CN108564219A - train operation section seat price optimization control method - Google Patents
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Abstract
The present invention relates to train operation economic benefit control methods.The invention discloses a kind of train operation section seat Price optimization control methods.A, according to the bus stop click and sweep sectional of train running interval；B, the price gear number of each section is set, each section price gear number is not exactly the same；C, optimization programming model is established, seat resource constraint is set；D, each section price gear number maximum value is determinedOther OD section price gear numbersWhen, it is also configured to FMax；E, optimization programming model is established according to the condition of step d settings, and model is modified to obtain the equivalent maximum gain of train.This invention simplifies calculating, and computer is facilitated to carry out Modeling Calculation.When being highly suitable for passenger train difference section scale of price quantity being freely set, the computer expression problem of each matrix in plan model is solved.
Description
Technical field
The present invention relates to train operation economic benefit control methods, in particular to train operation section seat price
Optimal control method.
Background technology
Currently, there is a few countries railway such as the U.S., Germany, France to perform multi gear admission fee.It is beautiful from the point of view of disclosed document
The states such as state, France execute train number each OD (Origin-Destination) section of multi gear admission fee all simultaneously using identical more
Shelves admission fee strategy.In addition, network-type airline, each sections OD are equally multi gear admission fees.And Chinese high ferro network prosperity, respectively
A OD sections face different market competition environments, some OD sections face the competing of other means of transportation (aviation, bus) fierceness
It strives, some sections are then monopolized by high ferro completely, if that when executing multi gear admission fee to attract passenger flow, each OD sections just should
There is different admission fee strategies, should then execute multi gear admission fee than the section if any market competition, attract Price Sensitive passenger, stroke
Distance is shorter, and the section demand price that high ferro plays leading position is then nonelastic, can directly execute the fixation admission fee of national regulation, obtain
Take optimal income.
Train is fixed by multiple websites, single train seat storage resources, the operational research of the optimal available classics of income
Model acquires.Uniformly establish the Optimized model of each section multi gear price.For example G1 train numbers, circuit share Beijing, Jinan, south
Capital, four, Shanghai website, including following 6 OD sections：
[Beijing-Jinan], [Beijing-Nanjing], [Beijing-Shanghai]；[Jinan-Nanjing], [Jinan-Shanghai]；[on Nanjing-
Sea].
If 3 grades of prices are arranged in each section, operational research Optimized model can be established：
Maximizing：
Constraints is：A·XODF≤Cl, to any single section l； (2)
0≤XODF≤EDODF, to any ODF； (3)
Wherein, formula (1) indicates that total revenue maximizes expression formula.ODF represents F grades of section OD price gear numbers；fODFFor OD
F grades of prices of section；XODFThe number of positions of certain ODF is distributed in expression；EDODFIndicate the requirement forecasting value to certain ODF.
Formula (2) indicates that the passenger number on each single section is no more than train seating capacity quantity.A=(aij) m × n be association square
Battle array indicates the relationship of ODF and section position resource；If certain product j occupies resource i, then aij=1, if being not take up resource i,
Then aij=0；J-th of column vector A of matrix AjExpression product j is associated with situation with resource；M is the number of product j, i.e. ODF's
Number；N is the number of resource i, i.e., single the number of sections subtract 1 equal to train bus stop quantity；
Formula (3) indicates that the demand of each ODF is more than 0 and is less than or equal to requirement forecasting value.
Such Optimized model is easily set up, and formula (1), formula (2), formula (3) may be designed to matrix, and receive
Enter computer modeling calculating.
Still by taking G1 train numbers as an example, setting website Beijing is 1, Jinan 2, Nanjing 3, Shanghai 4, f in formula (1)ODFIt can
Become matrix：
[f121 f122 f123 f131 f132 f133 f141 f142 f143 f231 f232 f233 … f341 f342 f343]
Equally, XODFSimilar conversion can also be done, formula (2) and formula (3) can also make the conversion of matrix.
