CN115439181A - Parking space allocation method based on auction mechanism - Google Patents
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Abstract
The invention discloses a parking space allocation method based on an auction mechanism, which comprises the following steps: s1: acquiring a parking space sharing interval, an hourly lease price and a total lease price of a parking space supplier, and generating a parking space supply matrix; s2: acquiring a preferred parking space using interval, a secondary parking space selecting using interval and an hourly use price of a parking space demander, and generating a preferred parking space demand matrix and a secondary parking space demand matrix according to the preferred parking space using interval and the secondary parking space selecting using interval; s3: generating a bidding lease hour price, a bidding lease total price and a bidding use hour price; s4: shared berth allocation is performed. The invention provides a new idea for optimizing parking space sharing and improving the shared market participation willingness of citizens, maximizes the number of parking space demanders and ensures the benefits of parking space suppliers and a parking platform.
Description
Technical Field
The invention belongs to the technical field of intelligent parking, and particularly relates to a parking space allocation method based on an auction mechanism.
Background
The increasing holding of motor vehicles makes the urban parking problem more serious. Due to the fact that parking demands of different business-state parking lots have time differences, the parking supply and demand space-time distribution is staggered, and therefore the utilization rate of the whole parking resources of the city is low.
In order to realize effective utilization of parking resources, parking resource management measures based on parking space sharing and distribution gradually come into the view of the public under the promotion of internet technology and sharing economy. The existing research on parking space sharing is mostly started from multiple angles such as single parking space allocation, multi-parking space allocation, static reservation allocation and dynamic reservation allocation, and a series of effective allocation schemes are provided by researching on the target of optimal perception utility of a user, maximum platform income or regional overall parking space load balance. However, most of the research scenes are that the government or the parking platform purchases parking right for residents at a uniform price and then shares the parking right with the residents in a mode of selling the parking right to the parking demanders at a fixed price. The sharing mode cannot fully consider price cognition of different groups to the shared berths, and has certain limitation. In addition, there is still no research on how to encourage both parking space supply and demand parties to share and carry out fair and reasonable profit distribution for the shared parking interest stakeholders.
Disclosure of Invention
The invention provides a parking space allocation method based on an auction mechanism to solve the problems.
The technical scheme of the invention is as follows: a parking space allocation method based on an auction mechanism comprises the following steps:
s1: acquiring a parking space sharing interval, an hourly lease price and a total lease price of a parking space supplier, and generating a parking space supply matrix according to the parking space sharing interval;
s2: acquiring a preferred parking space using interval, a secondary parking space using interval and an hourly use price of a parking space demander, and generating a preferred parking space demand matrix and a secondary parking space demand matrix according to the preferred parking space using interval and the secondary parking space using interval;
s3: respectively generating a bidding lease hour price and a bidding lease total price according to the lease price per hour and the lease total price, and generating a bidding use hour price according to the use price per hour;
s4: and sharing the parking space according to the parking space supply matrix, the parking space preferred demand matrix, the parking space secondary-selection demand matrix, the bidding lease hour price, the bidding use hour price and the bidding lease total price.
The invention has the beneficial effects that: the invention provides a new idea for optimizing berth sharing and improving the shared market participation willingness of citizens. By designing a berth sharing bilateral auction mechanism, on one hand, berth suppliers with different travel purposes, different education levels and different professions can autonomously set berth lease prices according to self conditions, so that the berth supply quantity is maximized, and the problem of insufficient supply and demand of berths in a film district is solved; on the other hand, the parking position demanders can independently set the use price of the parking position according to the self weight watching degree of the shared parking position obtained at this time, and obtain the use right of the parking position by bidding with other parking position users, so that the number of the parking position demanders is maximized, and the benefits of the parking position suppliers and the parking platform are guaranteed.
Further, in step S1, generating the berthage-offer matrix includes the substeps of:
s11: obtaining parking space sharing time interval T and parking space supply starting time T of parking space supplier i s And a parking space supply termination time T i e ；
S12: dividing the berth sharing time interval T into K time windows and providing a starting time T according to the berth i s And a parking space supply termination time T i e Generating a berth-sharing interval [ T ] i s ,T i e ]；
S13: according to the berth sharing interval [ T i s ,T i e ]And K time windows, generating a berth-supply matrix S M×K 。
The beneficial effects of the above further scheme are: in the invention, the sharable time of the parking space supplier is divided into a plurality of continuous time windows with equal length, so that the model calculation and the management of an operator are facilitated, and when the set time windows are small enough, the allocation can be more flexibly carried out.
