JP2001155049A - Facility locating method, facility location planning device and storage medium recorded with facility location planning program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a facility locating method, a facility location planning device and a storage medium recorded with program, with which a facility location capable of expecting a lot of users or actual demands by deforming a spatial mutual operation model. SOLUTION: Concerning the method and the device for finding the facility location capable of expecting a lot of users (actual demands) of facilities and the storage medium recoded with program, a latent supply for each facility to be located, the latent demand of the facility for each user, the maximum actual demand, that can be estimated (maximum actual demand) and the distance attenuation parameter of mutual operation are applied by a facility location technology, for which the spatial mutual operation model is used.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for determining a facility arrangement in which a large number of users in a public facility, a store or the like is expected using an information processing apparatus, and a facility arrangement planning apparatus.
And a readable storage medium on which a program is recorded.

[0002]

2. Description of the Related Art A conventional planning technique for finding a facility arrangement with a large number of users by using a model for estimating a user's facility selection and the number of times of facility use includes a Huff model (Huff.DL,
A Programming Solution for Approximation an Optimu
m Retail Location, Land Economics, 42, 1996) and gravity models (Reilly, WJ, The law of retail gravitat
ion, Putmans and Sons, 1931). In the facility placement planning technology using a Huff model or gravity model, the possible locations of the facilities are limited, and the estimated number of users is compared for all possible combinations.
A means for determining the facility location is employed.

A facility placement planning technique using a spatial interaction model is a facility placement technique that maximizes the locational surplus (eg, Beaumont; Spatial Interaction).
Models and The Location-Allocation Problem, Jouran
al of Regional Science, 20, 1980), and facility location technology that minimizes estimated travel costs (eg, Hidehiko Tanimura; Mathematical Planning, Asakura Shoten 1986, Yoshiaki Aoki et al .; Regional facility location method using genetic algorithm) Architectural Institute of Japan, 484, 1996).

[0004]

Conventional techniques for finding a facility arrangement that allows for a large number of users by using a model that makes the facility selection of the user and the number of times the facility be used elastic include a Huff model and a gravity model. There is a technology to determine the location of facilities using this. However, the technology for finding a facility arrangement using a Huff model, a gravity model, or the like is based only on a mere analogy of Newton's law of gravity and has a problem of lack of accuracy. Based on statistical evidence, there is a highly explanatory spatial interaction model (also called an entropy model), but there is a problem that a conventional unconstrained spatial interaction model cannot find a significant facility location . In addition, in the conventional layout planning technique, obtaining the layout of a plurality of facilities solves a combination problem of the settable possible points, and the accuracy of the facility position is poor.
In addition, when the number of facilities is large, the number of combinations becomes explosively large, and there is a problem that it is difficult to obtain a facility arrangement.

An object of the present invention is to solve the above-mentioned problems of the prior art. More specifically, the present invention provides a facility layout method, a facility layout planning device, and a storage medium storing a program, which transform a spatial interaction model and specify a facility layout in which a large number of users or an actual demand can be expected. That is.

[0006]

According to the present invention, a conventional space interaction model which makes the number of times a facility is used by a user or the amount of actual demand for a facility elastic is modified to set the upper limit of the number of times the facility is used or the amount of actual demand. And means for determining the facility arrangement in the continuous space.

The above means will be described in detail below. First, the variables used in the spatial interaction model and their notations are organized and described.

The demand point indicating the position of the user is represented by y_j (J = 1,
2, .., m), and supply point x indicating facility location _i (I = 1, 2, ..
n), demand point y_jSupply point x_iDistance to c_ij, Facility regulations
The potential supply of supply points to be set for_i,demand
Of demand points to be set based on the facility's
Let u be the potential demand that represents the potential demand_jAt all supply points
Is the sum of the impacts (the potential supply multiplied by the decay rate)
Supply level μ_j, Influence from all demand points (potential
The demand level, which is the sum of the demand multiplied by the decay rate)
_i , Demand point y_jDemand for the number of uses of facilities by the above users
Point y_jDemand in Japan O_j Is the feed point x_iTo the above facilities
Supply point x number of users_iThe actual supply at D_i, Demand
Key point y_jTop user supply point x_iThe number of times the above facilities were used
Demand point y_jAnd feed point x_iT interaction_ij, Facilities and users
Parameter that determines the decay rate of the interaction due to the distance
Expressed as β. The conventional unconstrained spatial interaction model
The parameters that should be set by the person who places the facilities in
v_i(I = 1, 2, ..n), u_j(J = 1, 2, ..m), β.

In a conventional unconstrained space interaction model in which the number of times of use of a facility or the actual demand of a user for the facility is elastic, Equations 1, 2, 3, 4, 5, and 6 are used. Holds.

