CN102789599A - Operation shop bottleneck recognition method based on cluster analysis and multiple attribute decision making - Google Patents

Abstract

The invention provides an operation shop bottleneck recognition method based on a cluster analysis concept and a multiple attribute decision making theory. The method comprises the following steps of 1, utilizing dispatching optimization scheme as input of bottleneck recognition, determining feature attributes of a bottleneck recognition device and calculating the feature attribute values of the device according to the dispatching optimization result; 2, acquiring clustering clusters of the device under different distances and a parent-child relationship dendritic structure chart thereof on the basis of the similarity of a characteristic attribute excavating machine of the device by utilizing a hierarchical clustering method; 3, determining cluster centers of two sub-clusters of a final clustering cluster, comparing the attribute values of the cluster centers on the basis of a TOPSIS method and determining bottleneck clusters containing few device members; and 4, sequentially comparing sub-clusters of the bottleneck clusters and gradually obtaining main bottleneck clusters of different orders. According to the embodiment of the invention, the method provided by the invention can be used for solving the multi-bottleneck recognition problem which cannot be solved by the existing method.

Description

A kind of job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM)

Technical field

The present invention relates to job shop bottleneck distinguishment technical field, be specially a kind of job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM).

Background technology

Present job shop bottleneck recognition methods is main with the index method mainly, and the index method can be divided into equipment class, in goods class, effective output class, four types of bottleneck recognition methodss such as time class.

Equipment class: index Direct Recognition system bottlenecks such as machine burden, machinery processing capacity are mostly adopted in the recognition methods of this type bottleneck, perhaps discern the bottleneck machine to historical data, emulated data according to indexs such as machinery utilization rate, the busy not busy rates of machine production capacity.The poorest machine of define system working ability is the bottleneck of system, or the maximum machine of definition load is the bottleneck of system.Yet load is maximum or the poorest machine of machinery processing capacity is not real bottleneck, and at most, load and machinery processing capacity can only be as the prior imformations of bottleneck identification.

In the goods class: definition has that the machine of the longest average latency is the bottleneck of system, or the machine that definition has maximum queue length is the system bottleneck machine.Such bottleneck recognition methods all is through the method for carrying out bottleneck identification in the goods index in the formation before the machine, yet when a plurality of machine buffer zone workpiece to be processed queue lengths when identical or buffer zone formation is overflowed simultaneously, the accurate bottleneck of recognition system.

Effective output class: the definition bottleneck is for having the most responsive machine that influences to the effective output of system; " susceptibility " (Sensitivity) bottleneck of index measurement system is proposed; Obstruction (Blockage) and hungry (Starvation) situation through analyzing every machine have proposed the instrument of bottleneck indicator (Bottleneck indicator) as bottleneck identification.Such bottleneck recognition methods is paid close attention to the influence degree of machine to system's output from effective output angle of system, is different from the distinguishing indexes in traditional cost world; Find out the machine that system's output is had the greatest impact; Be one of focus of studying both at home and abroad now, but need set up the model of production system, production system is had relatively high expectations; Generally be applicable to streamline workshop (Flow Shop), can't discern job shop (Job Shop) bottleneck.

The time class: the state of machine is divided into active and inactive two states, and definition has that the longest on average to continue the machine of the time of enlivening be the bottleneck of system, has proposed mobile bottleneck method of identification (Shifting Bottleneck Detection Method).This method is carried out data mining to manufacturing system history log file, can be used for the bottleneck identification of complication system, and is workable; And the identification of the bottleneck that can be used to drift about; Have very strong practicality, still rigid providing enlivened and sluggish definition, do not consider the factor in the actual production.

There are following three types of problems in existing bottleneck recognition methods.

1) bottleneck identification is found the solution with the optimization of scheduling problem and is separated.Existing bottleneck recognition methods proposes the bottleneck distinguishing indexes mostly earlier, according to index historical data or emulated data is carried out the bottleneck differentiation again; These bottleneck recognition methodss obviously are independent of bottleneck identification outside the optimizing scheduling, and the bottleneck that identifies is the real bottleneck of nonsystematic also.

2) the bottleneck distinguishing indexes utilizes insufficient.Document carries out bottleneck identification through single index mostly, the identification of many indexs of minority literature research bottleneck.There is document that the TOC theory is combined with the Pareto method; Take all factors into consideration utilization factor, cost consumption index, judge " area " that utilization factor and cost are formed, think that the big equipment of " area " value is bottleneck; This method adopts utilization factor and two indexs of cost to carry out bottleneck identification; Have certain meaning, but just two indexs are carried out the simple two-dimensional combination, do not have versatility and science.There is document to choose machinery utilization rate, the processing and utilization factor, three indexs of production bottleneck rate, formulates an index judge rule then and carry out bottleneck identification based on method of emulation.Can find out that existing many indexs combined method is simple, or to the simple addition subtraction multiplication and division of a plurality of indexs, or formulate the if-then decision rule.

