CN105809291A - Public electric bicycle system operation mode design method - Google Patents

Abstract

The invention discloses a public electric bicycle system operation mode design method. The method comprises the steps of: 1) obtaining basic materials of a city planning to establish a public electric bicycle system; 2) establishing and solving an operation main body optimal combination model based on 0-1 integer programming, and determining the operation main body of the public electric bicycle system under the target of government investment minimization; 3) establishing and solving a commercial resource distribution model based on dynamic programming, and determining an optimal distribution scheme of commercial resources under the target of enterprise profit maximization; and 4) according to the solving results of the 2) and 3) and combined with the practical condition of the city planning to establish the public electric bicycle system, carrying out detailed operation mode design. According to the invention, the new method is provided for the design of the operation mode of the public electric bicycle system, the precision and the reliability of public electric bicycle system operation mode design are improved, the establishing work of the urban public electric bicycle system is effectively promoted, and the method has practical popularization value.

Description

A kind of public electronic bicycle system operation mode method for designing

Technical field

The present invention relates to urban traffic control field, refer in particular to a kind of based on Zero-one integer programming model public electronic Bicycle operation mode method for designing.

Background technology

Public bicycles system is worldwide risen in recent years, becomes the main traffic of the short distance trip in many cities Share mode.But bicycle mode itself expends muscle power, rides apart from limited, in China's part, particularly south tier 2 cities Experience of riding is the best, is the most day by day substituted by the electric bicycle of the most comfortable, laborsaving, low-carbon (LC), distance of riding.But, many The appearance of many electric bicycles also brings an a lot of difficult problem to urban traffic control: electric bicycle violation phenomenon is many, accident rate Height, all brings greatly interference to motor vehicles and pedestrian traffic, and China's electric bicycle management system is the most backward simultaneously, fails Adapt to the new situations of current power bicycle development.Develop public electronic bicycle system, efficent use of resources beyond doubt, meet While resident's low cost low-carbon (LC) trip requirements, one of feasible way that electric bicycle is effectively managed.

The at present both at home and abroad research to public electronic bicycle system operation mode be still blank, more concentrates on public The discussion of bicycle system.The mode that He Bo, Lu Qing et al. buy according to perfect market, market segment and government's tradition is entered Row sort research.Jiang Tianwen, Diao Shenghuan, Zeng Runxi then think public bicycles operation mode be divided into private enterprise's construction mode, Government's traditional purchase model and PPP pattern.Current public bicycles system operation pattern cuts both ways, and in practice, operation The dividing mode of pattern is also and nisi.It is visible, if current class can be changed in electric bicycle operation mode designs Operation mode method for designing single under system, finds and more meets the synthesized modeling that in practice, treatment in accordance with local conditions flexible design requires.

The present invention will set up based on 0-on the basis of induction and contrast domestic and international public bicycles system typical case's operation mode Subject of operation's optimum combined model of 1 integer programming and commercial resource based on dynamic programming distribution model, thus obtain one Public electric bicycle operation mode method for designing based on Zero-one integer programming model.

Summary of the invention

It is an object of the invention to overcome the shortcoming and defect of prior art, it is provided that a kind of based on Zero-one integer programming model Public electronic bicycle system operation mode method for designing, break through conventional empirically design public electric bicycle operation The method of pattern so that the design more science of public electric bicycle operation mode, builds public electronic bicycle system If playing great impetus.

For achieving the above object, technical scheme provided by the present invention is: a kind of public electronic bicycle system operation mould Formula method for designing, comprises the following steps:

1) obtain and plan to build the basic data in city of vertical public electronic bicycle system, altogether include the data of three aspects: Public electronic bicycle system cost budgeting data, government department for public electronic bicycle system financial budget data, Didding enterprise related data；

2) set up and solve management body optimum combined model based on Zero-one integer programming, determining that governmental input minimizes The management body of public electronic bicycle system under target；

3) set up and solve commercial resource based on dynamic programming distribution model, determining that enterprise getting profit maximizes business under target The optimal distributing scheme of industry resource；

4) according to step 2) and step 3) solving result, in conjunction with the reality in the city planning to build vertical public electronic bicycle system Border situation, carries out detailed operation mode design.