Further, in step S13, a parking space supply matrix S M×K The calculation formula of (2) is as follows:
S M×K ＝[s ik ]
wherein s is ik Represents a variable of 0 to 1, T i s Indicates the initial time of berth supply, T i e The system comprises a plurality of auction units, a plurality of auction units and a plurality of time windows, wherein the auction units comprise a berth supply termination time, Z represents an integer set, t represents a divided time interval, i =1,2, \8230, M, K, M represents the number of suppliers participating in auction, and K represents the number of time windows.
Further, in step S2, the generating of the parking space preferred demand matrix and the parking space secondary demand matrix includes the following sub-steps:
s21: initial time for obtaining preferred parking space using of parking space demander
Starting time for secondary berth selection
Preferred parking space use termination time
And the time of stopping the use of the next berth selection
S22: according to the preferred starting time of parking space use
And preferred parking space use termination time
Generating a preferred parking space usage window
According to the starting time of the secondary berth selection
And the time of stopping the use of the next berth selection
Generating a secondary berth-selecting use interval
S23: for the preferred parking space
And the use interval of the next berth selection
Carrying out standardization processing to obtain a standardized preferred parking space
And the standardized use interval of the secondary berth selection
S24: preferred parking space usage intervals based on standardization
And standardizing the use interval of the secondary berth selection
Generating a parking space preferred demand matrix D N×K And berth time selectionMatrix D 'is solved' N×K 。
The beneficial effects of the further scheme are as follows: in the invention, the standardized processing of the using time interval of the demander expands the parking time of the demander to a certain extent, namely, the auction platform reserves part of elastic time for the demander, which is beneficial to reducing overtime parking behavior of the demander; in addition, a first-selection interval and a second-selection interval are set for the demanders, the reservation time of the demanders is allowed to be flexibly adjusted by the platform, and therefore the parking space utilization rate and the winning rate of the demanders are improved.
Further, in step S23, the preferred parking space usage interval is standardized
The calculation formula of (2) is as follows:
wherein,
represents the lower limit of the normalized preferred parking space usage interval,
represents an upper bound on the normalized preferred parking space usage interval,
indicating a preferred starting point of parking space usage,
indicating the preferred parking space use termination time;
standardized use interval for secondary berth selection
The calculation formula of (c) is:
wherein,
represents the lower limit of the normalized secondary berth selection use interval,
represents the upper limit of the normalized secondary berth selection use interval,
indicating the starting time of the secondary berth-selecting use,
indicating the using termination time of the secondary berth selection;
in step S24, the preferred demand matrix D of the berth N×K The calculation formula of (c) is:
D N×K ＝[d jk ]
wherein, d jk Represents a variable of 0 to 1;
berth secondary selection demand matrix D' N×K The calculation formula of (2) is as follows:
D’ N×K ＝[d’ jk ]
wherein d is jk ' denotes a variable 0-1, K =1,2, \ 8230, K, K denotes the number of time windows, and Z denotes an integer set.
Further, in step S3, the rental hour price is bid
The calculation formula of (2) is as follows:
wherein,
the rental price per hour is indicated,
representing a number of supplier violations, η representing a penalty factor;
in step S3, the total price of the bid rental
The calculation formula of (2) is as follows:
wherein,
represents a total rental price;
in step S3, the price of the hour of use is bid
The calculation formula of (c) is:
wherein,
the price of use per hour is indicated,
representing the number of violations by the customer.
The beneficial effects of the above further scheme are: in the invention, the auction platform considers a default punishment mechanism, the default times of the supply and demand parties are recorded into the shared parking credit, and if the default times are more, the auction priority of the platform can be reduced, thereby being beneficial to standardizing the sharing behavior of users.
Further, step S4 comprises the following sub-steps:
s41: respectively generating a preferred required parking space distribution matrix sigma M×N And secondary demand's berth allocation matrix sigma' M×N ；
S42: parking space allocation matrix sigma according to preferred requirements M×N Sub-selection required parking space distribution matrix sigma' M×N The method comprises the following steps of constructing a unit price bidding distribution mode and a total price bidding distribution mode, and determining a disturbance factor of the bidding distribution mode, wherein the unit price bidding distribution mode comprises a berth supply matrix, a berth first-choice demand matrix, a berth second-choice demand matrix, a bidding lease hour price, a bidding use hour price and a bidding lease total price;
s43: respectively calculating the income of a unit price bid distribution mode and the income of a total price bid distribution mode according to the disturbance factors of the bid distribution mode to complete shared berth distribution,
the beneficial effects of the above further scheme are: in the invention, the auction platform sets two bidding strategies of unit price bidding and total price bidding, considers the heterogeneity of sharing time, breaks the limitation of the traditional one-to-one auction, and realizes the matching of 'one-to-many' auction supply and demand under the parking space sharing autonomous pricing scene.
