CN112150187B - Competitive facility site selection method considering various customer selection rules - Google Patents
Competitive facility site selection method considering various customer selection rules Download PDFInfo
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Abstract
The invention provides a competitive facility site selection method considering various customer selection rules, which is characterized by comprising the following steps: the method comprises the following steps: determining the proportion of customers, and collecting market information: determining the proportion of customers adopting the deterministic rule, the probabilistic rule and the multi-deterministic rule through investigation; collecting information of existing facilities and demand points in the market area; step (2), calculating the pedestrian flow of the site selection enterprise: classifying the customers of each demand point according to a customer selection rule, calculating the pedestrian volume which can be obtained by the siting enterprise at each demand point based on the customer classification, and summing to obtain the overall pedestrian volume which can be obtained by the siting enterprise; step (3) aiming at the problem of competitive plane single facility site selection considering various customer selection rules, establishing a site selection model, and determining the position and quality level of a new facility to maximize the people flow of an enterprise site selection; step (4), solving an address selection model: and (4) calculating to obtain a satisfactory solution by adopting a particle swarm algorithm, and providing a corresponding facility site selection scheme.
Description
Technical Field
The invention provides a competition facility site selection method in a continuous space, belonging to the technical field of site selection of continuous space facilities; particularly, a site selection model is established for the site selection problem of facilities with different selection rules of different customers, and the ambiguity of the proportion of the customers is considered.
Background
The facility site selection is a hot problem of domestic and foreign research for many years, and in competitive facility site selection, how to select a proper position for a new facility to improve the effective pedestrian flow of site-selecting enterprises to a greater extent is a primary objective of researching the problem.
The location of a facility is influenced by a number of factors, of which one important aspect is the selection behavior of the customer. How customers choose between facilities in the market area will affect the amount of people available to the siting enterprise. The enterprise needs to consider the selection behavior of various customers when addressing the facility. Current siting research summarizes customer selection behavior into three customer selection rules:
(1) Determining a rule: the customer visits only the facility that is most attractive to him/her.
(2) Probability type rule: customers distribute their needs to all facilities in an area in proportion to the attractiveness of all facilities in that area.
(3) Multiple deterministic rules: customers visit the facilities in each business that are most attractive to them, and demand is distributed among these facilities in proportion to their attractions.
Traditional siting studies typically assume that customers are homogenous, i.e., all customers visit the facility with the same selection rules. However, under current competitive market conditions, where consumers have more choices and different preferences, the assumption of customer homogenization may not reflect the reality of all facility location problems. Since the selection behavior of the customer has a significant influence on the site selection decision of the enterprise, the customer is classified based on the customer selection rule from the practical situation, and the reasonable site selection decision is made, so that the method has practical significance. Therefore, the problem of competitive plane single facility site selection of various customer selection rules is considered in research, customers are classified based on the customer selection rules, an effective site selection model for improving the traffic of site selection enterprises is provided, the site selection model can be more fit with problem backgrounds, and the site selection decision quality is improved.
Disclosure of Invention
In order to solve the problem of plane competitive site selection with heterogeneous customers, the invention provides a competitive plane single facility site selection method considering various customer selection rules. Based on three customer selection rules, the method classifies the customers and is more suitable for the actual behaviors of the customers; meanwhile, based on the primary objective of a decision maker required to be realized by facility site selection, the people flow maximization is provided, a site selection optimization model is established, the model is solved through a particle swarm algorithm, an example is designed to explain the effectiveness of the model and the algorithm, and finally the effectiveness is compared with the original site selection problem adopting a single customer selection rule, so that the optimization method provided by the invention can effectively reduce the loss of site selection enterprises, and the corresponding optimal site selection decision can provide a better site selection scheme for the decision maker.