In step 2) in, set up and solve management body optimum combined model based on Zero-one integer programming, determine that government throws Enter to minimize the management body of public electronic bicycle system under target, comprise the steps of:

2.1) decision variable is determined:

I, j, k, l are respectively construction fund, construction work, budgets for operation and the i-th of operation operation, j, k, l potential confession To main body, i=0 represents government, and i ≠ 0 represents enterprise；

n_i(i=1,2,3,4) it is the number of system each factor supply main body；

F_ci、F_oj、O_ck、O_olBe respectively the construction fund of i-th potential supply main body offer, jth potential supply main body carries The equivalent fund of construction work amount, the l potential supply main body that the budgets for operation of confession, kth potential supply main body provide carry The equivalent fund of the operation workload of confession；

F_ct、F_ot、O_ct、O_otThe construction fund of government's offer, managed fund, the equivalent fund of construction work, management are provided The maximum of the equivalent fund of operation；

F is construction fund and the equivalent fund sum of construction work amount of public electronic bicycle system construction needs；

O is the budgets for operation that public electronic bicycle system construction needs and the equivalent fund sum runing workload；

The equivalent fund sum of the resource that R can provide for each factor supply main body for government；

x_am={ 0,1}；(a=1,2,3,4；M=i, j, k, l), work as x_am=1, this main body is as the supplying party of this key element； Work as x_am=0, this main body is not as the supplying party of this key element；

2.2) object function is determined: object function is that minimization government is building and runing in public electronic bicycle system Input:

Min Z=F_c0+F_o0+O_c0+O_o0···(1)

2.3) constraints is determined:

1. system each factor supply main body the most at least selects the constraints of one:

$\begin{array}{cccc}\underset{i=0}{\overset{n_1}{\Σ}}{x}_{1i}\≥\mathrm{1...}\left(2\right)& \underset{j=0}{\overset{n_2}{\Σ}}{x}_{2j}\≥1;\mathrm{...}\left(3\right)& \underset{k=0}{\overset{n_3}{\Σ}}{x}_{3k}\≥1;\mathrm{...}\left(4\right)& \underset{l=0}{\overset{n_4}{\Σ}}{x}_{4l}\≥1;\mathrm{...}\left(5\right)\end{array}$

②Ge supply subject infusion of financial resources sum needs the constraints of fund no less than system:

$\begin{array}{cc}\underset{i=0}{\overset{n_1}{\Σ}}{x}_{1i}{F}_{ci}+\underset{j=0}{\overset{n_2}{\Σ}}{x}_{2j}{F}_{oj}+R\≥F;\mathrm{...}\left(6\right)& \underset{i=0}{\overset{n_3}{\Σ}}{x}_{3i}{O}_{ci}+\underset{i=0}{\overset{n_4}{\Σ}}{x}_{4i}{O}_{oi}\≥O;\mathrm{...}\left(7\right)\end{array}$

3. governmental input fund is not more than the constraints of government finance budget:

F_c0≤F_ctx₁₀···(8) F_o0≤F_otx₂₀···(9)

O_c0≤O_ctx₃₀···(10) O_o0≤O_otx₄₀··.(11)

4. the constraints added according to the concrete condition in the city respectively planning to build vertical public electronic bicycle system；

2.4) model solution: model can use implicit enumeration method to solve, in the case of dimension is relatively big, uses QM for Integer programming module in Windows software solves；

2.5) solving result is explained, determine the supply subject of the public each key element of electronic bicycle system.

In step 3) in, set up and solve commercial resource based on dynamic programming distribution model, determine that enterprise getting profit is maximum Change the optimal distributing scheme of commercial resource under target, comprise the steps of:

3.1) static problem is converted into dynamic problem: the process of government allocated commercial resource be divided into by the number of enterprise N each stage, process according to sequencing distribution commercial resource, then be defined as follows variable:

R_kFor government allocated to the equivalent fund of the resource of kth enterprise；

S_kFor government allocated to the equivalent fund of the resource of kth enterprise to the n-th enterprise；

f_k+1(S_k) be government be S by equivalence fund_kResource distribute to kth to maximum profit during the n-th enterprise；

g_k(R_k) equivalence fund is R by government_kResource profit when distributing to kth enterprise；

3.2) fundamental equation of dynamic programming problems is determined:

$\left\{\begin{array}{c}{f}_k\left(S_k\right)=\underset{0\≤R_k\≤S_k}{\max }\left\{g_k\right(R_k)+f_{k+1}(S_k-R_k\left)\right\}\mathrm{...}\left(12\right)\\ f_{n+1}\left(S_{n+1}\right)=\mathrm{0........................}\left(13\right)\\ k=n,n-1,\mathrm{...},2,\mathrm{1..................}\left(14\right)\end{array}\right.$

In the model, (12) are state transition equation, represent that each enterprise getting profit is maximum；(13) it is boundary condition；(14) Represent the numbering of enterprise；

3.3) model solution: the method that the employing of this model starts backstepping the most forward from the last stage solves；Asking In the case of topic dimension is relatively big, use QM for DOS software or Program；

3.4) solving result is explained, determine the optimal distributing scheme of the commercial resource that government provides.

