CN106845676A - A kind of method for being applied to solve extensive unequal-area facility layout problem - Google Patents
A kind of method for being applied to solve extensive unequal-area facility layout problem Download PDFInfo
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Abstract
A kind of method for being applied to solve extensive unequal-area facility layout problem, step is as follows：Step one：Divide extensive sample；Step 2：Set up the solving model of the facility layout problem of small-scale unequal-area；Step 3：Set up initial feasible solution；Step 4：Optimization initial feasible solution；By above step, establish the plan model for solving small-scale facility layout problem and the methodology for having formulated the extensive unequal-area facilities planning problem of solution, and the approximate optimal solution of the facility layout problem of extensive unequal-area can be obtained, material transportation cost is saved, while also saving the time spent by extensive problem layout solution procedure.
Description
Technical field
The present invention provides a kind of method for being applied to solve extensive unequal-area facility layout problem, and it can be used to set
The excessive situation about directly can not be solved within effective time of department's quantity of location problem is applied, is obtained within effective time extensive
The approximate optimal solution of problem, belongs to Industrial Engineering facility layout field.
Background technology
Facility layout problem originates from early stage manufacturing plant design as the important branch in Industrial Engineering field.If
It is the facilities such as workshop, storehouse, office to composition factory to apply planning, and ensures that enterprise is normally produced as enterprise's conveying material
The transportation facility such as communications and transportation circuit, utilities pipeline.Facilities planning is to carry out industrial necessary condition, inside facility
Whether arrangement reasonable, if meet the material transportation demand between each department and whether farthest cost-effective be all
Facility layout problem needs what is solved.The quality of facility layout will directly influence the overall performance of whole production system, such as thing
Stream, information flow, production capacity, production efficiency, production cost and production safety etc..The good manufacturing system layout of one design
Material treatment effeciency can be accelerated, reduced in the residence time of product, greatly improve the production efficiency of enterprise.Asked for facility layout
The research of topic is a lot, and being substantially all can only accurately solve no more than 11 optimal solutions of the problem of department, and to big
Scale issue is generally using heuritic approach approximate solution.
The present invention is proposed a kind of for solving extensive unequal-area facility layout problem on foregoing Research foundation
Method.The method includes the mixed-integer programming model of pretreatment, foundation based on mixing distance to data and tries to achieve initial solution
Optimize with to initial solution, the approximate optimal solution of extensive problem is drawn within effective time has weight for complicated production system
Want meaning.
The content of the invention
1st, purpose：It is applied to solve extensive unequal-area facility layout problem it is an object of the invention to provide a kind of
Method.The situation of optimal location cannot be accurately solved under the solution large-scale complex condition of production.In for designing production distribution, with
Reach the minimum purpose of material transportation cost.
The extensive unequal-area facility layout problem refers to solution equal more than the area of 15 departments and each department
The layout of unequal facility layout problem simultaneously makes material transportation cost minimum.
2nd, technical scheme：
The present invention is a kind of method for being applied to solve extensive unequal-area facility layout problem, the tool that the method is realized
Body step is as follows：
Step one：Divide extensive sample
The extensive sample refer to department's quantity of the unequal-area facility layout problem being solved more than 15, and
The area of all departments is unequal；Such sample is referred to as extensive sample, and the facility layout problem for such sample cannot be straight
Connect accurate solution；
The way for dividing extensive sample is as follows：Sample is drawn using the method for bottom-up hierarchical clustering
Point, it first regards each sample in extensive sample as an initial clustering cluster, then again in each step of algorithm operation
Find out two closest clustering clusters to merge, the process is constantly repeated, until reaching default clustering cluster number；Will be big
Scale sample divide specific practice be：Because extensive sample can provide the material transportation amount between each department pair, and amount
Material transportation just should be measured inverse, and will not have by bigger the two departments apart from nearer when the sample is for hierarchical clustering
There is the value between the department pair of material transportation to take 9 (value is bigger, and a cluster is not converged into more)；Using R softwares, (R is complete set
Data processing, calculate and graphics software system) carry out hierarchical clustering, wherein the method choice " the class method of average " for clustering
(average)；And family tree is done to cluster result, determine that those departments are classified as a clustering cluster according to family tree.
