CN104408521A - Evaluation method of reconfigurable manufacturing system, based on PROMETHEE - Google Patents

Abstract

The invention discloses an evaluation method of a reconfigurable manufacturing system, based on PROMETHEE. The evaluation method comprises the steps that a decision maker formulates evaluation schemes before making a decision; each evaluation scheme comprises a plurality of evaluation indexes; different preference functions are respectively selected according to characteristics of the evaluation indexes; each scheme is evaluated through each evaluation index and a corresponding preference index value is computed; preference indexes are computed; the total preference relation between a scheme a and other schemes in a selectable scheme set A is computed; scheme ordering rules are formulated; the schemes are comprehensively ordered according to the defined ordering rules, and a complete ordering index phi (a) is defined, so as to cover the shortage of part of ordering indexes, and an ordering result is obtained according to the complete order index phi (a). The evaluation method has the benefits that the decision process is more close to the practicality, so that a more accurate evaluation result is obtained.

Description

A kind of Reconfigurable Manufacturing System evaluation method based on PROMETHEE

Technical field

The invention belongs to statistical technique field, relate to a kind of Reconfigurable Manufacturing System evaluation method based on PROMETHEE.

Background technology

Along with economic development, manufacturing industry intensified competition, customer demand is more cunning and diversified, cause being on the increase of product category, the fluctuating widely of the market demand, add the continuous innovation of science and technology, launch window reduces all the more, and existing manufacturing system appears gradually in defect, novel manufacturing system research becomes focus gradually, pursues with the high-quality product of low-cost production to obtain competitive edge.At present, Reconfigurable Manufacturing System (Reconfigurable Manufacturing System, RMS) as the model of novel manufacturing system of future generation, accurate function and ability need can be provided according to customer requirement, attract large quantities of researchist to drop in the research ranks of Reconfigurable Manufacturing System (RMS).

Reconfigurable Manufacturing System (RMS) just should consider the Rapid Variable Design of how to tackle market at the beginning of design on structure, hardware and software, thus can deal with the change in market with the productive capacity in the fastest speed adjustment part family and production function.If manufacturing system is not start just to consider reconstruct in design, so, if system needs reconstruct afterwards, restructuring procedure will be very very long.In economic environment fast changing now, very long reconstitution time is flagrant, is also unpractical, and whether so evaluate the possibility whether a manufacturing system has reconstruct, or have reconstitution, be vital.How to carry out reasonably evaluating to Reconfigurable Manufacturing System Design scheme is the problem that this patent solves.

At present, evaluation for manufacturing system is mainly angularly analyzed from process time, processing cost, material handling cost, system capacity, the single index of independent consideration or consider multiple index, adopt the analytical approachs such as fuzzy evaluation, Comprehensive Fuzzy Evaluation, analytical hierarchy process, the various aspects of performance of manufacturing system is evaluated.

Although at present for the evaluation study outstanding achievement of manufacturing system, for the evaluation study of Reconfigurable Manufacturing System (RMS) also in the starting stage, there is following problem:

(1) a lot of researchist have ignored Reconfigurable Manufacturing System (RMS) must from the reconfigurability just considering system at the beginning of design

(2) part research evaluates Reconfigurable Manufacturing System (RMS) from the index of manufacturing cost, these manufacturing system general character of output merely, and does not have consideration to have the evaluation index of Reconfigurable Manufacturing System (RMS) feature.

(3) fuzzy assessment method subjectivity is too strong, thus may cause unpredictable error.

(4) the distinguishing hierarchy process of analytical hierarchy process is complicated and have subjectivity, and the relation between level is difficult to definition.

Summary of the invention

The object of the present invention is to provide a kind of Reconfigurable Manufacturing System evaluation method based on PROMETHEE, solve existing reconfiguration system fuzzy assessment method subjectivity too strong, the problem that error is too large.