If it is required that 3 grades of prices are arranged in section [Beijing-Shanghai], other 5 sections all only have one grade of regular price.So
Optimized model above is as follows：
Maximizing：
Constraints：A·XODF≤Cl, to any single section l； (5)
0≤XODF≤EDODF, to any ODF. (6)
Or 3, it is 3 when [Beijing, the Shanghai] OD=, remaining is 1 (7)
Wherein, when OD is [Beijing, Shanghai], there is third gear price, other sections only have one grade of price, and such model is not
Convenient type (4), formula (5), formula (6) are converted into matrix.Particularly, if train is more by website, each section price gear number
Arbitrary setting, is all had any problem with matrix come expression formula (4), formula (5) and formula (6), the especially incidence matrix A in formula (5) is most
For difficulty, and then influences computer modeling and calculate.
Invention content
The main purpose of the present invention is to provide a kind of train operation section seat Price optimization control methods, simplify and calculate
Method facilitates computer to carry out Modeling Calculation.
To achieve the goals above, according to the one side of the specific embodiment of the invention, a kind of train operation is provided
Section seat Price optimization control method, which is characterized in that include the following steps：
A, according to the bus stop click and sweep sectional of train running interval；
B, the price gear number of each section is set, each section price gear number is not exactly the same；
C, optimization programming model is established, seat resource constraint is：
A·XODF≤Cl, the section l between any adjacent sites
The expression formula indicates that the passenger number on each single section is no more than train seating capacity quantity；
Wherein, OD (Origin-Destination) indicates the beginning and the end section that train serves the passengers；ODF represents section OD valences
F grades of lattice gear number；XODFThe number of positions of certain ODF is distributed in expression；L indicates the section of adjacent sites；ClIt indicates on section l
Total number of positions；A=(aij) m × n be incidence matrix, indicate ODF and section position resource relationship；If certain product j is accounted for
With resource i, then aij=1, if being not take up resource i, aij=0；J-th of column vector A of matrix AjIndicate product j and resource
It is associated with situation；M is the number of product j, the i.e. number of ODF；N is the number of resource i, i.e., single the number of sections are equal to train and stop
Quantity of standing subtracts 1；
D, each section price gear number maximum value is determinedOther OD section price gear numbersWhen, it is also configured to FMax；
E, optimization programming model is established according to the condition of step d setting, and model is modified to obtain train equivalent
Maximum gain.
Further, in step c, optimization programming model is：
Maximizing：
Constraints is：A·XODF≤Cl, to any single section l； (2)
0≤XODF≤EDODF, to any ODF； (3)
Wherein, formula (1) indicates that total revenue maximizes expression formula；For the price gear number of section OD；fODFFor OD sections F
Shelves price；XODFThe number of positions of certain ODF is distributed in expression；EDODFIndicate the requirement forecasting value to certain ODF；Formula (3) indicates each
The demand of ODF is more than 0 and is less than or equal to requirement forecasting value.
Further, step e is specially：
Correct the f in Optimized model formula (1)ODF, there is no ODF section price gear numbers price fODFIt is set as negative normal
It counts, the ODF demand desired values ED being not present in formula (3)ODFIt is set as arbitrary positive value.
Further, step e is specially：
Correct the ED in Optimized model formula (3)ODF, there is no OD sections it is expected demand EDODF0 is set as, in formula (1)
The price f for the ODF section price gear numbers being not presentODFIts value may be configured as arbitrarily determining value.
The effect of the present invention is simplified calculation method, and computer is facilitated to carry out Modeling Calculation.The present invention allows each OD sections
Scale of price quantity is identical, facilitates with computer expression incidence matrix A, is highly suitable for passenger train difference section and freely sets
When setting scale of price quantity, the computer expression problem of each matrix in plan model is solved.And further correction model
So that model solution result is equivalent, be conducive to the optimization running income for obtaining train.
The present invention is described further With reference to embodiment.The additional aspect of the present invention and advantage will be
It gives out in the middle part of following description, partly will become apparent from the description below, or practice through the invention is recognized.
Specific implementation mode
It should be noted that in the absence of conflict, specific implementation mode, embodiment in the application and therein
Feature can be combined with each other.The following contents will now be combined, and the present invention will be described in detail.
In order to make those skilled in the art be better understood from the present invention program, below in conjunction with specific embodiment party of the present invention
Formula, embodiment carry out clear, complete description, it is clear that institute to the technical solution in the specific embodiment of the invention, embodiment
The embodiment of description is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the specific reality in the present invention
Mode, embodiment are applied, those of ordinary skill in the art are obtained every other without making creative work
Embodiment, embodiment should all belong to the scope of protection of the invention.