Different bottleneck recognition methodss has defined different bottleneck distinguishing indexes; These bottleneck indexs have all been described the ability that machine becomes bottleneck from different angles; It is the bottleneck characteristic attribute of machine; But the bottleneck distinguishing indexes that existing bottleneck recognition methods is selected is too unilateral, does not have fully to excavate the bottleneck characteristic property of machine.

3) many bottlenecks Study of recognition is less, and existing many bottlenecks are divided does not have scientific basis mostly.Often there are a plurality of bottlenecks in production system, and promptly bottleneck is not unique, and the identification of many bottlenecks also is difficult to the identification of single bottleneck, and the research of present many bottlenecks aspect is less.Have document index for selection value greater than preceding 30% machine of average index value as the bottleneck machine owing to be artificially selected scope, do not have scientific basis, rationality can't guarantee.

Summary of the invention

The technical matters that solves

For solving the problem that prior art exists; The present invention proposes a kind of job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM); Take into full account the relation of scheduling scheme and bottleneck identification; Take all factors into consideration the various attributes (index) of machine; Definition machine burden, machinery utilization rate, enliven the time, enliven deviation, susceptibility, the effective output of unit, at the characteristic attribute of measurement indexs such as goods queue length, OEE as bottleneck, obtain the bottleneck characteristic attribute of each machine based on the optimizing scheduling scheme of input, utilize the hierarchical clustering algorithm in the cluster analysis to find the similarity between the corresponding a plurality of attributes of each machine; Obtain clustering cluster and structure thereof; Utilizing multiple attributive decision making method to judge bottleneck clustering cluster wherein according to the set membership of each bunch between to the clustering cluster under the different diversity factoies on the basis of cluster result then, obtaining bottleneck bunch and set membership thereof under the different diversity factoies, the final user is according to the own suitable diversity factor of processing power selection; Obtain the bottleneck bunch of appropriate scale, corresponding to many bottlenecks or single bottleneck.

Technical scheme

To the above-mentioned defective that when discerning the job shop resource bottleneck, exists, the present invention proposes a kind of new job shop bottleneck bunch recognition methods based on cluster thought and Multiple Attribute Decision Making Theory.The first, with of the input of optimizing scheduling scheme, confirm the machine characteristic attribute of identification bottleneck, according to the characteristic attribute value of optimizing scheduling object computer device as bottleneck identification.The second, adopt the hierarchical clustering method, excavate the similarity of machine based on the characteristic attribute of machine, obtain the clustering cluster and the set membership tree structure figure thereof of machine under the different distance.The 3rd, confirm bunch center of two submanifolds of final clustering cluster, based on the TOPSIS method property value at bunch center relatively, determine the bottleneck bunch that comprises minority machine member.The 4th, the submanifold of bottleneck bunch is compared successively, progressively obtain the main bottleneck bunch of different orders.

Bunch being meant to distribute of indication of the present invention concentrates on the individual collections in a certain scope.Closer and similarity is than higher with distance individual in twos in the cluster, and individual in twos distance is distant and similarity is lower between different bunches.The present invention is divided into the clustering cluster of different scales, the cluster result dendrogram that obtain have set membership with the resource of job shop in different distances through the hierarchy clustering method in the cluster analysis.

The machine of indication of the present invention bunch is the collection of machines with high similarity.

Technical scheme of the present invention is:

Said a kind of job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM) is characterized in that: may further comprise the steps:

Step 1: pre-service:

Step 1.1: the optimizing scheduling scheme Ω of input job shop:

Ω={ { B ₁₁..., B _V1..., B _E1; C ₁₁..., C _Vl..., C _E1; Z ₁₁..., Z _Vl..., Z _E1..., { B _1i..., B _Vi..., B _Ei; C _Li..., C _Vi..., C _Ei; Z _1i..., Z _Vi..., Z _Ei..., { B _1m..., B _Vm..., B _Em; C _Lm..., C _Vm..., C _Em; Z _1m..., Z _Vm..., Z _EmWherein, B _ViRepresent v ∈ E={1,2 ..., e} workpiece be at i ∈ M={1, and 2 ..., the beginning process time on the m} platform machine, C _ViRepresent v the machine time of workpiece on i platform machine, Z _ViRepresent the frock setup time of v workpiece on i platform machine;

Step 1.2: the characteristic attribute collection of setting up machine is X={X ₁, X ₂..., X _j..., X _n, j is the characteristic attribute label of machine, j ∈ N={1, and 2 ..., n};

Step 1.3: the optimizing scheduling scheme Ω according to step 1.1, calculate the characteristic attribute value of each machine, and set up the characteristic attribute matrix F AM=(x of machine _Ij) _{M * n}, x _IjBe j characteristic attribute value of i machine; And with the FAM standardization, obtain characteristic attribute standardization matrix F AM '=(x ' _Ij) _{M * n}

Step 2: the characteristic attribute standardization matrix F AM ' based on step 1 obtains, carry out hierarchical clustering to machine:

Step 2.1: every machine all is initialized as an independently machine bunch C _k={ A _k, C _kRepresent k machine bunch, A _kRepresent k platform machine, k=1 ..., m; Set up machine bunch set C={C ₁, C ₂..., C _mAnd cluster result set C '={ C ₁, C ₂..., C _m;