The technical solution adopted in the present invention is carried out according to following steps:

Step 1: decision maker is before carrying out decision-making, work out evaluation of programme, each evaluation of programme includes several evaluation indexes, characteristic according to evaluation index selects different preference functions respectively, utilize each evaluation index to evaluate each scheme more respectively, calculate corresponding preference function value;

Step 2: the calculating of preference function; By the comparative result of all evaluation indexes of two schemes that compares in conjunction with weight vectors according to formula

$\mathrm{\π}(a,b)=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i{p}_i(a,b)}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i}$

Calculate, thus draw the preference function of a scheme relative to another scheme, be defined as π (a, b), wherein, 0≤π (a, b)≤1, as π (a, b) more close to 1 time, illustrate compared with scheme b, decision maker is preference scheme a more;

The total preference relation of other schemes in step 3: scheme a and possibility set A is as follows:

${\mathrm{\φ}}^{+}\left(a\right)=\underset{x\∈A}{\mathrm{\Σ}}\mathrm{\π}(a,x)---\left(41\right)$

${\mathrm{\φ}}^{-}\left(a\right)=\underset{x\∈A}{\mathrm{\Σ}}\mathrm{\π}(x,a)---\left(42\right)$

Wherein, φ ⁺(a) represent compared with other schemes, decision maker for the preference of scheme a, φ ⁺a (), more close to 1, illustrates that decision maker more tends to selection scheme a, otherwise the selected possibility of scheme a will be very low, be even zero; φ ^-a () represents compared with other schemes, decision maker is for the detest degree of scheme a, and namely decision maker is more prone to the degree of other schemes, works as φ ^-(a) more close to 0 time, illustrate that decision maker more tends to selection scheme a, otherwise illustrate and select, scheme a will be a very bad decision;

Step 4: schemes ranking Rulemaking;

Wherein, P ⁺, P ^-expression scheme a has superiority more relative to scheme b, and namely decision maker more prefers to scheme a; I ⁺, I ^-do not have dividing of obvious quality between expression scheme a and scheme b, namely decision maker does not have preference for these two schemes;

Ordering rule according to definition carries out integrated ordered to scheme:

Wherein, P ^Ιrepresent decision maker more preference scheme a, namely as (φ ⁺(a) > φ ⁺(b) & φ ^-(a) < φ ^-(b)) or (φ ⁺(a) > φ ⁺(b) & φ ^-(a)=φ ^-(b)) or (φ ⁺(a)=φ ⁺(b) & φ ^-(a) < φ ^-(b)) time, scheme a has superiority than scheme b; I ^Ιit doesn't matter, namely as (φ to represent two schemes ⁺(a)=φ ⁺(b) & φ ^-(a)=φ ^-(b)) time, which probability decision maker select be the same; R represents that scheme a and scheme b cannot compare, i.e. (φ ⁺(a) > φ ⁺(b) & φ ^-(a) > φ ^-(b));

Step 5: definition completely sequence index φ (a) makes up the deficiency of partial ordered index:

φ(a)＝φ ⁺(a)-φ ^-(a) (46)

Ranking results according to the index φ (a) that sorts completely draws:

Wherein, P ^Πrepresent decision maker more preference scheme a; I ^Πrepresent that decision maker does not have preference to two schemes.

Further, described 6 evaluation indexes are respectively: retractility (S, Scalability), convertibility (C _v, Convertibility), diagnosticability (D, Diagnosability), modularization (M, Modularity), integration (I, Integrability), customize (C _m, Customisation).

Further, described preference function comprises:

1. common preference function;

2. accurate judge preference function;

3. linear preference function;

4. level preference function;

5. there is the linear preference function in irrelevance region;

6. Gauss's preference function.

Further, the computation process of described weight vectors is:

Step 1: the numerical value of the every a line in comparator matrix is connected and takes advantage of, and open n power, shown in (25):

$c_i=\sqrt[n]{\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{A}_{\mathrm{ij}}}---\left(25\right)$

Step 2: the weight solving each criterion according to formula (26), (27):

$w_i=\frac{c_i}{C}---\left(26\right)$

$C=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_i---\left(27\right)$

Step 3: draw final weight vectors:

W＝{w _i|i＝1,2,...n}。

The invention has the beneficial effects as follows and to make in decision process more closing to reality, thus obtain evaluation result more accurately.