In order to achieve the above object, the present invention provides a competitive facility site selection method considering various customer selection rules, comprising the steps of:
determining the proportion of customers, and collecting market information: determining the proportion of customers adopting the deterministic rule, the probabilistic rule and the multi-deterministic rule through investigation; collecting information of existing facilities and demand points in the market area: the information of the existing facilities comprises the position and quality information of the existing facilities of the site selection enterprises and the competition enterprises, and the information of the demand points comprises the position and demand amount information of each demand point;
step (2), calculating the pedestrian flow of the addressed enterprise: classifying the customers of each demand point according to a customer selection rule, calculating the pedestrian volume which can be obtained by the siting enterprise at each demand point based on the customer classification, and summing to obtain the overall pedestrian volume which can be obtained by the siting enterprise;
step (3) aiming at the problem of competitive plane single facility site selection considering various customer selection rules, establishing a site selection model, and determining the position and quality level of a new facility to maximize the people flow of an enterprise site selection;
step (4), solving an address selection model: and (4) calculating to obtain a satisfactory solution by adopting a particle swarm algorithm, and providing a corresponding facility site selection scheme.
Further, the step (2) is specifically as follows:
defining a symbol system:
m existing facilities number;
n demand points;
k number of enterprises;
i demand point index number, i =1, \ 8230;, n;
c, index number of enterprise, c =1, \8230, k, wherein the enterprise with index number 1 is an address selecting enterprise;
j has a facility index number, j =1, \8230, m, from
To/>
Belonging to enterprise 1; slave->
To>
Belonging to enterprise 2; 8230; slave/slave unit>
To>
Belongs to enterprise k; wherein
P i Position of point of need i, P i ＝(P i1 ，P i2 )；P i1 Is the abscissa, P, of the position of the demand point i i2 Is the ordinate of the position of the demand point i;
w i demand of demand point i, w i >0；
f j Location of existing facility j, f j ＝(f j1 ，f j2 )；f j1 As the abscissa of the location of facility j, f j2 Is the ordinate of the facility j position;
d ij the distance between the demand point i and the facility j,
α j quality level of facility j, α j >0；
α min Minimum quality level, alpha, of new installation min >0；
α max Maximum quality level, alpha, of new installations max >α min ；
S, selecting a site area of a new facility;
g (-) distance as a function of the influence of attraction, a continuous non-negative non-decreasing function;
u ij attraction of facility j to demand point i or customer feeling at demand point iEffect of facility j received, u ij ＝α j /g(d ij )；
x decision variables, location of new installation, x = (x) 1 ，x 2 )；x 1 As abscissa, x, of new facility position 2 Is the ordinate of the new facility position;
alpha decision variables, quality level of the new facility;
d i (x) The distance between the demand point i and the new facility at x;
u i (x, α) attraction of a new facility at x and at a quality level α to a demand point i;
a (x, α) a set of demand points, the facilities of the selected enterprise, including existing facilities of chain 1 and new facilities at x, quality level α, the greatest appeal to these demand points being greater than the facilities of other enterprises,
w Di (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are deterministic;
M D (x, α) total traffic available to enterprise 1 when all customers at all demand points are deterministic;
w Pi (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are probabilistic;
M P (x, α) total traffic available to enterprise 1 when all customers at all demand points are probabilistic;
w Mi (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are multi-determinate;
M M (x, α) total traffic available to enterprise 1 when all customers at all demand points are multi-determinate;
w Fi (x, α) the traffic of demand points i that the enterprise 1 can obtain when classifying customers based on the customer addressing rules;
M F (x, α) total traffic available to enterprise 1 when classifying customers based on customer addressing rules;
the deterministic rules deem that the customer will only visit the facility with the greatest appeal to the customer, and will not consider other facilities; when assuming that all customers of the demand point i are of a certain type, the amount of traffic of the demand point i that can be obtained by the enterprise 1 is:
wherein w i Representing the demand of demand point i, and a (x, α) is the set of demand points where the facility of the addressed enterprise has a greater maximum attraction than the facilities of other enterprises;
when assuming that all customers at all demand points are deterministic, enterprise 1 can obtain the total traffic:
probabilistic rules assume that a customer distributes his needs to all facilities in an area in proportion to his/her perceived appeal from each facility; when assuming that all customers are probabilistic, the traffic of demand points i that can be obtained by enterprise 1 is:
wherein u is ij Is the attraction of facility j to demand point i, u ij ＝α j /g(d ij ) And u is i (x, α) is the attractiveness of the new facility to customers of demand point i(ii) a The function g (d) in the attraction function is a continuous non-negative and non-decreasing function; the form of the function g (d) is defined as g (d) = d η ，η>0；
When assuming that all customers at all demand points are probabilistic, enterprise 1 can obtain the total traffic:
in the multi-decision rule, customers always choose to visit facilities of different enterprises with the greatest attraction, and the probability that the customers visit the facilities is proportional to the attraction of the facilities; when all customers are of the multi-deterministic type, the traffic of demand points i that can be obtained by the enterprise 1 is as follows:
wherein the content of the first and second substances,
is the greatest appeal of all existing facilities of enterprise c to customers of demand point i,
when assuming that all customers at all demand points are multi-definitional, the total traffic available to enterprise 1 is:
considering that different customers can visit the facility according to different selection rules in actual life, the customers of each demand point are divided into three categories according to the selection rules; the relative proportions of three customers with different demand points are different, and the determination of the demand point i is determinedThe relative proportions of guests, probabilistic customers, and multi-decision customers are expressed as
Based on the customer classification, the flow of people at demand point i that enterprise 1 can obtain is:
after the customers at all demand points are classified according to the customer selection rule, the total pedestrian volume that can be obtained by the enterprise 1 is as follows:
further, the step (3) is specifically as follows:
aiming at the problem of competitive single-plane facility site selection, under the conditions that various customer selection rules are considered, site selection areas are met, the quality level of site selection facilities and the like are restrained, a site selection model for maximizing the site selection enterprise people flow is established, and the site selection model is specifically represented as follows:
maxΠ(x，α)＝M F (x，α)
s.t.α∈[α min ，α max ]，
x∈S
constraint alpha epsilon [ alpha ] min ，α max ]The minimum value and the maximum value which can be obtained in practice by the quality level of the facility are given; the plane area addressed by the new facility is denoted by S.
Further, the step (4) is specifically as follows:
designing a particle swarm algorithm to obtain a satisfactory solution; inputting the position, the demand quantity and the customer proportion of each demand point, the position and the quality level of the existing facility, the site selection area and the range of the new facility quality level in the algorithm, and iteratively obtaining the site selection position and the quality level of the new facility through the algorithm, wherein the specific steps are as follows:
step 4.1: randomly generating an initial population;
step 4.2: calculating an adaptation value of each particle;
step 4.3: obtaining an individual historical optimal solution and a global historical optimal solution through comparison;
step 4.4: updating the population based on the individual historical optimal solution and the global historical optimal solution;
step 4.5: repeating the step 4.2 to the step 4.4 until the maximum iteration times;
step 4.6: and returning the particles with the maximum target value as the optimal solution.
Compared with the prior art, the invention has the following beneficial effects:
1. compared with the existing research on the plane competition addressing problem, the method provided by the invention considers the customer selection behavior more fitting to the reality, classifies the customers based on three customer selection rules, researches the facility addressing problem based on customer classification, and has practical significance.
2. Aiming at the problem of competitive plane single facility site selection considering various customer selection rules, a facility site selection model is provided, and from the perspective of a decision maker, the position and the quality level of a new facility are determined so as to maximize the people flow of an enterprise site selection.
3. Based on a facility site selection model, a particle swarm algorithm is designed, efficient and rapid solution is achieved, the large-scale facility site selection problem can be solved within an acceptable time, and a satisfactory solution is obtained. The effectiveness of the model and the algorithm is proved by an example.
4. Compared with the original facility site selection problem based on a single customer rule, the optimization method provided by the invention can effectively reduce the loss of site selection enterprises, and the corresponding site selection result can provide a better decision scheme for decision makers.
Drawings
FIG. 1 is a schematic diagram of three customer selection rules;
FIG. 2 is a schematic diagram of a competitive flat sheet facility siting problem that takes into account various customer selection rules;
FIG. 3 is a flow chart of a particle swarm algorithm.