Step 2.2: adopt in bunch set of arest neighbors method computing machine the distance B between the machine in twos bunch _Sl(C _p, C _q), C _p, C _qAny two machines bunch in the expression machine bunch set obtain one group of distance value between machine bunch in twos:

Dsl(C _p,C _q)＝min{d(A _α,A _β)|A _α∈C _p,A _β∈C _q}

Wherein, d (A _α, A _β) expression machine A _αWith machine A _βBetween Euclidean distance:

$d(A_{\mathrm{\α}},A_{\mathrm{\β}})=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(x_{\mathrm{\αj}}^{\′}-x_{\mathrm{\βj}}^{\′})}^2}$

Step 2.3: get that step 2.2 obtains one group two corresponding machine bunch C of minimum value in the distance value between machine bunch in twos _hAnd C _l, in machine bunch set C, delete C _hAnd C _l, add C simultaneously _M+t, C _M+t=C _h∪ C _l, and at the middle interpolation C of cluster result set C ' _M+t, t representes the cycle index of step 2.2 ~ step 2.3;

Step 2.4: circulation carry out step 2.2 ~ step 2.3, and when having only an element among the machine bunch set C, end loop gets into step 3;

Step 3: the characteristic attribute standardization matrix F AM ' based on step 1 obtains, gather C '={ C according to the cluster result that step 2 obtains ₁, C ₂..., C _m, C _M+1..., C _M+t, carry out bottleneck bunch identification:

Step 3.1: adopt the TOPSIS method to confirm C _M+tNext stage submanifold C _M+t-1And C _M+t-2Bunch center c _M+t-1And c _M+t-2, the highest member of evaluation of estimate in the submanifold that said bunch of center refers to ask through the TOPSIS method;

Step 3.2: adopt relatively c of TOPSIS method _M+t-1And c _M+t-2, obtaining the high submanifold center of evaluation of estimate and be more excellent submanifold center, the corresponding submanifold in more excellent submanifold center is C _M+tThe more excellent submanifold of characteristic attribute; The more excellent submanifold of characteristic attribute is a bottleneck bunch;

Step 4: the characteristic attribute standardization matrix F AM ' that obtains based on step 1, the bottleneck that obtains according to step 3 bunch, carry out bunch identification of main bottleneck:

Step 4.1: the bottleneck that obtains with step 3 bunch is the 0th rank master's bottleneck bunch PBC ₀Set up main bottleneck bunch set PBC={PBC ₀;

Step 4.2: adopt the TOPSIS method to confirm r rank master's bottleneck bunch PBC _rNext stage submanifold C _α, C _βBunch center c _αAnd c _β

Step 4.3: adopt relatively c of TOPSIS method _αAnd c _β, obtain r rank master's bottleneck bunch PBC _rThe more excellent submanifold of characteristic attribute; R rank master's bottleneck bunch PBC _rThe more excellent submanifold of characteristic attribute be r+1 rank master's bottleneck bunch PBC _R+1With the r+1 rank master's bottleneck bunch PBC that obtains _R+1Add and advance main bottleneck bunch set PBC;

Step 4.4: circulation step 4.2 ~ step 4.3, when the machine member number in the main bottleneck bunch was 1, end loop obtained main bottleneck bunch set PBC.

Said a kind of job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM), it is characterized in that: the characteristic attribute collection of machine comprises: machine burden, machinery utilization rate, enliven the time, enliven deviation, susceptibility, the effective output of unit, in goods queue length, overall equipment efficiency.comprehensive efficiency of equipment.

Beneficial effect

For most of scheduling problem, the main bottleneck bunch (bunch member is 1 o'clock) that bottleneck method of identification of the present invention obtains is consistent with present recognition methods, has obtained to have candidate's bottleneck bunch set and the respective distances thereof of set membership simultaneously.Along with reducing of distance between clustering cluster, bunch scale is also along with diminishing, and final bottleneck bunch only comprises 1 member.And being different from present method, the present invention can also solve the existing indeterminable many bottlenecks identification problem of method.

Bottleneck recognition methods that the present invention is proposed and mobile bottleneck method of identification (Shifting Bottleneck Detection Method) and orthogonal test bottleneck method of identification compare.24 standard examples selecting JSSP problem LA class are as the compare test example, are respectively the typical problem of 6 kinds of different scales of 10 * 5,15 * 5,10 * 10,15 * 10,20 * 10,30 * 10, and every kind of scale is chosen 4 examples, totally 24 examples.The present invention uses Immune Evolutionary Algorithm that 24 standard examples of the JSSP problem LA class selected are optimized and finds the solution, and carries out bottleneck identification with the optimal scheduling scheme that obtains; The evaluation attributes collection of selected machine is the X={ machine burden when carrying out bottleneck identification, and the machinery utilization rate is on average enlivened the time }, and the hypothesis decision maker does not have the preference of attribute.A bottleneck bunch recognition result is seen table 1.