Further, in step S41, the preferred desired parking space allocation matrix σ is selected M×N The calculation formula of (2) is as follows:
σ M×N ＝[δ ij ]
wherein, delta ij Represents a variable of 0 to 1;
in step S41, the secondary selection required berth allocation matrix sigma' M×N The calculation formula of (c) is:
σ’ M×N ＝[δ’ ij ]
wherein, delta' ij Represents a variable of 0 to 1;
in step S42, the constraint conditions of the unit price bid allocation method include a first constraint condition, a second constraint condition, and a third constraint condition; the constraint conditions of the total price bidding distribution mode comprise a first constraint condition, a second constraint condition, a third constraint condition and a fourth constraint condition;
the expression of the first constraint is δ ij ∈{0,1},δ’ ij ∈{0,1}；
The second constraint is expressed as
Wherein M represents the number of suppliers participating in the auction, and N represents the number of demanders participating in the auction;
the expression of the third constraint is
Wherein K represents the number of time windows, s ik Represents a variable of 0 to 1, d jk Denotes a variable of 0 to 1, d' jk Represents a variable of 0 to 1;
the expression of the fourth constraint is
In step S42, the calculation formula of the perturbation factor Δ of the bid allocation scheme is:
Δ＝Δ 1 -Δ 2
wherein, delta 1 Means that the parking space supplier with low price and long sharing time is matched with the long-time parking demand priority, delta 2 The preferred parking interval of the demander is preferentially distributed when the preferred parking interval and the secondary parking interval of the demander meet the requirements, omega represents a minimum coefficient,
indicating a preferred matching supplier with a low bid and a long sharing time,
representing a bid lease hour price;
in step S43, the bid allocation profit maxW of the unit price bid allocation method all1 The calculation formula of (c) is:
wherein,
the price of the bidding use hour is shown, T is a time interval, and T is a berth sharing time period;
in step S43, the total bid allocation method bid allocation profit maxW all2 The calculation formula of (2) is as follows:
wherein, y i Represents a variable of 0 to 1, and,
representing a bid lease total price.
Drawings
FIG. 1 is a flow chart of a method for allocating parking spaces;
FIG. 2 is a diagram of supplier berth allocation in a monovalent bid mode;
FIG. 3 is a diagram of supplier berth allocation in total bid mode.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a parking space allocation method based on an auction mechanism, which includes the following steps:
s1: acquiring a parking space sharing interval, an hourly lease price and a total lease price of a parking space supplier, and generating a parking space supply matrix according to the parking space sharing interval;
s2: acquiring a preferred parking space using interval, a secondary parking space using interval and an hourly use price of a parking space demander, and generating a preferred parking space demand matrix and a secondary parking space demand matrix according to the preferred parking space using interval and the secondary parking space using interval;
s3: respectively generating a bidding lease hour price and a bidding lease total price according to the lease price per hour and the lease total price, and generating a bidding use hour price according to the use price per hour;
s4: and sharing the parking space according to the parking space supply matrix, the parking space preferred demand matrix, the parking space secondary-selection demand matrix, the bidding lease hour price, the bidding use hour price and the bidding lease total price.
In the embodiment of the present invention, in step S1, generating the parking lot provisioning matrix includes the following sub-steps:
s11: obtaining the parking space sharing time T and the parking space supply starting time T of the parking space supplier i s And a parking space supply termination time T i e ；
S12: the berth sharing time interval T is divided into K time windows according toInitial time T of parking space supply i s And a parking space supply termination time T i e Generating a berth-sharing interval [ T ] i s ,T i e ](ii) a The start-stop time of the submission must fall on the time window node, so that the berthage sharing interval can be generated.
S13: according to berth sharing interval [ T ] i s ,T i e ]And K time windows, generating a berth-supply matrix S M×K 。
In the embodiment of the present invention, in step S13, the parking space supply matrix S M×K The calculation formula of (2) is as follows:
S M×K ＝[s ik ]
wherein s is ik Represents a variable of 0 to 1, T i s Indicates the time of the start of parking space supply, T i e The system comprises a plurality of auction units, a plurality of auction units and a plurality of time windows, wherein the auction units comprise a berth supply termination time, Z represents an integer set, t represents a divided time interval, i =1,2, \8230, M, K, M represents the number of suppliers participating in auction, and K represents the number of time windows. When s is ik If =0, it indicates that the parking space provided by the i-th parking space provider is available in the k-th time window. In the same way, s ik =1 indicates that the parking space is not available.