Description of reference numerals:
1. demand point
2. Existing facilities of Enterprise 1
3. Existing facilities of Enterprise 2
4. Attraction of facilities to demand points
5. Determining selection behavior of customers
6. Probabilistic customer selection behavior
7. Selection behavior of multiple deterministic customers
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
The invention provides a competitive facility site selection method considering various customer selection rules, which comprises the following steps:
(1) The present invention addresses the problem of competitive flat single facility siting in view of multiple customer selection rules with the goal of determining the location and quality level of new facilities for siting enterprises to maximize enterprise traffic. Considering that different customers have different selection rules in the problem, classifying the customers based on the customer selection rules to make the site selection decision more optimal, and determining the customer proportion of different demand points through investigation;
(2) Calculating the pedestrian volume which can be obtained by the site selection enterprise at each demand point based on the customer classification, and summing to obtain the total pedestrian volume which can be obtained by the site selection enterprise;
(3) Aiming at the requirement of a decision maker on improving the pedestrian flow, a pedestrian flow maximization site selection model is provided, and the position and the quality level of a new facility are determined so as to maximize the pedestrian flow of a site selection enterprise. The method is improved on the basis of the traditional site selection model, and the influence of the heterogeneity of various customers, namely different customers with different selection rules on the site selection result is considered;
(4) Designing a particle swarm algorithm to solve the site selection model, calculating to obtain a satisfactory solution, and providing a corresponding facility site selection scheme.
The method comprises the following steps:
(1) Defining a symbol system:
m existing facilities number;
n demand points;
k number of enterprises;
i requires a point index number, i =1, \8230, n;
c, index number of enterprise, c =1, \8230, k, wherein the enterprise with index number 1 is an address selecting enterprise;
j has a facility index number, j =1, \ 8230;, m, from
To>
Belonging to enterprise 1; slave->
To>
Belonging to enterprise 2; 8230; slave->
To/>
Belongs to enterprise k; wherein
P i Position of demand point i, P i ＝(P i1 ，P i2 )；P i1 Is the abscissa, P, of the position of the demand point i i2 Is the ordinate of the position of the demand point i;
w i demand of demand point i, w i >0；
f j Location of existing facility j, f j ＝(f j1 ，f j2 )；f j1 As the abscissa of the location of facility j, f j2 Is the ordinate of the facility j position;
d ij the distance between the demand point i and the facility j,
α j quality level of facility j, α j >0；
α min Minimum quality level, alpha, of new installation min >0；
α max Maximum quality level, alpha, of new installations max >α min ；
S, selecting a site area of a new facility;
g (-) distance is a function of influence of attraction force, and a continuous non-negative non-decreasing function is formed;
u ij attraction of facility j to demand point i or utility, u, of facility j as perceived by a customer at demand point i ij ＝α j /g(d ij )；
x decision variables, location of new installation, x = (x) 1 ，x 2 )；x 1 As abscissa, x, of new facility location 2 Is the ordinate of the new facility position;
alpha decision variables, quality level of the new facility;
d i (x) The distance between the demand point i and the new facility at x;
u i (x, α) New facility pair demand Point i at x and quality level αThe attractive force of (c);
a (x, α) a set of demand points, the facilities of the selected enterprise, including existing facilities of chain 1 and new facilities at x, quality level α, the greatest appeal to these demand points being greater than the facilities of other enterprises,
w Di (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are deterministic;
M D (x, α) total traffic available to enterprise 1 when all customers at all demand points are of a defined type;
w Pi (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are probabilistic;
M P (x, α) total traffic available to enterprise 1 when all customers at all demand points are probabilistic;
w Mi (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are multi-determinate;
M M (x, α) total traffic available to enterprise 1 when all customers at all demand points are multi-determinate;
w Fi (x, α) the traffic of demand points i that the enterprise 1 can obtain when classifying customers based on the customer addressing rules;
M F (x, α) total traffic available to enterprise 1 when classifying customers based on customer addressing rules;
(2) Certain rules consider that a customer will only visit the facility with the greatest appeal to the customer and will not consider other facilities with less appeal. When it is assumed that all customers of the demand point i are of a certain type, the traffic of the demand point i that can be obtained by the enterprise 1 is:
wherein w i Representing the demand of demand point i, and a (x, α) is the set of demand points where the facility of the addressed enterprise has a greater maximum attraction than the other enterprise facilities.