Table 1:

Can find out that by table 1 for most of scheduling problem, the bottleneck bunch (bunch member is) that bottleneck method of identification of the present invention obtains is consistent with mobile bottleneck method of identification and orthogonal test bottleneck method of identification at 1 o'clock; Candidate's bottleneck bunch set and the respective distances thereof of set membership have been obtained to have simultaneously.Along with reducing of distance between clustering cluster, bunch scale is also along with diminishing, and final bottleneck bunch only comprises 1 member.Candidate's bottleneck bunch set and clustering architecture that the bottleneck bunch recognition methods that the present invention proposes can provide science to divide, and existing bottleneck recognition methods was lost efficacy mostly when in the face of many bottlenecks identification problem.

The difference of the bottleneck recognition result of three kinds of bottleneck recognition methodss has proved absolutely that the bottleneck definition affects the bottleneck recognition result.Move bottleneck method of identification definition on average continuing the to enliven bottleneck machine that the longest machine of temporal summation is a system; The factor (machine) that the orthogonal experiment definition has the greatest impact for test index is the bottleneck machine of system; Bottleneck method of identification of the present invention is a kind of being based on bunch and structure, considers the bottleneck decision making package method of a plurality of bottleneck characteristic attributes, is different from the classic method according to machine single factors definition identification bottleneck, is a kind of integrated recognition method of bottleneck.

Bottleneck method of identification of the present invention and mobile bottleneck method of identification recognition result similarity are higher relatively; Reason is: in present case, adopted machine on average to continue the time of enlivening as one of index; Be based on and on average continue to enliven time index and carried out improving and the bottleneck recognition methods that proposes and move the bottleneck method of identification, two kinds of methods have all received the influence that on average continues to enliven time factor.

It can also be seen that by table 1 the maximum machine of load not necessarily is exactly a bottleneck: for the small-scale example, the recognition result of machine that machine utilization is maximum and orthogonal test method of identification, mobile bottleneck method of identification is more identical; And for larger problem, the maximum machine of load is bigger with the otherness of the recognition result of back two kinds of methods, and this has explained just in time that also tradition carries out bottleneck with the machine utilization maximum and discern the deficiency that exists, as: LA21, LA22, LA27.

Description of drawings

Fig. 1: schematic flow sheet of the present invention;

The hierarchical clustering result of Fig. 2: LA09 and bottleneck bunch recognition result and procedure chart.

Embodiment

The present invention is mainly used in the job shop production control process; Identify the operation bottleneck through method of the present invention, make the dispatcher rationally pay close attention to bottleneck and non-bottleneck, improve the efficient of organization of production; The production capacity in workshop is maximized the use, increase economic efficiency.

The judgement of bottleneck machine should be taken all factors into consideration each attribute of machine.The bottleneck identifying is defined as according to the bottleneck characteristic attribute synthesis judges that decision-making obtains the process of bottleneck bunch.

Present embodiment selects the standard example LA09 of JSSP problem LA class to carry out bottleneck bunch identifying explanation.Use Immune Evolutionary Algorithm that the LA09 standard example of the JSSP problem LA class selected is optimized in advance and find the solution, carry out bottleneck identification with the optimal scheduling scheme that obtains; The evaluation attributes collection of selected machine is the X={ machine burden when carrying out bottleneck identification, and the machinery utilization rate is on average enlivened the time }, and the hypothesis decision maker does not have the preference of attribute.Cluster result is as shown in table 2, and bunch identification of dendrogram and bottleneck is as shown in Figure 2.

Do in the face of the method in the present embodiment down and further describe:

Said a kind of job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM) may further comprise the steps:

Step 1: pre-service:

The manufacture process scheduling is the production planning management of manufacturing enterprise and the important step of control.It is the key that improves job shop product whole manufacturing process controlling level that the optimization of Job Shop scheduling problem is found the solution.The identification of optimizing scheduling scheme and bottleneck is closely bound up, even under identical processing tasks and capacity of equipment, the corresponding system bottleneck of different optimizing scheduling schemes maybe also can difference.The Immune Evolutionary Algorithm CHIEA (Clonal Selection and Hyper Mutations Based Immune Evolution Algorithm) that the present invention adopts existing document to propose carries out optimizing scheduling to Job Shop problem and finds the solution; Give full play to the ability of bottleneck, realize the maximization of scheduling scheme overall performance index.

Step 1.1: the Optimization Dispatching prioritization scheme Ω that imports the job shop that obtains through Immune Evolutionary Algorithm:

Ω＝{{B ₁₁,…,B _v1,…,B _e1;C ₁₁,…,C _v1,…,C _e1;Z ₁₁,…,Z _v1,…,Z _e1},…,{B _1i,…,B _vi,…,B _ei;C _li,…,C _vi,…,C _ei;Z _li,…,Z _vi,…,Z _ei},…,{B _1m,…,B _vm,…,B _em;C _1m,…,C _vm,…,C _em;Z _lm,…,Z _vm,…,Z _em}}

Wherein, B _ViRepresent v ∈ E={1,2 ..., e} workpiece be at i ∈ M={1, and 2 ..., the beginning process time on the m} platform machine, C _ViRepresent v the machine time of workpiece on i platform machine, Z _ViRepresent the frock setup time of v workpiece on i platform machine;

Step 1.2: the characteristic attribute collection of setting up machine is X={X ₁, X ₂..., X _j..., X _n, j is the characteristic attribute label of machine, j ∈ N={1, and 2 ..., n}.Generally speaking, to Job Shop scheduling problem, machine characteristic property set commonly used comprises: machine burden, machinery utilization rate, enliven the time, enliven deviation, susceptibility, the effective output of unit, in goods queue length, overall equipment efficiency.comprehensive efficiency of equipment.The evaluation attributes collection of selected machine is the X={ machine burden in the present embodiment, and the machinery utilization rate is on average enlivened the time }.