The present invention compared with prior art, has the advantage that and beneficial effect:

The present invention, on the basis of induction and contrast domestic and international public bicycles system typical case's operation mode, sets up based on 0-1 Subject of operation's optimum combined model of integer programming and commercial resource based on dynamic programming distribution model, thus obtain a kind of base Public electric bicycle operation mode method for designing in Zero-one integer programming model.First to public electronic bicycle system Operation mode is studied；First Zero-one integer programming model and dynamic programming model are applied to the design work of operation mode In, it is achieved that the optimum combination of system operation main body and the optimal allocation of commercial resource；Breach conventional operation mode design work The limitation of pure qualitative analysis in work so that operation mode be designed with scientific basis；Can transport flexibly according to the situation of various places Battalion's model, strong adaptability, there is stronger promotional value.

Accompanying drawing explanation

Fig. 1 is the workflow diagram of the present invention

Fig. 2 is public electronic bicycle system operation mode design diagram in embodiment.

Detailed description of the invention

Below in conjunction with specific embodiment, the invention will be further described.

As it is shown in figure 1, the public electric bicycle operation mode method for designing described in the present embodiment, it is based on 0-1 integer Plan model, comprises the following steps:

1) obtain and plan to build the basic data in city of vertical public electronic bicycle system, altogether include the data of three aspects: Public electronic bicycle system cost budgeting data, government department for public electronic bicycle system financial budget data, Didding enterprise related data.Wherein, described public electronic bicycle system cost budgeting data includes building of system Construction needs If the equivalent fund of fund, managed fund, construction work and management operation equivalent fund, can from city public electrical salf-walking The program results file of car system obtains cost budgeting data；Described government department is for the wealth of public electronic bicycle system Political affairs budget data includes can be used in construction fund amount, the pipe that public electronic bicycle system is built in government department's financial budget Reason capital quantity, the equivalent capital quantity of construction work, the equivalent capital quantity of management operation and the equivalent capital quantity of commercial resource, permissible From the annual financial budget of government department is reported, obtain government department provide for the financial budget of public electronic bicycle system Material；The quantity that described didding enterprise related data includes didding enterprise, the construction fund amount that can provide, managed fund amount, build Be provided as the equivalent capital quantity of industry, the management equivalent capital quantity of operation, enterprise get a profit situation this year, fund has situation and government The wish of cooperation and conventional achievement etc., can obtain didding enterprise related data from the tender document of each enterprise.Collect Data is as follows:

Certain tier 2 cities government planning sets up public electronic bicycle system, and the cost budgeting of this system is as shown in table 1 below. In government's financial budget, multipotency provides 80,000,000 yuan and business that equivalent fund is 6,000,000 yuan for public electronic bicycle system Resource.

The public electronic bicycle system cost budgeting of table 1 (unit: ten thousand yuan)

(note: the construction period is First Year the first half)

Having seven enterprises to participate in the bid of project, fund and the workload that each can provide are as shown in table 2 below, Qi Zhongqi Industry C, D, E, F are ready that accepting government uses the mode of Resource exchange service.

Table 2 didding enterprise data (unit: ten thousand yuan)

2) set up and solve management body optimum combined model based on Zero-one integer programming, determining that governmental input minimizes The management body of public electronic bicycle system under target, comprises the following steps:

2.1) decision variable is determined:

I, j, k, l are respectively construction fund, construction work, budgets for operation and the i-th of operation operation, j, k, l potential confession To main body, i=0 represents government, and i ≠ 0 represents enterprise；

n_i(i=1,2,3,4) is the number of system each factor supply main body, individual；

F_ci、F_oj、O_ck、O_olBe respectively the construction fund of i-th potential supply main body offer, jth potential supply main body carries The equivalent fund of construction work amount, the l potential supply main body that the budgets for operation of confession, kth potential supply main body provide carry The equivalent fund of the operation workload of confession, Wan Yuan；