The traffic available to enterprise 1 is:
probabilistic rules assume that a customer distributes his or her needs to all facilities in an area in proportion to his or her perceived appeal from each facility. When assuming that all customers are probabilistic, the traffic of demand points i that can be obtained by enterprise 1 is:
wherein u is ij Is the attraction of facility j to demand point i, u ij ＝α j /g(d ij ) And u is i (x, α) is the attractiveness of the new facility to customers of demand point i. The function g (d) in the attraction function is a continuous non-negative and non-decreasing function. The form of the function g (d) is generally defined as g (d) = d η ，η>0。
The traffic available for enterprise 1 is:
in a multi-decision rule, a customer will always choose to patronize the facilities of a different business that have the greatest appeal to him, and the probability that the customer will patronize these facilities is proportional to the attractiveness of these facilities. When all customers are of the multi-deterministic type, the traffic of demand points i that can be obtained by the enterprise 1 is as follows:
wherein the content of the first and second substances,
is the greatest appeal of all existing facilities of enterprise c to customers of demand point i,
the traffic available for enterprise 1 is:
considering that different customers in actual life can visit the facilities according to different selection rules, the customers of each demand point are divided into three categories according to the selection rules; the relative proportions of three customers of different points of demand are different, and the invention expresses the relative proportions of definitive, probabilistic and multiple definitive customers of a point of demand i as
Based on the customer classification, the flow of people at demand point i that enterprise 1 can obtain is:
after the customers at all demand points are classified according to the customer selection rule, the total pedestrian volume that can be obtained by the enterprise 1 is as follows:
(3) Aiming at the problem of competitive single-plane facility site selection, under the conditions that various customer selection rules are considered, site selection areas are met, the quality level of site selection facilities and the like are restrained, a site selection model for maximizing the site selection enterprise people flow is established, and the site selection model is specifically represented as follows:
maxΠ(x，α)＝M F (x，α)
s.t.α∈[α min ，α max ]，
x∈S.
constraint alpha epsilon [ alpha ] min ，α max ]The minimum and maximum values that can be achieved in practice for the quality level of the installation are given. The plane area addressed by the new facility is denoted by S.
(4) And designing a particle swarm algorithm to obtain a satisfactory solution.
The position, the demand quantity and the customer proportion of each demand point, the position and the quality level of the existing facility, the site selection area and the range of the new facility quality level are input in the algorithm, and the site selection position and the quality level of the new facility are obtained through algorithm iteration. The specific steps of the algorithm are as follows:
step 4.1: randomly generating an initial population;
and 4.2: calculating an adaptation value of each particle;
step 4.3: obtaining an individual historical optimal solution and a global historical optimal solution through comparison;
step 4.4: updating the population based on the individual historical optimal solution and the global historical optimal solution;
step 4.5: and repeating the step 4.2 to the step 4.4 until the maximum iteration number is reached.
The present invention is further analyzed in detail by taking the problem of site selection of facilities of 3 existing facilities and 7 demand points as an example. First, information about the problem is gathered such as: location and quality level of existing facilities, location and demand (population density) of demand points, proportion of three types of customers for each demand point, etc. The addressing space is a square continuous space of 10 x 10. The facility quality level ranged from [0.5,5].
The 3 types of customer selection rules in fig. 1 are deterministic rules, probabilistic rules, and multi-deterministic rules, respectively. The invention mainly considers the problem of site selection of the plane single facilities with different selection rules of different customers. FIG. 2 illustrates the problem of the present invention requiring optimization, particularly the continuous space facility addressing of customers with heterogeneous selection rules under competitive market conditions. Fig. 3 is a particle swarm algorithm designed by the invention, and a result of site selection is finally obtained.