Step 1.3: the optimizing scheduling scheme Ω according to step 1.1, calculate the characteristic attribute value of each machine, and set up the characteristic attribute matrix F AM=(x of machine _Ij) _{M * n}, x _IjBe j characteristic attribute value of i machine; And with the FAM standardization, obtain characteristic attribute standardization matrix F AM '=(x ' _Ij) _{M * n}The computing method that above-mentioned machine characteristic attribute commonly used all can be looked into through pertinent literature like the computing method of machinery utilization rate U (i) are:

$U\left(i\right)=\frac{\underset{v=1}{\overset{e}{\mathrm{\Σ}}}(C_{\mathrm{vi}}-B_{\mathrm{vi}}+Z_{\mathrm{vi}})}{\mathrm{MA}}i\∈M$

Wherein MA is the maximum completion date of system.And for example enlivening time AP (i) computing method is:

$\mathrm{AP}\left(i\right)=\frac{\underset{v=1}{\overset{e}{\mathrm{\Σ}}}(C_{\mathrm{vi}}-B_{\mathrm{vi}}+Z_{\mathrm{vi}})}{S_i},i\∈M$

S wherein _iMachine i's enlivens the time period number in the expression optimizing scheduling scheme.

Step 2: the characteristic attribute standardization matrix F AM ' based on step 1 obtains, carry out hierarchical clustering to machine:

The present invention finds the hierarchical structure of job shop resource with respect to the bottleneck identification problem through hierarchy clustering method, confirm corresponding to resource under the different distance form bunch.Clustering method mainly comprises: based on the clustering method of dividing, and hierarchy clustering method and based on the probability clustering of mixture model.Task based on the clustering method of dividing is to be divided into k disjoint point set to data set, and the point that makes each subset is homogeneity as far as possible.That is to say, be applicable to based on the clustering method of dividing and attempt to find an optimal dividing to be divided into data the occasion of specified quantity cluster.Hierarchy clustering method, the occasion of the cluster structures that is suitable for trying to find out.Based on the probability clustering of mixture model, the occasion that the distribution that is only applicable to suppose is very suitable.And, be difficult in advance know what the form of distribution is for a lot of problems, also there are relevant issues for the bottleneck identification problem.Therefore, hierarchy clustering method is particularly suitable for this problem.

This step utilizes the hierarchical clustering method in the cluster analysis to find the similarity between the corresponding a plurality of attributes of each machine, and the machine cohesion that under certain distance, will meet the cluster condition is clustering cluster, and the acquisition cluster result closes C ' and tree structure figure thereof.

Step 2.1: every machine all is initialized as an independently machine bunch C _k={ A _k, C _kRepresent k machine bunch, A _kRepresent k platform machine, k=1 ..., m; Set up machine bunch set C={C ₁, C ₂..., C _mAnd cluster result set C '={ C ₁, C ₂..., C _m;

Step 2.2: adopt in bunch set of arest neighbors method computing machine the distance B between the machine in twos bunch _Sl(C _p, C _q), C _p, C _qAny two machines bunch in the expression machine bunch set obtain one group of distance value between machine bunch in twos:

D _sl(C _p,C _q)＝min{d(A _α,A _β)|A _α∈C _p,A _β∈C _q}

Wherein, d (A _α, A _β) expression machine A _αWith machine A _βBetween Euclidean distance:

$d(A_{\mathrm{\α}},A_{\mathrm{\β}})=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(x_{\mathrm{\αj}}^{\′}-x_{\mathrm{\βj}}^{\′})}^2}$

Step 2.3: get that step 2.2 obtains one group two corresponding machine bunch C of minimum value in the distance value between machine bunch in twos _hAnd C _l, in machine bunch set C, delete C _hAnd C _l, add C simultaneously _M+t, C _M+t=C _h∪ C ₁, and at the middle interpolation C of cluster result set C ' _M+t, t representes the cycle index of step 2.2 ~ step 2.3; Make up dendrogram simultaneously;

Step 2.4: circulation carry out step 2.2 ~ step 2.3, and when having only an element among the machine bunch set C, end loop gets into step 3;

Step 3: the characteristic attribute standardization matrix F AM ' based on step 1 obtains, gather C '={ C according to the cluster result that step 2 obtains ₁, C ₂..., C _m, C _M+1..., C _M+t, carry out bottleneck bunch identification:

This step is on hierarchical clustering result's basis, with the hierarchical clustering final clustering cluster C of all member compositions under the ultimate range on the dendrogram as a result _M+tAs input, use based on the submanifold comparative approach at bunch center and relatively judge its two sub-clusters bunch down, try to achieve the more excellent submanifold of attribute and be bottleneck bunch BC, bottleneck and non-bottleneck are distinguished.