F_ct、F_ot、O_ct、O_otThe construction fund of government's offer, managed fund, the equivalent fund of construction work, management are provided The maximum of the equivalent fund of operation, Wan Yuan；

F is construction fund and the equivalent fund sum of construction work amount of public electronic bicycle system construction needs, ten thousand Unit；

O is the budgets for operation that public electronic bicycle system construction needs and the equivalent fund sum runing workload, ten thousand Unit；

The equivalent fund sum of the resource that R can provide for each factor supply main body for government, Wan Yuan.

x_am={ 0,1}；(a=1,2,3,4；M=i, j, k, l), work as x_am=1, this main body is as the supplying party of this key element； Work as x_am=0, this main body is not as the supplying party of this key element.

2.2) object function is determined: object function is that minimization government is building and runing in public electronic bicycle system Input:

Min Z=F_c0+F_o0+O_c0+O_o0···(1)

2.3) constraints is determined: this model comprises four class constraintss.

1. system each factor supply main body the most at least selects the constraints of one:

$\begin{array}{cccc}\underset{i=0}{\overset{n_1}{\Σ}}{x}_{1i}\≥\mathrm{1...}\left(2\right)& \underset{j=0}{\overset{n_2}{\Σ}}{x}_{2j}\≥1;\mathrm{...}\left(3\right)& \underset{k=0}{\overset{n_3}{\Σ}}{x}_{3k}\≥1;\mathrm{...}\left(4\right)& \underset{l=0}{\overset{n_4}{\Σ}}{x}_{4l}\≥1;\mathrm{...}\left(5\right)\end{array}$

②Ge supply subject infusion of financial resources sum needs the constraints of fund no less than system:

$\begin{array}{cc}\underset{i=0}{\overset{n_1}{\Σ}}{x}_{1i}{F}_{ci}+\underset{j=0}{\overset{n_2}{\Σ}}{x}_{2j}{F}_{oj}+R\≥F;\mathrm{...}\left(6\right)& \underset{i=0}{\overset{n_3}{\Σ}}{x}_{3i}{O}_{ci}+\underset{i=0}{\overset{n_4}{\Σ}}{x}_{4i}{O}_{oi}\≥O;\mathrm{...}\left(7\right)\end{array}$

3. governmental input fund is not more than the constraints of government finance budget:

F_c0≤F_ctx₁₀···(8)F_o0≤F_otx₂₀···(9)

O_c0≤O_ctx₃₀···(10)O_o0≤O_otx₄₀···(11)

4. the constraints added according to the concrete condition in the city respectively planning to build vertical public electronic bicycle system.

2.4) model solution: this model can use implicit enumeration method to solve.In the case of dimension is relatively big, QM can be used Integer programming module in for Windows software solves.

2.5) solving result is explained, determine the supply subject of the public each key element of electronic bicycle system.

Result of calculation is as shown in table 3 below.

The public electronic bicycle system supply subject of table 3 selects result

3) set up and solve commercial resource based on dynamic programming distribution model, determining that enterprise getting profit maximizes business under target The optimal case of industry resource distribution, comprises the following steps:

3.1) static problem is converted into dynamic problem: the process of government allocated commercial resource be divided into by the number of enterprise N each stage, process according to certain sequencing distribution commercial resource, then be defined as follows variable:

R_kFor government allocated to the equivalent fund of the resource of kth enterprise；

S_kFor government allocated to the equivalent fund of the resource of kth enterprise to the n-th enterprise；

f_k+1(S_k) be government be S by equivalence fund_kResource distribute to kth to maximum profit during the n-th enterprise；

g_k(R_k) equivalence fund is R by government_kResource profit when distributing to kth enterprise；

3.2) fundamental equation of dynamic programming problems is determined:

$\left\{\begin{array}{c}{f}_k\left(S_k\right)=\underset{0\≤R_k\≤S_k}{\max }\left\{g_k\right(R_k)+f_{k+1}(S_k-R_k\left)\right\}\mathrm{...}\left(12\right)\\ f_{n+1}\left(S_{n+1}\right)=\mathrm{0........................}\left(13\right)\\ k=n,n-1,\mathrm{...},2,\mathrm{1..................}\left(14\right)\end{array}\right.$

In the model, (12) are state transition equation, represent that each enterprise getting profit is maximum；(13) it is boundary condition；(14) Represent the numbering of enterprise.