Accompanying drawing explanation

Fig. 1 is 8 kinds of configuration schematic diagram that 6 lathes are formed;

Fig. 2 is scheme section ranking results figure (PROMETHEE Ι);

Fig. 3 is complete ranking results figure (PROMETHEE Ι Ι).

Embodiment

Below in conjunction with embodiment, the present invention is described in detail.

Six features of Reconfigurable Manufacturing System:

Reconfigurable Manufacturing System just should consider the Rapid Variable Design of how to tackle market at the beginning of design on structure, hardware and software, thus can deal with the change in market with the productive capacity in the fastest speed adjustment part family and production function.If manufacturing system is not start just to consider reconstruct in design, so, if system needs reconstruct afterwards, restructuring procedure will be very very long.Whether in economic environment fast changing now, very long reconstitution time is flagrant, is also unpractical, so evaluate the possibility whether a manufacturing system has reconstruct, or have reconstitution, need to investigate following main points feature.

Feature one: retractility (S, Scalability).A system has the scalability of productive capacity, and namely manufacturing system can carry out the lifting (reduction) of productive capacity as required.The manufacturing system with retractility can be made the change in market and changing fast, that is becomes originally to be reconstructed adjustment to original system with shorter reconstitution time, lower system reconfiguration, the mainly increase of lathe, deletion, replacement.The telescopicing performance of system is it is envisaged that carry out the adjustment of how many production capacities to manufacturing system according to turn of the market.Because retractility imparts the strain rate effect ability of manufacturing system, so be that Reconfigurable Manufacturing System needs one of condition possessed, one does not have the manufacturing system of retractility to need to pay huge cost to be reconstructed.

So, how to weigh the scalability of a Reconfigurable Manufacturing System? according to document [1] when the market demand changes, if existing Reconfigurable Manufacturing System only needs just can meet the need of market with less productive capacity adjustment amount, so the retractility of manufacturing system is just strong; If instead need to carry out larger productive capacity adjustment just can meet the need of market, so the retractility of manufacturing system will be very poor, or even zero, namely not there is scalability.In Reconfigurable Manufacturing System, the productive capacity retractility angle that how reposefully from adjustment System production capacity is met the need of market more of system is considered [2], how to evaluate product steadily retractable? consider in actual production process, the production history of enterprise is generally foundation with batch, so define the concept of an adjustment gradient herein, that is, the flexible of output is not arbitrary, but according to the ability of enterprise and manufacturing system, to adjust gradient for according to carrying out the flexible of production capacity.In addition, objectively there is a production capacity maximal value and production capacity minimum value in Reconfigurable Manufacturing System, Reconfigurable Manufacturing System forms a series of configuration by reconstruct, there is a production capacity in each configuration, the production capacity maximal value of manufacturing system that what in these configurations, production capacity was maximum be, similarly, what production capacity was minimum is production capacity minimum value.After defining adjustment gradient, maximum production capacity and minimum production capacity, the reconstruct that there is no harm in supposing the system terminates to maximum production capacity from minimum production capacity, so just can calculate reconstruct number of times according to adjustment gradiometer, so just can analyze the parameter such as cost, time, system-level adjustment amount, lathe level adjustment amount of each reconstruct, thus comprehensive quantification analysis is carried out, shown in (1) to the retractility of system.

$\frac{1}{{\mathrm{\&Delta;}}_{\max }-{\mathrm{\&Delta;}}_{\min }}\&times;\frac{1}{N_{\mathrm{\&Delta;}}}\underset{i=1}{\overset{N_{\mathrm{\&Delta;}}}{\mathrm{\&Sigma;}}}{{\mathrm{\&lambda;}}_i}^T{{\mathrm{\&lambda;}}_i}^C{\mathrm{\&alpha;}}_i{\mathrm{\&Delta;}}_i---\left(1\right)$

${\mathrm{\&lambda;}}_i^T=\frac{T_i}{{T_i}^p}---\left(2\right)$

${{\mathrm{\&lambda;}}_i}^C=\frac{C_i}{C_i^p}---\left(3\right)$

${\mathrm{\&alpha;}}_i=\frac{{\mathrm{\&omega;}}_1{N}_i^a+{\mathrm{\&omega;}}_2{N}_i^m}{N_i}---\left(4\right)$