Step 3.1: adopt the TOPSIS method to confirm C _M+tNext stage submanifold C _M+t-1And C _M+t-2Bunch center c _M+t-1And c _M+t-2, the highest member of evaluation of estimate in the submanifold that said bunch of center refers to ask through the TOPSIS method;

Step 3.2: adopt relatively c of TOPSIS method _M+t-1And c _M+t-2, obtaining the high submanifold center of evaluation of estimate and be more excellent submanifold center, the corresponding submanifold in more excellent submanifold center is C _M+tThe more excellent submanifold of characteristic attribute; The more excellent submanifold of characteristic attribute is bottleneck bunch BC.

Step 4: the characteristic attribute standardization matrix F AM ' that obtains based on step 1, the bottleneck that obtains according to step 3 bunch, carry out bunch identification of main bottleneck:

Bunch recognition methods of main bottleneck is same to be used based on the submanifold comparative approach at bunch center and finds the solution sub main bottleneck bunch; Calculate bunch center of input bunch subordinate's two sub-clusters bunch through utilizing the TOPSIS method; Utilize relatively bunch center of TOPSIS method then; Obtain optimum bunch center, and then obtain more excellent sub-clustering cluster.

Step 4.1: the bottleneck that obtains with step 3 bunch is the 0th rank master's bottleneck bunch PBC ₀Set up main bottleneck bunch set PBC={PBC ₀;

PBC ₀Be initial main bottleneck bunch, make that BC is 0 rank master's bottleneck bunch PBC ₀, bunch identification of the main bottleneck of follow-up son is that carry out on the basis with it.R is a counter, is changed to 0 when initial, is used to write down cycle index, and the main bottleneck of mark bunch exponent number is like PBC _r

Step 4.2: adopt the TOPSIS method to confirm r rank master's bottleneck bunch PBC _rNext stage submanifold C _α, C _βBunch center c _αAnd c _β

Step 4.3: adopt relatively c of TOPSIS method _αAnd c _β, obtain r rank master's bottleneck bunch PBC _rThe more excellent submanifold of characteristic attribute; R rank master's bottleneck bunch PBC _rThe more excellent submanifold of characteristic attribute be r+1 rank master's bottleneck bunch PBC _R+1With the r+1 rank master's bottleneck bunch PBC that obtains _R+1Add and advance main bottleneck bunch set PBC;

Step 4.4: circulation step 4.2 ~ step 4.3, when the machine member number in the main bottleneck bunch was 1, end loop obtained main bottleneck bunch set PBC.

Can be in the hope of different rank through above algorithm, corresponding to the main bottleneck bunch set of different distance in the cluster result dendrogram, exponent number is big more, but the more little main bottleneck bunch scale of clustering distance is more little important more.

The bottleneck recognition result is as shown in table 2, and dendrogram and bottleneck bunch are as shown in Figure 2 with main bottleneck bunch recognition result and process.

Table 2

In step 3 and step 4, all adopted disclosed sort method (the Technique for Order Preference by Similarity to Ideal Solution that approaches ideal solution; TOPSIS) find the solution the more excellent submanifold of bunch center and attribute, concrete steps are following:

Step 1 is set up the standardization decision matrix, when finding the solution bunch center, foundation be submanifold member's standardization decision matrix, when finding the solution the more excellent submanifold of attribute, foundation be the standardization decision matrix at each submanifold bunch center.Its objective is to convert various types of property values into nondimensional attribute, attribute can be compared each other.The present invention selects vectorial standardized method, with decision matrix D=(x _Ij) _{M * n}Convert standard decision matrix R=(r to _Ij) _{M * n}

$r_{\mathrm{ij}}=x_{\mathrm{ij}}/\sqrt{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="x\; ij"\; filenames="HDA00001857439500021.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{ij}}^{}},$ i∈M，j∈N

Step 2 entropy power method is confirmed attribute weight.

M platform machine and n the decision matrix D=(x that evaluation attributes form _Ij) _{M * n}(i ∈ M, j ∈ N) is for certain attribute X _jProperty value x _IjGap big more, then this attribute role in decision making package is big more, otherwise then more little.Information entropy is the tolerance of the information degree of disorder, and information entropy is big more, and the degree of disorder of information is high more, and its value is more little, and the unordered degree of system is more little, so the degree of order and the effectiveness thereof of available information entropy system information that evaluation obtains.The present invention adopts entropy power method, the weight vectors W=(ω that finds the solution n evaluation attributes ₁, ω ₂..., ω _n), entropy power method can be eliminated the artificial interference of each index weight calculation as far as possible, makes evaluation result more meet reality.Its calculation procedure is following:

Step 2.1 is calculated the nondimensionalization property value p of i platform machine under j the attribute with each property value standardization _Ij

$p_{\mathrm{ij}}=x_{\mathrm{ij}}/\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ij}},$ i∈M，j∈N

Step 2.2 is calculated the entropy E of j attribute _j

$E_j=-k\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{p}_{\mathrm{ij}}\ln p_{\mathrm{ij}},$ i∈M，j∈N

Wherein k representes a constant, and k=1/lnm (ln is a natural logarithm) has guaranteed 0≤E _j≤1.