3.3) model solution: this model can use and start the method for backstepping the most forward from the last stage and solve. In the case of problem dimension is relatively big, QM for DOS software or Program can be used.

3.4) solving result is explained, determine the optimal distributing scheme of the commercial resource that government provides.

It is calculated two optimal distributing schemes: (1) enterprise C distributes 1,000,000 yuan, enterprise D distributes 1,000,000 yuan, enterprise E divides Join 2,000,000 yuan, enterprise F distribute 2,000,000 yuan；(2) enterprise C distribute 1,000,000 yuan, enterprise D distribute 2,000,000 yuan, enterprise E distribution 200 Wan Yuan, enterprise F distribute 1,000,000 yuan.

4) according to step 2) and step 3) solving result, in conjunction with the reality in the city planning to build vertical public electronic bicycle system Border situation, carries out detailed operation mode design.Operation mode design result such as Fig. 2 institute of the public electronic bicycle system in this city Showing, in figure, dotted arrow represents that government gives to replace the equivalent fund of the commercial resource of service enterprise.

In sum, after using above scheme, the present invention is that the design of public electronic bicycle system operation mode carries Supply new method, it is possible to be effectively improved the accuracy and reliability of public electronic bicycle system operation mode design, effectively Promote the building-up work of the public electronic bicycle system in relevant city, there is actual promotional value, be worthy to be popularized.

The examples of implementation of the above are only the preferred embodiments of the invention, not limit the enforcement model of the present invention with this Enclose, therefore the change that all shapes according to the present invention, principle are made, all should contain within the scope of the present invention.

Claims (4)

1. a public electronic bicycle system operation mode method for designing, it is characterised in that comprise the following steps:

1) obtain the basic data in the city planning to build vertical public electronic bicycle system, altogether include the data of three aspects: public Electric bicycle system cost budget data, government department are for the financial budget data of public electronic bicycle system, bid Enterprise's related data；

2) set up and solve management body optimum combined model based on Zero-one integer programming, determining that governmental input minimizes target Under the management body of public electronic bicycle system；

3) set up and solve commercial resource based on dynamic programming distribution model, determining that enterprise getting profit maximizes business money under target The optimal distributing scheme in source；

4) according to step 2) and step 3) solving result, in conjunction with the actual feelings in the city planning to build vertical public electronic bicycle system Condition, carries out detailed operation mode design.

The public electronic bicycle system operation mode method for designing of one the most according to claim 1, it is characterised in that: Step 1) in, described public electronic bicycle system cost budgeting data includes the construction fund of system Construction needs, management money Gold, the equivalent fund of construction work and the equivalent fund of management operation, the program results of public electronic bicycle system from city File obtains cost budgeting data；Described government department includes political affairs for the financial budget data of public electronic bicycle system Mansion department financial budget can be used in the construction fund amount of public electronic bicycle system construction, managed fund amount, build and make The equivalent capital quantity of industry, the equivalent capital quantity of management operation and the equivalent capital quantity of commercial resource, from the annual wealth of government department Political affairs budget message obtains government department's financial budget data for public electronic bicycle system；Described didding enterprise is correlated with The quantity that data includes didding enterprise, the construction fund amount that can provide, managed fund amount, the equivalent capital quantity of construction work, Manage the equivalent capital quantity of operation, enterprise gets a profit situation this year, fund has wish and the conventional industry that situation is cooperated with government Achievement, obtains didding enterprise related data from the tender document of each enterprise.

The public electronic bicycle system operation mode method for designing of one the most according to claim 1, it is characterised in that Step 2) in, set up and solve management body optimum combined model based on Zero-one integer programming, determine that governmental input minimizes mesh The management body of public electronic bicycle system under mark, comprises the steps of:

2.1) decision variable is determined:

I, j, k, l are respectively construction fund, construction work, budgets for operation and the i-th of operation operation, j, k, l potential supply master Body, i=0 represents government, and i ≠ 0 represents enterprise；

n_i(i=1,2,3,4) it is the number of system each factor supply main body；

F_ci、F_oj、O_ck、O_olBe respectively the construction fund of i-th potential supply main body offer, jth potential supply main body provides The offer of the equivalent fund of construction work amount that budgets for operation, kth potential supply main body provide, the l potential supply main body The equivalent fund of operation workload；