Step 2：Set up the solving model of the facility layout problem of small-scale unequal-area
The present invention sets up mixed-integer programming model and solves facility layout problem；The target of general facility layout problem is thing
Material cost of transportation C reach it is minimum, so object function is exactly material transportation amount between every a pair of departments be multiplied by distance multiplied by with
Transport is univalent (typically in order to succinctly omit)；
The object function is：
In above formula, fijLogistics transportation amount between expression department i and j, dijThe distance between expression department i and j, at this
In be using air line distance Horizontal range between expression department i and j,Between expression department i and j
Vertical range；
And the constraint that location problem needs meet has：All departments can not all exceed given area；Can not between department
Overlap；The length or the maximum of length-width ratio of the most long/short side of department can be limited in some cases；The solving model for establishing
By for the foundation of initial feasible solution；
The solving model of the facility layout problem of the small-scale unequal-area is as follows：
It is describedIt is the centre coordinate of department,It is the length of side of department, α (>=1) is the length-width ratio of department,
Represent the relative position relation between Liang Ge departments, LsRepresent the length of side of facility；
Step 3：Set up initial feasible solution
With reference to step one, two, initial feasible solution is set up, the foundation of initial feasible solution is comprised the following steps：
1. the clustering cluster for being drawn according to first step, area required for obtaining each clustering cluster will cluster interior door face
Product is added；Obtain the material transportation amount sum between cluster again, will a clustering cluster be considered as a department, only ask between each clustering cluster
Material transportation amount；
2. the use of the model of the facility layout problem of the small-scale unequal-area of solution of second step is solving model, tries to achieve
Layout scenarios between clustering cluster, obtain the particular location of each clustering cluster；The layout feelings inside each clustering cluster are tried to achieve simultaneously
Condition, obtains the position of each department and the determination area of each department and shape；
The initial feasible solution is just to determine the accurate location for drawing each department in extensive facility layout problem
And shape area；Do not know whether material transportation cost is minimum now；Because the department's number for being laid out solution every time is little,
Time required for the foundation of initial feasible solution is very short；
Step 4：Optimization initial feasible solution
Method using change field on the basis of with the initial feasible solution set up optimizes initial feasible solution, finally effective
The near-optimal solution of extensive unequal-area facility layout problem is drawn in time；
The change neighborhood method is a kind of systematically to change neighbour structure collection in search procedure and obtain expanding hunting zone
Locally optimal solution is obtained, then systematically changes neighbour structure collection expansion hunting zone again based on this locally optimal solution and find another
The process of locally optimal solution.
The word description of the specific implementation procedure of the step is as follows：
By above step, establish and solve the plan model of small-scale facility layout problem and formulated solution on a large scale
The methodology of unequal-area facilities planning problem, and the near-optimization of the facility layout problem of extensive unequal-area can be obtained
Solution, saves material transportation cost, while also saving the time spent by extensive problem layout solution procedure.
3rd, advantages of the present invention has two:One is to establish the plan model for solving facility layout problem, can be extremely short
Time in small-scale unequal-area facility layout problem accurate optimization solve；Two is to have formulated the extensive unequal-area of solution
The methodology of facilities planning problem, realizes and the approximate optimal solution of extensive location problem is solved.
Brief description of the drawings
Fig. 1 is the method for the invention flow chart.
Fig. 2 is the cluster family tree of large-scale data of the present invention.
Sequence number, symbol, code name are described as follows in figure：
X1-X30 is the department's code name in example TAM30 in Fig. 2 family trees.
Specific embodiment
Below in conjunction with accompanying drawing and case study on implementation, the present invention is described in further detail.
As shown in figure 1, describing the present invention in detail by taking classical example TAM30 as an example, the present invention is a kind of solution on a large scale not
The method of homalographic facility layout problem, there is used herein extensive classical example TAM30 as research object.The tool of calculation reason
Volume data is as shown in table 1：
Table 1TAM30 design parameters
A kind of method for being applied to solve extensive unequal-area facility layout problem of the present invention, as shown in Figure 1,
The method is comprised the following steps that：
Step one：Divide extensive sample
For sample, the logistics capacity between all departments is first imported into excel into a square matrix, by all of logistics
Amount numeral gets number, and do not have logistics capacity between department takes 9.Being then used by R softwares carries out hierarchical clustering, and cluster result is drawn
Family tree (as shown in Figure 2),
Step 2：Set up small-scale facility layout problem model
Characteristic of the present invention based on static unequal-area facility layout problem sets up mixed-integer programming model.Use constraint
Have：All departments must be all laid out specified wide by 45, and in 50 areas long, each equipment can not be overlapped.Based on using example
The characteristic of TAM30, the length-width ratio of all departments can not be more than 5.Object function is logistics distance and the thing between all departments pair
The summation of the product of flow, logistics distance uses Euler's distance.
Step 3：Set up initial feasible solution
By Fig. 2, the establishment step of example TAM30 initial solutions is as follows：
The first step：All departments are divided into 6 clustering clusters：First clustering cluster forgive department X1, X2, X4, X5, X7,
X14, X16, X29, X30, second clustering cluster forgive department X3, X6, X10, X17, X18, X23, and the 3rd clustering cluster forgives portion
Door X9, X15, X22, the 4th clustering cluster forgive department X8, X12, X19, X21, X28, the 5th clustering cluster forgive department X11,
X13, X20, X24, X26, the 6th clustering cluster forgive department X25, X27.
Second step：Material transportation total amount of six clustering clusters altogether between space required, and each clustering cluster is obtained respectively,
Solve six layout relationships of clustering cluster.
3rd step：The layout between six clustering cluster interior doors is calculated respectively, determines the centroid point of each department
Coordinate.Here it is initial feasible solution.