Wherein, S represents the telescopicing performance of Reconfigurable Manufacturing System, it is span dimensionless number between zero and one, when S more close to 1 time, so illustrate that the telescopicing performance of Reconfigurable Manufacturing System is better, on the contrary, when S more close to 0 time, then the telescopicing performance of Reconfigurable Manufacturing System is poorer, even not flexible ability; Δ _max, Δ _minrepresent production capacity maximal value and the production capacity minimum value of Reconfigurable Manufacturing System, for example, the Reconfigurable Manufacturing System of Fig. 1 contains 6 lathes, manufacturing system is by the total 1-8 of reconstruct totally 8 kinds of different configurations, often kind of corresponding production capacity of configuration, namely having 8 production capacities, there is maximal value and minimum value in these 8 production capacities, is exactly the production capacity maximal value Δ specified herein _maxwith production capacity minimum value Δ _min; Δ _irepresent adjustment gradient when Reconfigurable Manufacturing System is reconstructed, for example, when production capacity is in Δ by needs _minthe system of state is by reconstructing to reach production capacity for Δ _maxtime, need just can be completed by adjustment repeatedly according to adjustment gradient, when that is system is reconstructed, the production capacity of system changes according to adjustment gradient, and adjustment gradient can be constant, also can be variable; N _Δexpression system from production capacity minimum value to production capacity maximal value the adjustment gradient magnitude that exists, also namely production capacity minimum value needs the number of times that is reconstructed to production capacity maximal value; λ _i ^trepresent adjustment gradient delta _itime parameter; T _irepresent adjustment gradient delta _ithe reconstitution time needed; T _i ^prepresent the production cycle reconstructed for i-th time; λ _i ^crepresent adjustment gradient delta _icost parameter; C _irepresent adjustment gradient delta _ithe reconfiguration cost needed; C _i ^prepresent the production cost of i-th production cycle; α _irepresent adjustment gradient delta _ineed the system-level and lathe level adjustment parameter of carrying out, namely system-level parameters changes the adjustment of system configuration by the increase, minimizing, movement etc. of lathe, namely lathe level parameter carries out the adjustment such as machine tool chief axis variation, tool magazine replacing when configuration is constant; N _i ^arepresent system-level adjustment parameter, owing to can suppose that reconstruct is reconstructed from production capacity minimum value to production capacity maximal value, so only need the lathe quantity considering to increase; N _i ^mrepresent lathe level adjustment parameter, namely need the lathe quantity of carrying out increasing main shaft, changing the adjustment such as tool magazine; ω ₁, ω ₂represent the weight of system-level adjustment parameter and lathe level adjustment parameter, and ω ₁+ ω ₂=1; N _irepresent adjustment gradient delta _ibefore, the lathe quantity comprised in system.

Feature two: convertibility (C _v, Convertibility).The responding ability of Reconfigurable Manufacturing System, except scalability, also needs the transfer capability of consideration system.The transfer capability of Reconfigurable Manufacturing System refers to the ability [3] of system according to market demand rapid adjustment production function, the i.e. ability of manufacturing system adjustment production function, the production power and energy carried out when being included in part family the production power and energy and part family change that carry out when producing dissimilar part.When Reconfigurable Manufacturing System is changed, need to carry out the replacement of lathe, the variation etc. of lathe configuration changes the production function of original manufacturing system.