The particle swarm algorithm is designed by adopting real number coding, the position of each particle corresponds to one solution of the problem, and the position of each particle is represented by one three-dimensional variable because three decision variables (new facility position abscissa, new facility position ordinate and new facility quality level) exist in the model of the invention. And updating the position and the speed of the particle swarm through the historical optimal information, and achieving the optimal state through multiple iterations. And setting the maximum iteration number of the particle swarm algorithm to be 200. The algorithm is used for solving a facility site selection problem, and the site selection results and relative losses of a facility site selection model based on single customer rule assumption and a facility site selection model based on customer classification are shown in table 1, which illustrates the effectiveness of the model and the algorithm provided by the invention.
TABLE 1
| Site selection model | Abscissa of the circle | Ordinate of the curve | Quality level | Flow of people | Relative loss |
| Shaping | 4.97 | 7.72 | 2.17 | 204.38 | 15.09％ |
| Probability type | 3.81 | 8.36 | 3.52 | 220.97 | 8.20％ |
| Multiple determinants | 3.91 | 8.34 | 3.32 | 228.16 | 5.21％ |
| Customer classification | 3.97 | 8.55 | 2.58 | 240.71 |
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.
Claims (2)
1. A competitive facility site selection method that considers a plurality of customer selection rules, characterized by: the method comprises the following steps:
determining the proportion of customers, and collecting market information: determining the proportion of customers adopting the deterministic rule, the probabilistic rule and the multi-deterministic rule through investigation; gathering information of existing facilities and demand points in the market area: the information of the existing facilities comprises the position and quality information of the existing facilities of the site selection enterprises and the competition enterprises, and the information of the demand points comprises the position and demand amount information of each demand point;
step (2), calculating the pedestrian flow of the site selection enterprise: classifying the customers of each demand point according to a customer selection rule, calculating the pedestrian volume which can be obtained by the siting enterprise at each demand point based on the customer classification, and summing to obtain the overall pedestrian volume which can be obtained by the siting enterprise;
step (3) aiming at the problem of competitive plane single facility site selection considering various customer selection rules, establishing a site selection model, and determining the position and quality level of a new facility to maximize the people flow of an enterprise site selection;
step (4), solving an address selection model: calculating to obtain a satisfactory solution by adopting a particle swarm algorithm, and providing a corresponding facility site selection scheme;
the step (2) is specifically as follows:
defining a symbol system:
m number of existing facilities;
n demand points;
k number of enterprises;
i requires a point index number, i =1, \8230, n;
c, index number of enterprise, c =1, \ 8230, k, wherein the enterprise with index number 1 is the address selection enterprise;
j has a facility index number, j =1, \ 8230;, m, from
To/>
Belonging to enterprise 1; slave/slave unit>
To/>
Belonging to enterprise 2; 8230; slave/slave unit>
To>
Belongs to enterprise k; wherein->
P i Position of point of need i, P i ＝(P i1 ,P i2 )；P i1 Is the abscissa, P, of the position of the point of interest i i2 Is the ordinate of the position of the demand point i;
w i demand, w, of demand points i i >0；
f j Location of existing facility j, f j ＝(f j1 ,f j2 )；f j1 As the abscissa of the location of facility j, f j2 Is the ordinate of the facility j position;
d ij the distance between the demand point i and the facility j,
α j quality level of facility j, α j >0；
α min Minimum quality level, alpha, of new installation min >0；
α max Maximum quality level, alpha, of new installations max >α min ；
S, selecting a site area of a new facility;
g (-) distance as a function of the influence of attraction, a continuous non-negative non-decreasing function;
u ij the attractiveness of a facility j to a demand point i or the utility of a facility j as perceived by a customer at the demand point i,
x decision variables, location of new installation, x = (x) 1 ,x 2 )；x 1 As abscissa, x, of new facility position 2 Is the ordinate of the new facility position;
alpha decision variables, quality level of new facilities;
d i (x) The distance between the demand point i and the new facility at x;
u i (x, α) attraction of a new facility at x and a quality level α to a demand point i;
a (x, α) a set of demand points, the facilities of the selected enterprise, including existing facilities of chain 1 and new facilities at x, quality level α, the greatest appeal to these demand points being greater than the facilities of other enterprises,