In the step S1, the quotation information is not clear among suppliers in the bidding process, the suppliers only allow one-time bidding, and if the bidding time is not in the right, the qualification of the renting parking space of the current parking space is lost.
In the embodiment of the present invention, in the step S2, the generating of the parking space preferred demand matrix and the parking space secondary preferred demand matrix includes the following sub-steps:
s21: obtaining preferred parking position use starting time of parking position demander
Starting time for secondary berth selection
Preferred parking space use termination time
And the time of stopping the use of the next berth selection
In order to increase the bid rate of the parking demander, the invention allows the demander to submit two time windows;
s22: according to the preferred starting time of parking space use
And preferred parking space use termination time
Generating a preferred parking space usage window
According to the use starting time of the secondary berth selection
And the time of using the secondary parking space
Generating a secondary berth-selecting use interval
S23: for the preferred parking space usage interval
And secondary berth-selecting use interval
Carrying out standardization processing to obtain a standardized preferred parking space
And the standardized use interval of the secondary berth selection
Since the section in which the demander expects to use the shared parking lot is difficult to fall on the specified time window node completely, the section in which the demander uses, which is submitted in S21, needs to be standardized;
s24: based on standardized preferred parking space
And the standardized use interval of the secondary berth selection
Generating a parking space preferred demand matrix D N×K And berth secondary election demand matrix D' N×K 。
In the embodiment of the present invention, in step S23, the preferred parking space usage interval is standardized
The calculation formula of (2) is as follows:
wherein,
represents a lower bound on the normalized preferred parking space usage window,
represents an upper bound on the normalized preferred parking space usage interval,
presentation headThe selected parking space uses the starting time,
indicating the preferred parking space use termination time;
standardized use interval for secondary berth selection
The calculation formula of (2) is as follows:
wherein,
represents the lower limit of the normalized secondary berth selection use interval,
represents the upper limit of the normalized secondary berth selection use interval,
indicating the starting time of the secondary berth-selecting use,
indicating the using termination time of the secondary berth selection;
in step S24, the preferred demand matrix D of the berth N×K The calculation formula of (2) is as follows:
D N×K ＝[d jk ]
wherein d is jk Represents a variable of 0 to 1;
berth secondary selection demand matrix D' N×K The calculation formula of (2) is as follows:
D’ N×K ＝[d’ jk ]
wherein, d jk ' denotes a variable from 0 to 1, K =1,2, \ 8230, K, K denotes the number of time windows, and Z denotes an integer set. When d is jk ,d jk ' =1, this indicates that the jth demander has a parking space using requirement in the kth period, d jk ,d jk And' =0 indicates no berthing requirement.
In the step S2, the price quoting information is not clear among the demanders in the process of price quoting, the demanders only allow one-time price bidding, and if the price bidding is not in the process of price bidding, the using qualification of the parking space is lost.
In the embodiment of the invention, in step S3, after comprehensively considering factors such as supplier shared parking default conditions and the like, the auction platform submits the lease price to be converted into the bid lease price, and if supplier i has default behaviors, the platform submits the lease hour price when the supplier submits the lease hour price
Based on the number of historical defaults
Raising a certain amount, bidding lease hour price
The calculation formula of (2) is as follows:
wherein,
the rental price per hour is indicated,
representing a number of supplier violations, η representing a penalty factor;
in step S3, the total price of the bid rental
The calculation formula of (2) is as follows:
wherein,
represents a total rental price;
in step S3, after comprehensively considering factors such as the payment condition of the demander, the shared parking default condition and the like, the auction platform submits the use price of the demander to convert the use price to obtain the bidding use price. If the demander j has default behavior, the platform will consider that its bid is lower than the offer and the price is lower when it submits the hour of use
Based on the number of historical defaults
Reducing a certain amount and bidding price in use hours
The calculation formula of (2) is as follows:
wherein,
the price of use per hour is indicated,
indicating the number of violations by the customer.
In an embodiment of the present invention, step S4 includes the following sub-steps:
s41: respectively generating a preferred required berthage allocation matrix sigma M×N And secondary demand's berth allocation matrix sigma' M×N ；
S42: berthage allocation matrix sigma according to preferred requirements M×N Sub-selection required parking space distribution matrix sigma' M×N The method comprises the following steps of constructing a unit price bidding distribution mode and a total price bidding distribution mode, and determining a disturbance factor of the bidding distribution mode, wherein the unit price bidding distribution mode comprises a berth supply matrix, a berth first-choice demand matrix, a berth second-choice demand matrix, a bidding lease hour price, a bidding use hour price and a bidding lease total price;
s43: and respectively calculating the income of the unit price bid distribution mode and the income of the total price bid distribution mode according to the disturbance factors of the bid distribution mode, and completing shared berth distribution.