Step 2.3 is calculated the errored message degree d of j attribute _j

d _j＝1-E _j，j∈N

Work as d _jWhen big more, attribute is important more.

Step 2.4 pair errored message degree carries out normalization and calculates weight.

If the decision maker does not have the preference between attribute, can think that according to uncertain theory this n evaluation attributes have identical preference, then

${\mathrm{\&omega;}}_j=d_j/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{d}_j,$ j∈N

If the decision maker has preference for property set, establishing subjective weight is λ _j, so further revise above-mentioned formula, obtain the comprehensive weight of attribute j

${\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="j"\; filenames="HDA00001857439500021.png"\; state="\{\{state\}\}">j</figure-callout>}}^0={\mathrm{\&lambda;}}_j{d}_j/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j{d}_j,$ j∈N

Step 3 is set up the weighting standard decision matrix.

The evaluation attributes weight vectors W=(ω that entropy power method is tried to achieve ₁, ω ₂..., ω _j..., ω _n),

Be used for standardization decision matrix R=(r _Ij) _{M * n}In, the weighting standard decision matrix V that obtains.

V＝(v _ij) _m×n＝(ω _jr _ij) _m×n，i∈M，j∈N

Step 4 is confirmed ideal solution and negative ideal solution.

$A^{+}=\{\left(\underset{i}{\max }{v}_{\mathrm{ij}}\right|j\&Element;J),\left(\underset{i}{\min }{v}_{\mathrm{ij}}\right|j\&Element;J^{\&prime;})|i\&Element;M\}=\{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00001857439500011.png,HDA00001857439500021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1^{+},{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00001857439500021.png"\; state="\{\{state\}\}">v</figure-callout>}}_2^{+},...,v_j^{+},...,v_n^{+}\}$

$A^{-}=\{\left(\underset{i}{\min }{v}_{\mathrm{ij}}\right|j\&Element;J),\left(\underset{i}{\max }{v}_{\mathrm{ij}}\right|j\&Element;J^{\&prime;})|i\&Element;M\}=\{v_1^{-},v_2^{-},...,v_j^{-},...,v_n^{-}\}$

Wherein J is a benefit type community set, and J ' is a cost type community set.A ⁺Being ideal solution, is a virtual optimum solution, and its each property value all reaches the optimal value in the evaluation object; A ^-Being negative ideal solution, is the poorest virtual separating, and its each property value all reaches the worst-case value in the evaluation object.

Step 5 is through the distance between n dimension Euclid each machine of distance calculation and ideal solution and the negative ideal solution.Each machine to the distance of ideal solution does

$S_{i^{+}}=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{(v_{\mathrm{ij}}-v_j^{+})}^2},$ i∈M，j∈N

Equally, the distance to negative ideal solution does

$S_{i^{-}}=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{(v_{\mathrm{ij}}-v_j^{-})}^2},$ i∈M，j∈N

Step 6 is calculated the approach degree of each machine and ideal solution.A _iWith ideal solution A ⁺Approach degree be defined as

$C_{i^{+}}=S_{i^{-}}/(S_{i^{+}}+S_{i^{-}}),$ $0<C_{i^{+}}<1,$ i∈M

Obviously, if A _i=A ⁺, approach degree so

If A _i=A ^-, approach degree When

During convergence 1, machine A _iAttribute near ideal solution.

Step 7 recognition system optimum solution.Descending according to approach degree

; Each machine is arranged, and the maximum machine of definition approach degree

is that system optimal is separated.

The core of this method be utilize hierarchical clustering with resource division become under the different level of difference bunch, each rank master's bottleneck bunch under multiple attribute decision making (MADM) identification bottleneck bunch and the different level of difference that bunch carries out to obtaining then.Cluster is used identical machine characteristic attribute during with multiple attribute decision making (MADM).The multiple attributive decision making method of selecting TOPSIS to use as algorithm, through the ideal solution and the negative ideal solution of structure multiattribute problem, and with near ideal solution with away from two each schemes of benchmarking exercise of negative ideal solution.