The system converting scaling law [3] that Maier-Speredelozzi etc. propose, carries out quantitative test by the transfer capability of system.Transform scaling law and mainly consider system configuration, lathe, these three factors of material handling facility, the method only considered some special configurations, and limitation is obvious.In fact the content of the people such as Maier-Speredelozzi research is for manufacturing system but not Reconfigurable Manufacturing System, do not analyze from the angle of part family, consider the characteristic of Reconfigurable Manufacturing System, herein from the angle of part family, the transfer capability of Reconfigurable Manufacturing System is analyzed.The conversion of Reconfigurable Manufacturing System comprises the conversion between conversion between the different parts in part family and part family.Because Reconfigurable Manufacturing System possesses the ability of all parts in processing parts race, therefore, during conversion between the different parts in part family, there is not the problems such as the increase of lathe, deletion, replacement, only need the adjustment carrying out the lathe levels such as main shaft (spindle) adjustment, cutter (tool) replacement, fixture (fixture) variation, when investigating the transfer capability in manufacturing system part family, need the lathe level adjustment carried out during the conversion of Water demand between two between part, and carry out total score and analyse; When changing between part family, normal conditions be need to consider lathe increase (add), delete (delete), replace the system-level adjustment such as (replace), mobile (move), but also exist and only carry out the adjustment of lathe level and just can complete situation about changing between part family; In addition, the similarity between part family also directly affects the complexity of conversion, therefore the similarity when analyzing the transfer capability between part family between Water demand part family.

According to above-mentioned analysis, Reconfigurable Manufacturing System transformational is quantized, shown in (5).

C _v＝ω ₁C ₁+ω ₂C ₂(5)

$C_1=\frac{1}{\frac{1}{2N_p-1}\underset{i=1}{\overset{N_p-1}{\mathrm{\&Sigma;}}}\underset{j=i+1}{\overset{N_p}{\mathrm{\&Sigma;}}}(N_{\mathrm{ij}}^s+N_{\mathrm{ij}}^t+N_{\mathrm{ij}}^f)}---\left(6\right)$

$C_2=\frac{1}{S_c\&times;(N_a+N_d+N_r+N_m)}---\left(7\right)$

Wherein, C _vrepresent the transfer capability of Reconfigurable Manufacturing System, C _vvalue between zero and one, more close to 1, illustrate that the transfer capability of Reconfigurable Manufacturing System is stronger, on the contrary just weak; C ₁, C ₂represent the transfer capability in Reconfigurable Manufacturing System part family and between part family respectively; ω ₁, ω ₂represent C respectively ₁, C ₂weight; N _prepresent the part kind that the part family that the manufacturing system of design can be competent at (ability possessing all types part in manufactured parts race) comprises, 2N _p-1 represents the total degree carrying out between different part in part family changing; N _ij ^srepresent the lathe quantity needing to carry out main shaft adjustment when production i-th kind of part converts production jth kind part to; N _ij ^trepresent the lathe quantity needing to carry out cutter adjustment when production i-th kind of part converts production jth kind part to; N _ij ^frepresent the lathe quantity needing to carry out fixture adjustment when production i-th kind of part converts production jth kind part to; S _crepresent the likeness coefficient between the part family that needs carry out changing, the method that the method that this coefficient can build according to part family carries out analyzing or adopt expert group to assess obtains, when needing the amount of adjustment the same when changing between part family, so likeness coefficient is larger, then illustrate that the transfer capability between original system part family is poorer; N _arepresent the lathe quantity needing when changing between part family to increase; N _drepresent the lathe quantity needing when changing between part family to delete; N _rthe lathe quantity of replacing (comprising lathe replacement, main shaft replacement, cutter replacement, fixture replacement) is needed when changing between expression part family; N _mrepresent the lathe quantity needing movement when changing between part family.

Feature three: diagnosticability (D, Diagnosability).The diagnosticability definition of Reconfigurable Manufacturing System: in order to reduce the quick diagnosis ability that the ramping time after reconstruct carries out.Be exactly specifically, diagnosticability can find the reason causing product quality fast, and the quick discovery of product quality defect reason and solution are the necessary requirements [4] of the productive capacity (ramping time, Ramp-up) reaching rapidly expection after realizing system reconfiguration.So diagnosticability is for significant Reconfigurable Manufacturing System, directly determine the system after reconstruct and whether there is realistic meaning, if the system that is after reconstruct can not reach the production capacity of expection fast, even if so reconfiguration cost is enough low, reconstitution time is enough short is also of no avail, because the system after reconstruct does not have actual value.