F_ct、F_ot、O_ct、O_otThe construction fund of government's offer, managed fund, the equivalent fund of construction work, management operation are provided The maximum of equivalent fund；

F is construction fund and the equivalent fund sum of construction work amount of public electronic bicycle system construction needs；

O is the budgets for operation that public electronic bicycle system construction needs and the equivalent fund sum runing workload；

The equivalent fund sum of the resource that R can provide for each factor supply main body for government；

x_am={ 0,1}；(a=1,2,3,4；M=i, j, k, l), work as x_am=1, this main body is as the supplying party of this key element；Work as x_am =0, this main body is not as the supplying party of this key element；

2.2) object function is determined: object function is that minimization government is in the throwing built and run in public electronic bicycle system Enter:

Min Z=F_c0+F_o0+O_c0+O_o0…(1)

2.3) constraints is determined:

1. system each factor supply main body the most at least selects the constraints of one:

$\begin{array}{cccc}\underset{i=0}{\overset{n_1}{\Σ}}{x}_{1i}\≥1...\left(2\right)& \underset{j=0}{\overset{n_2}{\Σ}}{x}_{2j}\≥1;...\left(3\right)& \underset{k=0}{\overset{n_3}{\Σ}}{x}_{3k}\≥1;...\left(4\right)& \underset{l=0}{\overset{n_4}{\Σ}}{x}_{4l}\≥1;...\left(5\right)\end{array}$

②Ge supply subject infusion of financial resources sum needs the constraints of fund no less than system:

$\begin{array}{cc}\underset{i=0}{\overset{n_1}{\mathrm{\Σ}}}{x}_{1i}{F}_{ci}+\underset{j=0}{\overset{n_2}{\mathrm{\Σ}}}{x}_{2j}{F}_{oj}+R\≥F;...\left(6\right)& \underset{i=0}{\overset{n_3}{\mathrm{\Σ}}}{x}_{3i}{O}_{ci}+\underset{i=0}{\overset{n_4}{\mathrm{\Σ}}}{x}_{4i}{O}_{oi}\≥O;...\left(7\right)\end{array}$

3. governmental input fund is not more than the constraints of government finance budget:

F_c0≤F_ctx₁₀…(8) F_o0≤F_otx₂₀…(9)

O_c0≤O_ctx₃₀…(10) O_o0≤O_otx₄₀…(11)

4. the constraints added according to the concrete condition in the city respectively planning to build vertical public electronic bicycle system；

2.4) model solution: model can use implicit enumeration method to solve, in the case of dimension is relatively big, uses QM for Integer programming module in Windows software solves；

2.5) solving result is explained, determine the supply subject of the public each key element of electronic bicycle system.

The public electronic bicycle system operation mode method for designing of one the most according to claim 1, it is characterised in that Step 3) in, set up and solve commercial resource based on dynamic programming distribution model, determine that enterprise getting profit maximizes business under target The optimal distributing scheme of industry resource, comprises the steps of:

3.1) static problem is converted into dynamic problem: be divided into n each by the number of enterprise the process of government allocated commercial resource Stage, process according to sequencing distribution commercial resource, then be defined as follows variable:

R_kFor government allocated to the equivalent fund of the resource of kth enterprise；

S_kFor government allocated to the equivalent fund of the resource of kth enterprise to the n-th enterprise；

f_K+1(S_k) be government be S by equivalence fund_kResource distribute to kth to maximum profit during the n-th enterprise；

g_k(R_k) equivalence fund is R by government_kResource profit when distributing to kth enterprise；

3.2) fundamental equation of dynamic programming problems is determined:

$\left\{\begin{array}{c}{f}_k\left(S_k\right)=\underset{0\≤R_k\≤S_k}{\max }\left\{g_k\left(R_k\right)+f_{k+1}\left(S_k-R_k\right)\right\}\mathrm{...}\left(12\right)\\ f_{n+1}\left(S_{n+1}\right)=\mathrm{0..............................................}\left(13\right)\\ k=n,n-1,...,2,\mathrm{1..........................................}\left(14\right)\end{array}\right.$

In the model, (12) are state transition equation, represent that each enterprise getting profit is maximum；(13) it is boundary condition；(14) represent The numbering of enterprise；

3.3) model solution: the method that the employing of this model starts backstepping the most forward from the last stage solves；Tie up in problem In the case of number is relatively big, use QM for DOS software or Program；

3.4) solving result is explained, determine the optimal distributing scheme of the commercial resource that government provides.