[0010]

(Equation 1)

[0011]

(Equation 2)

[0012]

(Equation 3)

[0013]

(Equation 4)

[0014]

(Equation 5)

[0015]

(Equation 6)

The user's estimated number of uses O _j and supply level μ
_j has a relationship as shown in FIG. The number of uses O _j of the facility at the demand point y _j increases in proportion to the supply level μ _j . Due to this property, in the unconstrained space interaction model, there is no competitive environment between facilities, so when finding a facility arrangement that maximizes the total number of users ΣO _j , all facilities gather at one point and it is optimal Arrangement (FIG. 2). However, it is unnatural to expect users in places with high supply levels to use excessive facilities, which is not an appropriate arrangement. Since such an inappropriate arrangement is the optimal arrangement, the spatial interaction model has been evaluated as a model with high explanatory power. The facility layout plan that anticipates actual demand was not technically feasible.

In the present invention, the number of times the user uses the facility is
The maximum value O for the actual demand of the user_jmax
Condition that the number of times the facility is used does not increase beyond a certain value
O_j≤O _jSet max (FIG. 3). This setting is the supply level μ_j
, The actual demand O to a certain extent_jIs empty
Obeys the interaction model_jThe actual demand above max
This is a setting that cannot be expected (Equation 7). In the present invention,
The upper limit is called the maximum actual demand. Thus the unconstrained type
Introducing the maximum manifest demand into the spatial interaction model
More accurately estimate the actual number of facility uses
Is possible, and significant facility allocation is based on the estimated number of users.
Can be obtained (FIG. 4). In the present invention
Is a facility layout using the spatial interaction model described above.
Provides a means to set the maximum apparent demand for
I do.

[0018]

(Equation 7)

The problem of finding the optimal arrangement that maximizes the number of users by introducing the maximum apparent demand into an unconstrained spatial interaction model is that the movement distance between y _j and x _i is proportional to the Euclidean distance. Then, it is formulated as shown in Expression 8.

[0020]

(Equation 8)

Equation 8 is a non-linear programming problem including non-differentiable points. O _j in the objective function is a function with {x ₁ , x ₂ , .. x _i , .., x _n } as variables but has a nondifferentiable point, and the conventional method maximizes the objective function Finding a solution is difficult.

For this reason, in the conventional technique, a means is used in which the possible locations are limited in advance, and the facility arrangement is examined by a combination of where the facilities are to be located at the limited possible locations. But by limiting the location it can point in advance, by means of is reduced to the problem of finding the optimal combination of x _i in which the above there is a limit to the facility location accuracy, the number of combinations when the number of facilities is increased explosively When there are many facilities to be arranged, it is difficult to obtain the arrangement.

Therefore, in the present invention, as a calculation technique for obtaining the facility arrangement, the arrangement {x ₁ , x ₂ ,..., X _i ..., x _n } of the facility that maximizes the number of users in a continuous space is obtained. Provide a means.

The steepest rising direction of O _j at x _i is given by equation (9).

[0025]

(Equation 9)

First, an appropriate initial value is given to the facility layout {x ₁ , x ₂ ,.., X _i ..., x _n } (step 1).

For all O _j (j = 1,2, .., m), {x ₁ ,
Find the steepest ascent direction at x ₂ ,., x _i .., x _n }. Total n
Xm rising directions are obtained (step 2).

Further, an adjustment coefficient h that satisfies Expression 10 is set (step 3).

[0029]

(Equation 10)

[0030] n × for each of m exponential, select y _j in a random order, x _{i (i} = 1 to upward of O _j,
2, .., n) respectively. At this time, in order for O _j to surely increase when moving x _i , O _j must be _equal to y _j
Since x _i is monotonically decreasing or invariant with respect to the distance, it is sufficient to move x _i closer to y _j or not. Therefore, _xi is moved using the recurrence formula of Equation 11 (Step 4).

[0031]

[Equation 11]

In equation (11), t is the number of iterations, ε (t) is a monotonically decreasing function asymptotically approaching zero as a learning coefficient, and h is an adjustment coefficient as in equation (1).
It is a function of x _i (i = 1,2, .., n) and y _j (j = 1,2, .., m) satisfying 0. By introducing the h, x _i because it is stochastically smaller moving beyond y _j be the a to approach the y _j, O _j will increase stochastically. As a result, F
Increases globally.

When all the y _js have made one round, 1 is added to t, and steps 2 to 4 are repeated. The process is terminated when the movement amount of x _i becomes equal to or less than a preset value and a predetermined accuracy is obtained (step 5).

In this arrangement calculation technique, since an asynchronous calculation process is performed, it is not necessary to determine the exact steepest rising direction of F {x _i }. Further, by making the order of handling O _j random, it is possible to avoid stochastic fluctuations in the search for a local maximum solution and to converge to a local local maximum.