Claims (2)

1. job shop bottleneck recognition methods based on cluster analysis and multiple attribute decision making (MADM) is characterized in that: may further comprise the steps:

Step 1: pre-service:

Step 1.1: the optimizing scheduling scheme Ω of input job shop:

Ω＝{{B ₁₁,…,B _v1,…,B _e1;C ₁₁,…,C _v1,…,C _e1;Z ₁₁,…,Z _v1,…,Z _e1},…,{B _1i,…,B _vi,…,B _ei;C _li,…,C _vi,…,C _ei;Z _li,…,Z _vi,…,Z _ei},…,{B _1m,…,B _vm,…,B _em;C _lm,…,C _vm,…,C _em;Z _lm,…,Z _vm,…,Z _em}}

Wherein, B _ViRepresent v ∈ E={1,2 ..., e} workpiece be at i ∈ M={1, and 2 ..., the beginning process time on the m} platform machine, C _ViRepresent v the machine time of workpiece on i platform machine, Z _ViRepresent the frock setup time of v workpiece on i platform machine;

Step 1.2: the characteristic attribute collection of setting up machine is X={X ₁, X ₂..., X _j..., X _n, j is the characteristic attribute label of machine, j ∈ N={1, and 2 ..., n};

Step 1.3: the optimizing scheduling scheme Ω according to step 1.1, calculate the characteristic attribute value of each machine, and set up the characteristic attribute matrix F AM=(x of machine _Ij) _{M * n}, x _IjBe j characteristic attribute value of i machine; And with the FAM standardization, obtain characteristic attribute standardization matrix F AM '=(x ' _Ij) _{M * n}

Step 2: the characteristic attribute standardization matrix F AM ' based on step 1 obtains, carry out hierarchical clustering to machine:

Step 2.1: every machine all is initialized as an independently machine bunch C _k={ A _k, C _kRepresent k machine bunch, A _kRepresent k platform machine, k=1 ..., m; Set up machine bunch set C={C ₁, C ₂..., C _mAnd cluster result set C '={ C ₁, C ₂..., C _m;

Step 2.2: adopt in bunch set of arest neighbors method computing machine the distance B between the machine in twos bunch _Sl(C _p, C _q), C _p, C _qAny two machines bunch in the expression machine bunch set obtain one group of distance value between machine bunch in twos:

D _sl(C _p,C _q)＝min{d(A _α,A _β)|A _α∈C _p,A _β∈C _q}

Wherein, d (A _α, A _β) expression machine A _αWith machine A _βBetween Euclidean distance:

$d(A_{\mathrm{\&alpha;}},A_{\mathrm{\&beta;}})=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x_{\mathrm{\&alpha;j}}^{\&prime;}-x_{\mathrm{\&beta;j}}^{\&prime;})}^2}$

Step 2.3: get that step 2.2 obtains one group two corresponding machine bunch C of minimum value in the distance value between machine bunch in twos _hAnd C _l, in machine bunch set C, delete C _hAnd C _l, add C simultaneously _M+t, C _M+t=C _h∪ C _l, and at the middle interpolation C of cluster result set C ' _M+t, t representes the cycle index of step 2.2 ~ step 2.3;

Step 2.4: circulation carry out step 2.2 ~ step 2.3, and when having only an element among the machine bunch set C, end loop gets into step 3;

Step 3: the characteristic attribute standardization matrix F AM ' based on step 1 obtains, gather C '={ C according to the cluster result that step 2 obtains ₁, C ₂..., C _m, C _M+1..., C _M+t, carry out bottleneck bunch identification:

Step 3.1: adopt the TOPSIS method to confirm C _M+tNext stage submanifold C _M+t-1And C _M+t-2Bunch center c _M+t-1And c _M+t-2, the highest member of evaluation of estimate in the submanifold that said bunch of center refers to ask through the TOPSIS method;

Step 3.2: adopt relatively c of TOPSIS method _M+t-1And c _M+t-2, obtaining the high submanifold center of evaluation of estimate and be more excellent submanifold center, the corresponding submanifold in more excellent submanifold center is C _M+tThe more excellent submanifold of characteristic attribute; The more excellent submanifold of characteristic attribute is a bottleneck bunch;

Step 4: the characteristic attribute standardization matrix F AM ' that obtains based on step 1, the bottleneck that obtains according to step 3 bunch, carry out bunch identification of main bottleneck:

Step 4.1: the bottleneck that obtains with step 3 bunch is the 0th rank master's bottleneck bunch PBC ₀Set up main bottleneck bunch set PBC={PBC ₀;

Step 4.2: adopt the TOPSIS method to confirm r rank master's bottleneck bunch PBC _rNext stage submanifold C _α, C _βBunch center c _αAnd c _β

Step 4.3: adopt relatively c of TOPSIS method _αAnd c _β, obtain r rank master's bottleneck bunch PBC _rThe more excellent submanifold of characteristic attribute; R rank master's bottleneck bunch PBC _rThe more excellent submanifold of characteristic attribute be r+1 rank master's bottleneck bunch PBC _R+1With the r+1 rank master's bottleneck bunch PBC that obtains _R+1Add and advance main bottleneck bunch set PBC;

Step 4.4: circulation step 4.2 ~ step 4.3, when the machine member number in the main bottleneck bunch was 1, end loop obtained main bottleneck bunch set PBC.

2. a kind of job shop bottleneck recognition methods according to claim 1 based on cluster analysis and multiple attribute decision making (MADM), it is characterized in that: the characteristic attribute collection of machine comprises: machine burden, machinery utilization rate, enliven the time, enliven deviation, susceptibility, the effective output of unit, in goods queue length, overall equipment efficiency.comprehensive efficiency of equipment.

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