The train operation section seat Price optimization control method of the present invention, there are two types of Price optimization control methods, respectively
Referred to as price sets negative method and demand zero setting method.The process flow of two methods is described separately below.
One, price sets negative method
According to the bus stop click and sweep sectional of train running interval；
The price gear number of each section is set, and each section price gear number is not exactly the same.Maximum price gear number is Other OD section price gear numbers F*≤FMaxWhen, it is also configured to FMax.In this way, the train maximum revenue mould
Type becomes：
Maximizing：
Constraints is：A·XODF≤Cl, the section l between any adjacent sites； (12)
0≤XODF≤EDODF, to any ODF； (13)
fODF=constant is born, as OD sections F*<F≤FMax (14)
In this way, it is only necessary to the f in amendment type (11)ODF, there is no ODF sections price fODFIt is set as arbitrarily negative normal
Number, the ODF demand desired values ED being not presentODFIt is set as any positive number.To make that formula (11) calculated value is maximum at this time, then dividing
The number of positions X of these ODF being not present of dispensingODFIt is necessarily 0, is equivalent to the ODF and is not present.If these are arranged to be not present
XODFFor positive value, it is evident that being multiplied by fODFThe value of formula (11) can be reduced, solution cannot be optimal.
In this way, each OD sections have identical scale of price quantity, matrix equation in formula (12) has just been easily set up,
Calculation process is carried out as conventional Programming Problems in Operations Research input computer.
Particularly, some commercialization plan model computer softwares calculate above-mentioned model, work as fODFWhen=0, can equally it obtain
XODF=0 optimum results, this is also in the protection category of the present invention.
Two, demand zero setting method
According to the bus stop click and sweep sectional of train running interval；
The price gear number of each section is set, and maximum price gear number isOther section price gear numbers F*
<FMaxWhen, it is also configured to FMax.In this way, train maximum revenue model becomes：
Maximizing：
Constraints is：A·XODF≤Cl, the section l between any adjacent sites； (16)
0≤XODF≤EDODF, to any ODF (17)
EDODF=0, as OD sections F*<F≤FMax (18)
In this way, the f being not present in setting formula (15)ODFValue is set as arbitrary positive value, in formula (17) there is no OD sections
It is expected that demand EDODFIt is set as 0.To meet formula (17) and (18) at this time, then distributing to the positional number for the ODF that these are not present
Measure XODFIt is necessarily 0, is equivalent to the ODF and is not present.
In this way, same reason, each section has identical price gear number, it is easy to set up the matrix side of formula (16)
Journey carries out operation as conventional operational research Solve problems input computer.
Embodiment 1 (linear programming model-price sets negative method)
The west started for 2017 is at high ferro D1917, by Xi'an (website 1), Guangyuan (website 2), Chengdu (website 3), altogether
Three websites.Section partition is：[Xi'an-Chengdu], [Xi'an-Guangyuan] and [Guangyuan-Chengdu], totally 3 sections.[Xi'an-at
All], [Xi'an-Guangyuan] only sets one grade of price, and [Guangyuan-Chengdu] has bus competition, and two grades of prices are arranged.
It is if being not processed total revenue maximization expression formula：
f121·X121+f131·X131+f231·X231+f232·X232 (19)
Constraints is：
0≤XODF≤EDODF (21)
Since only there is two-stage price in Guangyuan-Chengdu to all sections, other sections all only have one grade of price.For domestic big
Amount stops the different train number of website, above constraint equation (20) be inconvenient to be expressed with uniformly regular matrix, not side
Just computer is calculated.
It is as follows that operational research linear programming model is established with first method (price sets negative method)：
Determine each section maximum price gear number, this example FMax=2；
Establish Optimized model
Maximizing：
Constraints：A·XODF≤Cl, the section l between any adjacent sites； (23)
0≤XODF≤EDODF, to any ODF； (24)
fODF=-1, as OD sections F*<F≤FMax (25)
Wherein, formula (22), (25), which merge, is converted into expression matrix：
Maximizing：
Formula (23) is converted into expression matrix：
Formula (24) is converted into expression matrix：
0≤[X121 X122 X131 X132 X231 X231]
≤[ED121 ED122 ED131 ED12 ED231 ED231]
In this way, the price gear number of each section of unified train, is maximized FMax=2, only there is no ODF prices
fODFIt is set as negative value, the ODF demand desired values ED being not presentODFIt routinely predicts or estimates and obtain.Formula (22), formula (23), formula
(24), formula (25) is converted to Matrix Solving, and each element subscript is regular in each matrix, facilitates computer solving.