[0035]

[Function] By means of setting the maximum actual demand at each demand point, it becomes possible to plan the facility arrangement in anticipation of many actual demands in the facility arrangement technology using the spatial interaction model. In addition, the means for determining the facility arrangement that maximizes the number of users in the continuous space does not require preliminarily restricting the possible locations, and can determine the facility arrangement even when the number of facilities to be arranged is large.

[0036]

FIG. 5 is a flowchart showing an outline of processing according to the present invention. The present invention will be described with reference to FIG.

[0037] to set the distribution of demand points y _j in the region from the facility users of the distribution of geographic information (100), the potential from the characteristics of the expected demand for the users of the facilities of the position of the demand point y _j The demand u _j is set (101). Based on the number n of facilities to be arranged and the size and attractiveness of each facility to be arranged, the potential supply amount v _i (i = 1, 2,... N) of each facility is set (10).
2). The parameter β that determines the attenuation rate _{depending on} the distance between the interaction {T _ij } between the supply point {x _i } and the demand point {y _j } is set (10
3). Next, the upper limit of the expected manifestation demand to users of the facility on demand point y _j, set the maximum manifestation demand for each demand point _{y j O j max (104)} . The above settings may be stored in the information processing device in advance,
It may be performed by storing the information in an information processing device or a recording medium connected to the information processing device through the input device.

A rule for calculating the learning coefficient ε (t) and the adjustment coefficient h in Equations 10 and 11 is set (105), and a rule for terminating the calculation is set (106). These settings may be stored in the information processing device in advance, or may be performed by storing the information in the information processing device or a recording medium connected to the information processing device through the input device. Step 1 described in Means to solve the problem
(107), Step 2 (108), Step 3 (10
9), Step 4 (109) and Step 5 (110) are performed, and the facility arrangement that maximizes the number of users or the actual demand is obtained (111). Geographical information such as the distribution of users and the height of the supply level and the required facility arrangement are displayed on the output device (112), and the information is
It is stored in the information processing device, the recording device, or the recording medium (113).

If the above facility arrangement is satisfactory, the process ends. If you are not satisfied with the requested facility location, use the input device,
Any of the settings from (100) to (106) is redone, and the facility arrangement is determined again (114).

【Example】

FIG. 6 shows the distribution of demand points {yj}, the potential demand at each demand point {u _j }, the number n of facilities set at 5, and the potential supply amount v _{i of} each facility. In this example, the maximum apparent demand amount O _j max is set, an arrangement that maximizes the sum of the actual demand amounts of the facilities is obtained, and the arrangement is printed using an output device. The small white circles are the distribution of demand points, and the black circles are the locations of facilities. The level of supply level is indicated by contour lines.

[0041]

According to the present invention, it is possible to use the spatial interaction model to arrange facilities in consideration of the number of facility users.

[Brief description of the drawings]

FIG. 1 is a graph showing a relationship between a supply level and an actual demand in a conventional unconstrained spatial interaction model.

FIG. 2 is a graph showing a definition of a maximum actual demand.

FIG. 3 is a diagram showing that in the conventional unconstrained space interaction model, facility arrangements that maximize the number of users are concentrated on one point, and a significant arrangement cannot be obtained. It is easy to understand and shows the arrangement of facilities in one dimension.

FIG. 4 In the planning method according to the present invention, by setting the maximum actual demand, the actual demand amount is limited, and the facility arrangement that maximizes the number of users is not concentrated on one point, but a significant facility arrangement is obtained. It is a figure showing that it becomes possible. It is easy to understand and shows the arrangement of facilities in one dimension.

FIG. 5 is a flowchart showing a procedure for planning a facility arrangement.

FIG. 6 is an example of an implementation result in which a facility arrangement is obtained. Here, the input demand point distribution is indicated by white circles, and the obtained facility arrangement is indicated by black circles. The level of supply level is indicated by contour lines.

Claims (6)

[Claims] 1. A facility arrangement method using a spatial interaction model that makes the number of times of use of a facility or the amount of actual demand of a user for a facility elastic, wherein the number of uses of the facility or the actual demand of the user for the facility is provided. A facility arrangement method comprising means for setting an upper limit value for the amount. 2. The facility arrangement method according to claim 1, further comprising means for obtaining facility arrangement in a continuous space. 3. A facility layout planning apparatus for obtaining a facility layout using a space interaction model that makes the number of times of use of a facility or an actual demand amount of a user to the facility resilient, wherein And a means for setting an upper limit value to the actual demand amount of the facility. 4. A facility layout planning apparatus according to claim 3, further comprising means for obtaining a facility layout in a continuous space. 5. A storage medium having a program for arranging facilities in a predetermined area by using a spatial interaction model that makes the number of times of use of facilities or a user's actual demand for facilities elastic. A readable storage medium characterized by recording a facility arrangement program having means for setting an upper limit to the number of times or the actual demand for the facility. 6. A readable storage medium according to claim 5, wherein a program for obtaining a facility arrangement in a continuous space is stored.