The diagnosis capability of Reconfigurable Manufacturing System and the diagnosis operation quantity in system, diagnostic sample size, accuracy rate of diagnosis are relevant, in addition owing to embodying the diagnosis capability of manufacturing system between ramping time, therefore the quantification of diagnosticability can calculate by formula (8).

$D=\frac{1}{N_r}\underset{i=1}{\overset{N_r}{\mathrm{\&Sigma;}}}{{\mathrm{\&lambda;}}_i}^d{{\mathrm{\&lambda;}}_i}^s{{\mathrm{\&lambda;}}_i}^T{X}_i---\left(8\right)$

${{\mathrm{\&lambda;}}_i}^d=\frac{N_i^{d0}}{N_i^d}---\left(9\right)$

${{\mathrm{\&lambda;}}_i}^s=\frac{N_i^{s0}}{N_i^s}---\left(10\right)$

${{\mathrm{\&lambda;}}_i}^T=\frac{{T_i}^p}{{T_i}^r}---\left(11\right)$

Wherein, D represents the diagnosis capability of Reconfigurable Manufacturing System, and the value that the value of D is greater than 0, D is larger, and the diagnosis capability of illustrative system is stronger; N _rrepresent manufacturing system history reformulation number of times, N _rvalue be more than or equal to 1; X _iafter representing i-th reconstruct, manufacturing system carries out the accuracy rate of quality inspection before expansion to the product produced; N _i ^d0after representing i-th reconstruct, the lathe total quantity that manufacturing system has; N _i ^dafter representing i-th reconstruct, the quantity of diagnostic device in manufacturing system; λ _i ^drepresent the diagnostic device factor; N _i ^s0after representing i-th reconstruct, the product total quantity of producing when manufacturing system is diagnosed; N _i ^safter representing i-th reconstruct, the sample size extracted when manufacturing system is diagnosed; λ _i ^srepresent the sampling observation sample factor; T _i ^pafter representing i-th reconstruct, the production cycle of manufacturing system; T _i ^rafter representing i-th reconstruct, the ramping time of manufacturing system; λ _i ^trepresent the ramping time factor.

Feature four: modularization (M, Modularity).The definition of module: module is exactly an independently unit, this unit can very easily with other unit combine, reset, substitute, exchange build different structures or system [5].So-called modularization is exactly come deisgn product, system etc. according to the thought of module.Under normal circumstances, the modularization of Reconfigurable Manufacturing System is for the lathe in system, i.e. so-called modular machine tool.The modular machine tool of Reconfigurable Manufacturing System makes manufacturing system by meeting the need of market to the adjustment of modular machine tool (comprising functional requirement and production capacity demand), thus can reduce reconstitution time and ramping time when tackling turn of the market.

Reconfigurable Manufacturing System builds based on modular machine tool, so how weigh the modular capability of a system? consider that lathe module number is not The more the better, too much module can cause module management too loaded down with trivial details, the concept of module granularity (granularity) is therefore proposed, the value of granularity can with reference to normal distribution, namely there is a module number point makes module granularity reach best, namely module granularity is maximal value 1, and distribute as Central Symmetry, module number too much or very little, granularity will littlely be all even 0, namely the Module Division of this lathe is not ideal enough or do not realize modularization.In addition,

The independence of module also directly affects the reconstruct efficiency of system.From lathe level level, the independence of module is embodied in the interface quantity of lathe module, and interface quantity is fewer, and the coupling so between module is fewer, and so module independence is better; From system-level horizontal analysis, the independence of module, the namely independence of manufacturing cell, fewer across unit processing number of times, illustrate that the independence of manufacturing cell is better.To sum up, the modular capability quantizating index of Reconfigurable Manufacturing System is proposed, shown in (12).