In the embodiment of the present invention, in step S41, the allocation matrix is a decision matrix and represents a matching relationship between the supply and demand parties participating in the auction. If supplier i and requester j match successfully, δ ij Is 1, otherwise is 0. As the platform allows the berthage demanders to submit the preferred secondary selection double intervals, the berthage distribution matrix sigma of the preferred requirements M×N The calculation formula of (2) is as follows:
σ M×N ＝[δ ij ]
wherein, delta ij Represents a variable of 0 to 1;
in step S41, the berth allocation matrix sigma 'of secondary election demand' M×N The calculation formula of (2) is as follows:
σ’ M×N ＝[δ’ ij ]
wherein, delta' ij Represents a variable of 0 to 1;
in step S42, the auction platform allocates shared parking spaces based on two modes, namely, a unit price bid mode and a total price bid mode, with the goal of maximizing social welfare. Wherein the socio-welfare is expressed as the difference between the sum of bids from all bidding winning buyers (parking demanders) and the sum of bids from all bidding winning sellers (parking suppliers). Considering the difference of the bidding habits of the suppliers, the platform designs two modes of unit price bidding and total price bidding, and the income of the suppliers in the unit price bidding mode is the product of the lease hour price and the parking time of all the demanders matched with the lease hour price; whether the supplier matches several demanders in the total bid bidding mode, the income gained by the supplier is invariably the total price of its bid lease. The constraint conditions of the unit price bidding distribution mode comprise a first constraint condition, a second constraint condition and a third constraint condition; the constraint conditions of the total price bidding distribution mode comprise a first constraint condition, a second constraint condition, a third constraint condition and a fourth constraint condition;
the first constraint condition specifies that the distribution matrix of the model is a 0-1 matrix; the second constraint condition constrains the one-to-many relation of supply and demand matching, and indicates that the demander does not have a vehicle moving behavior and the first-choice parking time interval and the second-choice parking time interval cannot be repeatedly allocated; the third constraint condition ensures that no parking time conflict exists among the successfully distributed parking position demanders;
the expression of the first constraint is δ ij ∈{0,1},δ’ ij ∈{0,1}；
The expression of the second constraint is
Wherein M represents the number of suppliers participating in the auction, and N represents the number of demanders participating in the auction;
the expression of the third constraint is
Wherein K represents the number of time windows, s ik Represents a variable of 0 to 1, d jk Represents a variable of 0-1, d' jk Represents a variable of 0 to 1;
the fourth constraint is expressed as
In step S42, in order to avoid the non-unique optimal solution of the supply and demand distribution mode, a perturbation term is introduced, and a calculation formula of a perturbation factor Δ of the bid distribution mode is:
Δ＝Δ 1 -Δ 2
wherein, delta 1 Means to match the low-bid, long-shared parking space supplier with the long-time parking requester preferentially, delta 2 The preferred parking interval of the demander is preferentially distributed when the preferred parking interval and the secondary selection interval of the demander meet the requirements, omega represents a minimum coefficient and can be flexibly selected according to the supply and demand scale,
indicating a preferred matching berth provider with a low bid and a long share time,
represents a bid lease hour price;
in step S43, a bid allocation profit maxW of the unit price bid allocation system all1 The calculation formula of (c) is:
wherein,
the price of the bidding use hour is shown, T is a time interval, and T is a berth sharing time period;
in step S43, the total bid distributorFormula-based bid allocation revenue maxW all2 The calculation formula of (c) is:
wherein, y i Represents a variable of 0 to 1, and,
representing a bid lease total price. y is i For determining whether supplier i wins the bid. If the bidding wins, y i =1, otherwise y i ＝0。
In the present invention, the profit allocation may also be performed by using step S5, specifically:
step S5 includes the following substeps:
s51: calculating the income W of the operator in the parking lot according to the income of the unit price bid distribution mode and the total price bid distribution mode p ；
S52: according to the income W of operators in the parking lot p Calculating the total profit W of the supplier s And overall demander benefit W d ；
S53: according to total benefits W of suppliers s And total benefit W of the demanders d Calculating supplier utility separately
And utility of demanders
S54: according to utility of supplier
And utility of demanders
Calculating actual income P of supplier i s And the actual payment of the demander
And completing the revenue distribution.