Step 4：Optimization initial solution
The first step：The relative position relation in initial feasible solution between each department is fixed first, is then randomly choosed not
More than three departments.
Second step：The relative position relation between these departments and remaining department is decontroled, invocation step two is set up again
Mixed-integer programming model solve.When new desired value is that new layout then is replaced into the cloth of back less than original desired value
Office, otherwise maintains current arrangements constant.
3rd step：Circulation carries out first and second step, until continuous 100 times without new more excellent solution is produced, then stops circulation,
The layout that output is finally obtained, is exactly the near-optimization layout of example TAM30.
In sum, the present invention establishes a kind of method for being applied to and solving extensive unequal-area facility layout problem.
Studied with case TAM30, the average logistics cost for being capable of achieving to reduce about 10% within effective time, it was demonstrated that the present invention
Validity.The method is used, the unequal-area facility layout problem of large-scale data is solved, can be obtained within effective time
Go out approximate optimal solution, greatly improve solution efficiency, and logistics cost is greatly reduced.
Claims (1)
1. a kind of method for being applied to solve extensive unequal-area facility layout problem, it is characterised in that：What the method was realized
Comprise the following steps that：
Step one：Divide extensive sample
The extensive sample refers to that department's quantity of the unequal-area facility layout problem being solved is more than 15, and each portion
The area of door is unequal；Such sample is referred to as extensive sample, and the facility layout problem for such sample cannot be directly smart
Really solve；
The way for dividing extensive sample is as follows：Sample is divided using the method for bottom-up hierarchical clustering,
It first regards each sample in extensive sample as an initial clustering cluster, is then found out in each step of algorithm operation again
Two closest clustering clusters are merged, and the process is constantly repeated, until reaching default clustering cluster number；Will be extensive
Sample divide specific practice be：Because extensive sample can provide the material transportation amount between each department pair, and measure bigger
Material transportation just should be measured inverse by the two departments apart from nearer when the sample is for hierarchical clustering, and will be without thing
Expect that the value between the department pair of transport takes 9；Hierarchical clustering is carried out using R softwares, wherein the method choice " the class method of average " for clustering
That is average；And family tree is done to cluster result, determine that those departments are classified as a clustering cluster according to family tree；
Step 2：Set up the solving model of the facility layout problem of small-scale unequal-area
Set up mixed-integer programming model and solve facility layout problem；The target of general facility layout problem is material transportation cost
C reach it is minimum, so object function is exactly material transportation amount between every a pair of departments is multiplied by distance multiplied by transport unit price；
The object function is：
In above formula, fijLogistics transportation amount between expression department i and j, dijThe distance between expression department i and j, is used herein
Air line distance is Horizontal range between expression department i and j,It is vertical between expression department i and j
Distance；
And the constraint that location problem needs meet has：All departments can not all exceed given area；Can not be overlapped between department；
The length and the maximum of length-width ratio of the most long/short side of department can be limited in some cases；The solving model for establishing will be used for
The foundation of initial feasible solution；
The solving model of the facility layout problem of the small-scale unequal-area is as follows：
It is describedIt is the centre coordinate of department,It is the length of side of department, α (>=1) is the length-width ratio of department,Represent
Relative position relation between Liang Ge departments, LsRepresent the length of side of facility；
Step 3：Set up initial feasible solution
With reference to step one, two, initial feasible solution is set up, the foundation of initial feasible solution is comprised the following steps：
1. the clustering cluster for being drawn according to first step, area required for obtaining each clustering cluster will cluster interior door area phase
Plus；Obtain the material transportation amount sum between cluster again, will a clustering cluster be considered as a department, only seek the thing between each clustering cluster
Material freight volume；
2. the use of the model of the facility layout problem of the small-scale unequal-area of solution of second step is solving model, tries to achieve cluster
Layout scenarios between cluster, obtain the particular location of each clustering cluster；The layout scenarios inside each clustering cluster are tried to achieve simultaneously, are obtained
To the position of each department and the determination area and shape of each department；
The initial feasible solution be just to determine the accurate location that draws each department in extensive facility layout problem and
Shape area；Do not know whether material transportation cost is minimum now；Because the department's number for being laid out solution every time is little, initially
Time required for the foundation of feasible solution is very short；
Step 4：Optimization initial feasible solution
Method using change field on the basis of with the initial feasible solution set up optimizes initial feasible solution, finally in effective time
Inside draw the near-optimal solution of extensive unequal-area facility layout problem；
The change neighborhood method is that one kind systematically changes neighbour structure collection to expand hunting zone acquisition office in search procedure
Portion's optimal solution, then systematically another part is found in change neighbour structure collection expansion hunting zone again based on this locally optimal solution
The process of optimal solution；
The word description of the specific implementation procedure of the step is as follows：
By above step, establish and solve the plan model of small-scale facility layout problem and formulated solution on a large scale
The methodology of area facilities planning problem, and the approximate optimal solution of the facility layout problem of extensive unequal-area can be obtained,
Material transportation cost is saved, while also saving the time spent by extensive problem layout solution procedure.
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