M＝ω ₁M ₁+ω ₂M ₂(12)

$M_1=\frac{1}{N_r}\underset{k=1}{\overset{N_r}{\mathrm{\&Sigma;}}}\left(\frac{1}{\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{N}_i}\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{G}_i^M\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}\frac{1}{N_{\mathrm{ij}}}\right)---\left(13\right)$

$M_2=\frac{1}{N_r\&times;N_k}\underset{k=1}{\overset{N_r}{\mathrm{\&Sigma;}}}{G_k}^M\underset{l}{\overset{N_k}{\mathrm{\&Sigma;}}}\frac{1}{N_{\mathrm{kl}}}---\left(14\right)$

Wherein, M represents Reconfigurable Manufacturing System modular capability, and the value of M between zero and one, more can be better close to 1 specification module voltinism, otherwise then poorer; M ₁, M ₂represent lathe level and system-level modular capability respectively; ω ₁, ω ₂represent M respectively ₁, M ₂weight; N _rrepresent manufacturing system history reformulation number of times, N _rvalue be more than or equal to 1; P represents the operation quantity of Reconfigurable Manufacturing System, i.e. lathe quantity; N _irepresent the module number that i-th lathe comprises; G _j ^mrepresent the module granularity of jth platform lathe, value is between 0,1, and granularity is more close to 1, and Module Division is more reasonable; G _k ^mrepresent the module granularity of kth time reconstruct, character and G _jidentical; Ni _jrepresent the interface quantity of a jth module of i-th lathe; N _krepresent the element number after kth time reconstruct, namely system-level blocks quantity; N _klwhat represent l unit (system-level blocks) after kth time reconstruct processes number of times (i.e. system-level blocks interface quantity) across unit.

Feature five: integration (I, Integrability).The integration feature object of Reconfigurable Manufacturing System is the cost and the time that reduce reconstruct.Integration is mainly for the interface between software and hardware of system, in restructuring procedure, if the interface between software and hardware standard of lathe module is unified, correction (hardware interface adjustment and the control program adjustment) time so just needed and cost will be little, be even zero, so the integrated performance of weight manufacturing system, correction time when can install from module was analyzed, shown in (15) originally with becoming.

$I=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}({\mathrm{\&omega;}}_1{\mathrm{\&alpha;}}_j^h+{\mathrm{\&omega;}}_2{\mathrm{\&beta;}}_j^s)---\left(15\right)$

${\mathrm{\&alpha;}}_j^h=1-\frac{1}{2}(\frac{C_j^{\mathrm{ha}}}{C_j^h}+\frac{T_j^{\mathrm{ha}}}{T_j^h})---\left(16\right)$

${\mathrm{\&beta;}}_j^s=1-\frac{T_j^{\mathrm{sa}}}{T_j^s}---\left(17\right)$

Wherein, I represents the integrated performance of Reconfigurable Manufacturing System, and the value of I between zero and one, more can be better close to 1 specification module voltinism, otherwise then poorer; P represents the lathe quantity of manufacturing system; N _irepresent the module number that i-th lathe comprises; α _j ^hrepresent a jth module hardware adjustment parameter of i-th lathe; β _j ^srepresent a jth module software adjustment parameter of i-th lathe; ω ₁, ω ₂represent the weight of hardware adjustment parameter and software adjustment parameter respectively, and ω ₁+ ω ₂=1; C _j ^harepresent hardware modifications (adjust) cost of a jth module of i-th lathe; C _j ^hrepresent the hardware installation cost of a jth module of i-th lathe; T _j ^harepresent the hardware modifications time of a jth module of i-th lathe; T _j ^hrepresent the hardware installation time of a jth module of i-th lathe; T _j ^sarepresent the software interface correction time of a jth module of i-th lathe; T _j ^srepresent the software debugging time of a jth module of i-th lathe, from Restructuring Module, namely can realize the time of controlling functions to control program; System is when reconstructing, and the ratio shared by the regulation time of the Setup Cost of hardware and time and software is less, then the integrated performance of system is better.

Feature six: customize (C _m, Customisation).The object that Reconfigurable Manufacturing System customizes is to reduce reconfiguration cost [6], namely the product of customization is produced to reach the object saved production cost by reconstruct with the function customized, customize function and mean high plant factor, so need to analyze the plant factor of the every class part in part family.Reconfigurable Manufacturing System designs centered by part family, namely the Reconfigurable Manufacturing System designed must have the ability of all types workpiece in processing parts race, so when weighing the customization ability of a Reconfigurable Manufacturing System, need the efficiency that its part family of high spot reviews builds, be namely building up to reconfiguration unit from part family and build the complete time.To sum up, the customization performance of Reconfigurable Manufacturing System quantizes such as formula shown in (18).