In step S51, the parking lot operator profit W p The calculation formula of (c) is:
W p ＝θ·W all
where θ represents parking auction floor score proportional, W all The profit of two bidding distribution modes is shown;
in step S52, the total supplier benefit W s The calculation formula of (2) is as follows:
wherein I represents a supplier rejection rate, and J represents a requester rejection rate;
in step S52, the total benefit W of the consumers d The calculation formula of (2) is as follows:
in step S53, supplier utility
The calculation formula of (2) is as follows:
wherein,
representing the ratio of the reciprocal of the supplier's bid to the sum of the reciprocal of the bid of all winning suppliers,
represents a rental price per hour, M represents the number of suppliers participating in the auction;
in step S53, the utility of the demander
The calculation formula of (c) is:
wherein,
representing the ratio of the demander bid to the sum of all winning bidder bids,
indicating a desired payout of the demander, N indicating the number of demanders participating in the auction;
in step S54, the actual income P of the supplier i s The calculation formula of (2) is as follows:
wherein,
indicating a supplier expected income;
in step S54, the demander actually pays the fee
The calculation formula of (2) is as follows:
the technical solution of the present invention is further illustrated below with reference to examples:
s11, sharing the parking positionsShare period T = [ 7-19 00]Dividing the time interval into a plurality of continuous and equal-length time intervals t =30min to form K =24 time windows; for example, supplier i =1 submits a parking position supply start time T i s =7, end time T i e =18, generating a parking share interval [ 7-00]。
S12, according to the berth sharing interval submitted by the supplier, the berth supply matrixes of all suppliers in the embodiment are
S13, the supplier confirms the rent price per hour according to the expected price
And total rental price
Table 1 shows the hour lease price and total lease price for all suppliers in this embodiment, which is reduced to the product of the hour lease price and the lease hour for ease of calculation.
TABLE 1
S21, the auction platform allows the demander to submit two time windows, and table 2 shows that the preferred parking space use start time, stop time, and the next parking space use start time and stop time of all the demanders in this embodiment, for simplicity, a column "+1 00" is adjusted to represent that the next parking space of the demander is wholly delayed by 1 hour.
TABLE 2
And S22, standardizing the using intervals of the demanders submitted in the S21, and obtaining standardized secondary selection using intervals in the same way, wherein the processed results are shown in a table 3.
TABLE 3
S23, obtaining the first choice/second choice parking position using requirement after the demander is standardized according to the step S22, wherein the parking position first choice requirement matrix in the embodiment is
The secondary selection requirement matrix is
S24, confirming the hourly use price according to the expected price of the demander
And total price of use
Table 4 shows the total price of the hour usage and the total price of the usage of all the demanders in this embodiment, and the total price of the use of the demanders is reduced to the product of the hour usage price and the hour usage for the convenience of calculation.
TABLE 4
S31, according to the formula
Calculating supplier bid lease hour price
Wherein the η penalty factor is 0.2,
indicating the number of default times of supplier, obtaining the total price of the competitive lease with the same reason
As shown in table 5.
TABLE 5
S32, according to the formula
Calculating a price per hour bid for a requester
Wherein the η penalty factor is 0.2,
representing the number of times of the default by the requester as shown in table 6.
TABLE 6
S41, defining a decision variable berthage distribution matrix, and defining a decision variable sigma in a preferred berthage use period as the invention allows a demander to submit 2 berthage use periods M×N = binvar (M, N, 'full'), subsite usage period decision variable σ M×N ' = binvar (M, N, ' full '). Wherein, binvar represents that the decision matrix is a variable from 0 to 1, M and N represent the dimension of the decision matrix, and 'full' represents that the decision matrix is an asymmetric matrix.
And S421, taking the coefficient omega as 0.0001 to ensure that the disturbance term does not influence the social welfare maximum value. The perturbation term Δ is constrained according to the following equation.
S422, the unit price bidding mode can be solved directly according to the branch-bound method, and the allocation situation of the supplier berths is solved as shown in FIG. 2. The number in parentheses for the supplier number indicates the supplier bid for the rental hour price. The striped portion represents the supplier berth non-rental period and the blank represents the out-rentable period. Shaded fill indicates a requester assignment, the first number indicates a requester number, and the first item in parentheses indicates a requester bid hourly price.
S423, the total bid mode can be converted into a problem of M-time linear programming to search for a locally optimal solution, and the assignment of the supplier berths is solved as shown in fig. 3 below. Wherein the value in brackets of the supplier number is the total price bid for the rental supplier. The striped portion represents the supplier berth non-rental period and the blank represents the out-rentable period. Shaded fill indicates a requester assignment, the first number indicates a requester number, and the first item in parentheses indicates a requester bid hourly price.