Embodiment 2：(integer programming model --- demand zero setting method)
To the west of same at high ferro D1917 for, by Xi'an (website 1), Guangyuan (website 2), Chengdu (website 3), totally three
A website.Section partition is：[Xi'an-Chengdu], [Xi'an-Guangyuan] and [Guangyuan-Chengdu], totally 3 sections.[Xi'an-Chengdu],
[Xi'an-Guangyuan] only sets one grade of price, and [Guangyuan-Chengdu] has bus competition, and two grades of prices are arranged.
It is as follows to establish operational research integer programming model：
Determine each section maximum price grade quantity, this example FMax=2；
Establish Optimized model
Maximizing：
Constraints：A·XODF≤Cl, single section l between any adjacent sites； (27)
0≤XODF≤EDODF, to any ODF, XODFFor integer； (28)
EDODF=0, as OD sections F*<F≤FMax (29)
Wherein formula (26) is converted into expression matrix：
Formula (27) is converted into expression matrix：
Formula (28), formula (29) merging are converted into expression matrix：
0≤[X121 X122 X131 X132 X231 X231]≤[ED121 0 ED131 0 ED231 ED231]；
Wherein, XODFFor integer.
In this way, the price gear number of each section of unified train, is maximized FMax=2, only there is no scale of price
Demand desired value is set as 0, and (26), (27), (28) and (29) expression formula is converted to Matrix Solving, and element in each matrix
Subscript is regular, facilitates computer solving.
Claims (4)
1. train operation section seat Price optimization control method, which is characterized in that include the following steps：
A, according to the bus stop click and sweep sectional of train running interval；
B, the price gear number of each section is set, each section price gear number is not exactly the same；
C, optimization programming model is established, seat resource constraint is：
A·XODF≤Cl, the section l between any adjacent sites
The expression formula indicates that the passenger number on each single section is no more than train seating capacity quantity；
Wherein, OD (Origin-Destination) indicates the beginning and the end section that train serves the passengers；ODF represents section OD price shelves
Several F grades；XODFThe number of positions of certain ODF is distributed in expression；L indicates the section of adjacent sites；ClIndicate total on section l
Number of positions；A=(aij) m × n be incidence matrix, indicate ODF and section position resource relationship；If certain product j occupies money
Source i, then aij=1, if being not take up resource i, aij=0；J-th of column vector A of matrix AjExpression product j is associated with resource
Situation；M is the number of product j, the i.e. number of ODF；N is the number of resource i, i.e., single the number of sections are equal to train bus stop number
Amount subtracts 1；
D, each section price gear number maximum value is determinedOther OD section price gear numbersWhen,
It is also configured to FMax；
E, optimization programming model is established according to the condition of step d setting, and model is modified to obtain train equivalent most
Bigization income.
2. train operation section according to claim 1 seat Price optimization control method, which is characterized in that in step c,
Optimization programming model is：
Maximizing：
Constraints is：A·XODF≤Cl, the section l between any adjacent sites； (2)
0≤XODF≤EDODF, to any ODF； (3)
Wherein, formula (1) indicates that total revenue maximizes expression formula；For the price gear number of section OD；fODFFor F grades of valences of OD sections
Lattice；XODFThe number of positions of certain ODF is distributed in expression；EDODFIndicate the requirement forecasting value to certain ODF；Formula (3) indicates each ODF
Demand be more than 0 and be less than or equal to requirement forecasting value.
3. train operation section according to claim 2 seat Price optimization control method, which is characterized in that step e tools
Body is：
Correct the f in Optimized model formula (1)ODF, there is no ODF section price gear numbers price fODFIt is set as negative constant, formula
(3) the ODF demand desired values ED being not present inODFIt is set as arbitrary positive value.
4. train operation section according to claim 2 seat Price optimization control method, which is characterized in that step e tools
Body is：
Correct the ED in Optimized model formula (3)ODF, there is no ODF sections it is expected demand EDODFIt is set as 0, in formula (1) not
The price f of existing ODFODFIts value may be configured as arbitrarily determining value.
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