w Di (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are deterministic;
M D (x, α) total traffic available to enterprise 1 when all customers at all demand points are of a defined type;
w Pi (x, α) points of demand i all of which are probabilistic, enterprise 1 can obtain points of demandThe pedestrian volume of i;
M P (x, α) total traffic available to enterprise 1 when all customers at all demand points are probabilistic;
w Mi (x, α) the traffic of demand point i that enterprise 1 can obtain when all customers of demand point i are multi-determinate;
M M (x, α) total traffic available to enterprise 1 when all customers at all demand points are multi-determinate;
w Fi (x, α) the traffic of demand points i that the enterprise 1 can obtain when classifying customers based on the customer addressing rules;
M F (x, α) total traffic available to enterprise 1 when classifying customers based on customer addressing rules;
the deterministic rules deem that the customer will only visit the facility with the greatest appeal to the customer, and will not consider other facilities; when it is assumed that all customers of the demand point i are of a certain type, the traffic of the demand point i that can be obtained by the enterprise 1 is:
wherein w i Representing the demand of demand point i, and a (x, α) is the set of demand points where the facility of the addressed enterprise has a greater maximum attraction than the facilities of other enterprises;
when assuming that all customers of all demand points are deterministic, the total traffic available to enterprise 1 is:
probabilistic rules assume that a customer distributes his needs to all facilities in an area in proportion to the attractiveness he/she perceives from each facility; when assuming that all customers are probabilistic, the traffic of demand points i that can be obtained by enterprise 1 is:
wherein u ij Is the attraction of facility j to demand point i, u ij ＝α j /g(d ij ) And u is i (x, α) is the attractiveness of the new facility to customers of demand point i; the function g (d) in the attraction function is a continuous non-negative and non-decreasing function; the form of the function g (d) is defined as g (d) = d η ,η>0；
When assuming that all customers of all demand points are probabilistic, the total traffic available to enterprise 1 is:
in the multi-decision rule, customers always choose to visit the facilities of different enterprises with the greatest attractiveness, and the probability that the customers visit the facilities is proportional to the attractiveness of the facilities; when all customers are of the multi-deterministic type, the traffic of demand points i that can be obtained by the enterprise 1 is as follows:
wherein the content of the first and second substances,
is the greatest attraction of all existing facilities of business c to customers at demand point i, is->
When assuming that all customers at all demand points are multi-definitional, the total traffic available to enterprise 1 is:
considering that different customers can visit the facility according to different selection rules in actual life, the customers of each demand point are divided into three categories according to the selection rules; the relative proportions of three customers of different demand points are different, and the relative proportions of a definitive customer, a probabilistic customer and a multiple definitive customer of a demand point i are expressed as
Based on the customer classification, the flow of people at demand point i that enterprise 1 can obtain is:
when the customers at all demand points are classified according to the customer selection rules, the total pedestrian volume that can be obtained by the enterprise 1 is as follows:
2. a method for locating a competitive site in accordance with customer selection rules as claimed in claim 1, wherein: the step (4) is specifically as follows:
designing a particle swarm algorithm to obtain a satisfactory solution; inputting the position, the demand quantity and the customer proportion of each demand point, the position and the quality level of the existing facility, the site selection area and the range of the new facility quality level in the algorithm, and iteratively obtaining the site selection position and the quality level of the new facility through the algorithm, wherein the specific steps are as follows:
step 4.1: randomly generating an initial population;
step 4.2: calculating an adaptive value of each particle;
step 4.3: obtaining an individual historical optimal solution and a global historical optimal solution through comparison;
step 4.4: updating the population based on the individual historical optimal solution and the global historical optimal solution;
step 4.5: repeating the step 4.2 to the step 4.4 until the maximum iteration times;
step 4.6: and returning the particles with the maximum target value as the optimal solution.
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