S51, drawing the platform in proportion of theta =50%, W all (unit price) =210,w p (unit price) =105,W all (total price) =236.72,W p (total price) =118.36.
S52, calculating W s (unit price) =62.05,W d (unit price) =42.95, where I (unit price) =0.3, j (unit price) =0.43333; w is a group of s (total price) =63.13,w d (total price) =55.23, where I (total price) =0.35, j (total price) =0.4.
S53, unit price allocation, supplier utility in total bid mode, and requester utility are shown in tables 7 and 8.
TABLE 7
TABLE 8
S54, basis
The allocation unit price, actual income of the supplier in the total price bidding mode, and actual payment of the requester are shown in tables 9 and 10.
TABLE 9
The invention has the beneficial effects that: the invention provides a new idea for optimizing berth sharing and improving the shared market participation willingness of citizens. By designing a berth sharing bilateral auction mechanism, on one hand, berth suppliers with different travel purposes, different education levels and different professions can independently set berth lease prices according to self conditions, so that the berth supply quantity is maximized, and the problem of insufficient supply and demand of berths in a film district is solved; on the other hand, the parking position demanders can independently set the use price of the parking position according to the self weight watching degree of the shared parking position obtained at this time, and obtain the use right of the parking position by bidding with other parking position users, so that the number of the parking position demanders is maximized, and the benefits of the parking position suppliers and the parking platform are guaranteed.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the invention in its aspects.
Claims (8)
1. A parking space allocation method based on an auction mechanism is characterized by comprising the following steps:
s1: acquiring a parking space sharing interval, an hourly lease price and a total lease price of a parking space supplier, and generating a parking space supply matrix according to the parking space sharing interval;
s2: acquiring a preferred parking space using interval, a secondary parking space using interval and an hourly use price of a parking space demander, and generating a preferred parking space demand matrix and a secondary parking space demand matrix according to the preferred parking space using interval and the secondary parking space using interval;
s3: respectively generating a bidding lease hour price and a bidding lease total price according to the lease price per hour and the lease total price, and generating a bidding use hour price according to the use price per hour;
s4: and sharing the parking space according to the parking space supply matrix, the parking space preferred demand matrix, the parking space secondary-selection demand matrix, the bidding lease hour price, the bidding use hour price and the bidding lease total price.
2. The method for allocating parking spaces based on auction mechanism according to claim 1, wherein said step S1 of generating parking space supply matrix comprises the following substeps:
s11: obtaining parking space sharing time interval T and parking space supply starting time T of parking space supplier i s And a parking space supply termination time T i e ；
S12: the berth sharing time interval T is divided into K time windows, and the initial time T is supplied according to the berth i s And a parking space supply termination time T i e Generating a berth-sharing interval [ T ] i s ,T i e ]；
S13: according to the berth sharing interval [ T i s ,T i e ]And K time windows, generating a berth supply matrix S M×K 。
3. The auction mechanism-based space allocation method according to claim 2, wherein in step S13, the parking space supply matrix S M×K The calculation formula of (2) is as follows:
S M×K ＝[s ik ]
wherein s is ik Represents a variable of 0 to 1, T i s Indicates the time of the start of parking space supply, T i e Indicating a dock supply termination time, Z indicating an integer set, t indicating a time interval of division, i =1,2, \ 8230, M, k =1,2, \8230,k, M represents the number of suppliers participating in the auction, and K represents the number of time windows.
4. The method for allocating parking spaces based on auction mechanism according to claim 1, wherein in step S2, generating the parking space preferred demand matrix and the parking space secondary demand matrix comprises the following substeps:
s21: initial time for obtaining preferred parking space using of parking space demander
Starting time for secondary berth selection
Preferred parking space use termination time
And the time of stopping the use of the next berth selection
S22: according to the preferred starting time of parking space use
And preferred parking space use termination time
Generating a preferred parking space usage window
According to the use starting time of the secondary berth selection
And the time of using the secondary parking space
Generating secondary selectionParking space
S23: for the preferred parking space
And secondary berth-selecting use interval
Carrying out standardization processing to obtain a standardized preferred berth use interval
And the standardized use interval of the secondary berth selection
S24: based on standardized preferred parking space
And standardizing the use interval of the secondary berth selection
Generating a parking place preferred demand matrix D N×K And berth secondary election demand matrix D' N×K 。
5. The method for allocating parking spaces based on auction mechanism of claim 4, wherein in said step S23, the preferred parking space usage interval is standardized
The calculation formula of (2) is as follows:
wherein,
represents a lower bound on the normalized preferred parking space usage window,
represents an upper bound on the normalized preferred parking space usage interval,
indicating a preferred starting point of parking space usage,
indicating the preferred parking space use termination time;
standardized use interval for secondary berth selection
The calculation formula of (c) is:
wherein,
represents the lower limit of the normalized secondary parking space usage interval,
represents the upper limit of the normalized secondary parking space usage interval,
indicating the secondary berth-selection use starting time,
indicating the using termination time of the secondary berth selection;
in the step S24, the preferred demand matrix D of the parking space N×K The calculation formula of (2) is as follows:
D N×K ＝[d jk ]
wherein, d jk Represents a variable of 0 to 1;
berth secondary selection demand matrix D' N×K The calculation formula of (2) is as follows:
D' N×K ＝[d jk ']
wherein, d jk ' denotes a variable 0-1, K =1,2, \ 8230, K, K denotes the number of time windows, and Z denotes an integer set.
