 supply centre to 10 demand points is bottlenecks that the whole transport task of restriction is finished sooner; this transports also is simultaneously the bottleneck that reduces the risk probability of finishing all battlefield goods and materials transportation experiences; if finish the transportation of this part goods and materials with helicopter; then can be shortened to 25.71 minutes the time of finishing whole transport task; reduction is 34.80%; risk probability is reduced to 0.030 from 0.046; reduction is 34.78%

From to demand constraint condition D _v(v=1,18) analysis of shadow price as can be known, the size of price has truly reflected the complexity that the related constraint condition satisfies, shadow price is 0 to be meant in specific span, relevant constraint condition does not constitute influence to target function value, the easiest to be satisfied, promptly this resource is not in short supply, if increase this resource again the optimal value of objective function is further reduced, again for example, in order to satisfy constraint condition D ₁₀, the risk of transporting goods and materials to 10 demand points is 0.046,39.43 minutes consuming time, the shadow price of this constraint condition is a maximal value 37, illustrates that this condition is the most difficult to satisfy, can be by D with similar method _vThe complexity that satisfies, from difficulty to easy ordering: D ₁₀, D ₈, D ₁₆, D ₅, D ₃, D ₉..., to supply constraint condition S _u(u=19 ..., 29) analysis of shadow price as can be known, their shadow price is 0, therefore, in specific span, changes S _uValue target function value is not constituted influence, must be pointed out that shadow price is not changeless, can be along with D _vAnd S _uVariation and change, make the resource that does not constitute influence originally become influential resource, by analysis to shadow price, can adjust constraint condition targetedly, reach the purpose that reduces risk, carrying capacity and haulage time, because shadow price is the result who obtains under specific constraint condition, only in its valid interval, price just has relative stability

From finish the work the back each supply centre tank farm stock as can be seen, the stock in storage of 02 supply centre exhausts, obviously on the low side, and the stock in storage amount of 04 supply centre is obviously bigger than normal, and according to the antithesis analysis, the shadow price of their constraint condition is 0, this statement of facts: if there are more goods and materials 02 supply centre, there are goods and materials still less 04 supply centre, just may obtain better movement 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 of the mechanization combat division minimum risk transportation of obtaining is as shown in table 4,

Table 4: the improvement project of mechanization combat division minimum risk transportation (unit: ton, ton risk, probability, ton kilometre,, minute) 01 for point 02 for point 03 for point 04 for point 05 for point 06 for point The ton risk Risk probability Ton kilometre The truck number Need the time Upper limit shadow valency Lower limit shadow valency 01 demand point, 02 demand point, 03 demand point, 04 demand point, 05 demand point, 06 demand point, 07 demand point, 08 demand point, 09 demand point, 10 demand points, 11 demand points, 12 demand points, 13 demand points, 14 demand points 30.00 70.00 36.00 60.00 130.00 40.00 36.00 60.00 80.00 22 29.00 20.00 25.00 21.00 16.00 0.468 0.399 2.430 1.950 1.820 0.800 0.720 0.480 0.725 1.332 1.360 0.540 0.275 0.440 0.013 0.019 0.028 0.015 0.026 0.020 0.012 0.030 0.025 0.037 0.017 0.027 0.011 0.020 468.00 399.00 2430.00 1950.00 1820.00 800.00 720.00 480.00 725.00 1332.00 1360.00 540.00 275.00 440.00 3 2 6 9 3 3 4 1 2 3 5 2 2 2 11.14 16.29 24.00 12.86 22.29 17.14 10.29 25.71 21.43 31.71 14.57 23.14 9.43 17.14 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 0.00 0.00 0.00 0.00 13.00 19.00 25.00 14.00 26.00 20.00 12.00 30.00 25.00 37.00 17.00 27.00 11.00 20.00 Add up to 100.00 302.00 162.00 29.00 45.00 37.00 13.739 0.037 13739.00 49 31.71 ^* Quantity available 100.00 400.00 300.00 200.00 150.00 350.00 For the back surplus 0.00 98.00 138.00 171.00 105.00 313.00 Upper limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00 Lower limit shadow valency 0.00 0.00 0.00 0.00 0.00 0.00

* finish the minimum time that transport task needs

Analysis by his-and-hers watches 4 as can be known, the risk of finishing transport task is 0.037, amount of decrease is 19.57%, the time that needs shortens to 31.71 minutes, amount of decrease is 19.58%, the overall risk carrying capacity is reduced to 13.739 tons of risks, amount of decrease is 8.73%, total carrying capacity is reduced to 13739 ton kilometres, amount of decrease is 8.73%, antithesis the analysis showed that: shadow price is without any variation, but the scheme after improving is better, therefore, can also carry out reasonable configuration to the goods and materials of each supply centre, realize the Optimal Management of tank farm stock with said method.