6. The method for allocating parking spaces based on auction mechanism of claim 1, wherein in said step S3, the price of bidding lease hour is added
The calculation formula of (2) is as follows:
wherein,
the rental price per hour is expressed,
representing a number of supplier violations, and η representing a penalty factor;
in the step S3, the total price of the bidding lease
The calculation formula of (2) is as follows:
wherein,
represents a total rental price;
in the step S3, the price of the hour of use is bid
The calculation formula of (2) is as follows:
wherein,
the price of use per hour is indicated,
representing the number of violations by the customer.
7. The method for allocating parking spaces based on auction mechanism according to claim 1, wherein said step S4 comprises the following substeps:
s41: respectively generating a preferred required parking space distribution matrix sigma M×N And secondary demand berth allocation matrix sigma' M×N ；
S42: berthage allocation matrix sigma according to preferred requirements M×N And berth allocation matrix sigma 'of secondary selection demand' M×N The method comprises the following steps of constructing a unit price bid allocation mode and a total price bid allocation mode and determining a disturbance factor of the bid allocation mode, wherein the unit price bid allocation mode comprises a berth supply matrix, a berth first-choice demand matrix, a berth second-choice demand matrix, a bid lease hour price, a bid use hour price and a bid lease total price;
s43: and respectively calculating the income of the unit price bidding distribution mode and the income of the total price bidding distribution mode according to the disturbance factors of the bidding distribution mode, and finishing the sharing berth distribution.
8. The method of claim 7, wherein in step S41, a preferred required parking space allocation matrix σ is selected M×N The calculation formula of (2) is as follows:
σ M×N ＝[δ ij ]
wherein, delta ij Represents a variable of 0 to 1;
in the step S41, the berth distribution matrix sigma 'of secondary selection demand' M×N The calculation formula of (2) is as follows:
σ' M×N ＝[δ′ ij ]
wherein, delta' ij Represents a variable of 0 to 1;
in step S42, the constraint conditions of the unit price bid allocation method include a first constraint condition, a second constraint condition, and a third constraint condition; the constraint conditions of the total price bidding distribution mode comprise a first constraint condition, a second constraint condition, a third constraint condition and a fourth constraint condition;
the expression of the first constraint is δ ij ∈{0,1},δ′ ij ∈{0,1}；
The expression of the second constraint is
Wherein M represents the number of suppliers participating in the auction, and N represents the number of demanders participating in the auction;
the expression of the third constraint is
Wherein K represents the number of time windows, s ik Represents a variable of 0 to 1, d jk Represents a variable of 0-1, d' jk Represents a variable of 0 to 1;
the expression of the fourth constraint is
In step S42, the calculation formula of the perturbation factor Δ of the bid allocation method is:
Δ＝Δ 1 -Δ 2
wherein, delta 1 Means that the parking space supplier with low price and long sharing time is matched with the long-time parking demand priority, delta 2 The preferred parking interval of the demander is preferentially distributed when the preferred parking interval and the secondary parking interval of the demander meet the requirements, omega represents a minimum coefficient,
indicating a priority match with a low bid and a long share time supplier,
represents a bid lease hour price;
in step S43, the bid allocation profit maxW of the unit price bid allocation method all1 The calculation formula of (2) is as follows:
wherein,
the price of the bidding use hour is shown, T is a time interval, and T is a berth sharing time period;
in step S43, the total bid allocation method is used to allocate the total bid allocation profit maxW all2 The calculation formula of (c) is:
wherein, y i Represents a variable of 0 to 1, and,
representing a bid lease total price.
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