C _m＝λ _T×Y (18)

${\mathrm{\&lambda;}}_T=1-\frac{T_{\mathrm{pf}}}{T_p}---\left(19\right)$

$Y=\frac{1}{P}\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}\frac{N_i}{N}---\left(20\right)$

Wherein, C _mrepresent the customization ability of Reconfigurable Manufacturing System, between zero and one, the customization capability being worth larger illustrative system is stronger for value; λ _trepresent that part family builds the factor of influence of time; T _pfrepresent that being building up to reconfiguration unit from part family builds the complete time, the time building part family cost is more, and the customization ability of system is more weak; T _prepresent the production cycle; P represents the part kind that part family comprises; Y represents the plant factor of Reconfigurable Manufacturing System, and plant factor is higher, and the ability that illustrative system completes the processing of all types part in part family is stronger, customizes ability also stronger; N _irepresent that i-th kind of part needs the lathe quantity used; N represents the lathe total quantity comprised in Reconfigurable Manufacturing System; Customizing the meaning of index is that the machine tool utilization rate that part family builds in time shorter, production run is higher, and so the customization ability of manufacturing system is stronger.

Modularization, integration, diagnosticability, scalability can reduce the time reconfigured, customize, convertibility can reduce reconfiguration cost, so the reconstruct complexity of this main points characteristics determined of Reconfigurable Manufacturing System manufacturing system and reconfiguration cost.When a manufacturing system has these key features, so this system very high reconfigures ability by having.

PROMETHEE algorithm

Brans proposes PROMETHEE algorithm (Preference Ranking OrganizationMethod for Enrichment Evaluations) in nineteen eighty-two and solves Multiple-criteria Decision Problems (multi-criteria decisionmaking, MCDM), because it not only can process quantitative criteria, qualitative criteria can also be processed, so be widely used in the multi criteriaproblem such as system evaluation, equipment screening.

Evaluating form is the starting point that PROMETHEE algorithm is implemented, and in evaluation form, evaluates, { c1, c2, c3 in table from different criterions to existing scheme ... be evaluation index, { A1, A2, A3 ... it is the scheme needing to carry out evaluating.In the present invention, evaluation index is six features in said system.

Form evaluated by table 1

In addition, successful implementation PROMETHEE algorithm also to need two other important information:

(1) weight of criterion: because the importance of the criterion used in evaluate alternatives process is different, by giving different weights, makes last evaluation result more reasonable.

(2) selection of preference function: because different criterions has different characteristics, decision maker needs to select different preference functions to evaluate different schemes according to the characteristic of different criterion.

The weight of RMS evaluation index

Reconfigurable Manufacturing System evaluation index, i.e. six features mentioned above, but the importance of these six features is not duplicate, need the assignment of carrying out weight, generally, carry out the decision of weight according to the experience of decision maker, in order to increase the science of weight assignment, binding hierarchy analytic approach, the Importance of Attributes table of grading (as shown in table 2) utilizing Satty to propose compares between two to different criterions, draws comparative result matrix.

The importance rate table of table 2 evaluation index

Suppose there be n criterion, comparing the result drawn so is between two the matrix of n × n:

$A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& & a_{1n}\\ a_{21}& a_{22}& & a_{2n}\\ & & & \\ a_{n1}& a_{n2}& & a_{\mathrm{nn}}\end{array}\right]$

Wherein, a _ii=1, ai _j=1/a _ji, ai _j≠ 0.

Because the value in comparator matrix is generally provided by decision maker or expert, because expert also exists certain subjectivity when evaluating the importance of different criterion, so the inconsistency of judgement may be caused, reappraise with regard to needs when this inconsistency is serious.This inconsistency can utilize the eigenwert of comparator matrix to judge, concrete steps are as follows:

Step 1: ask comparator matrix each row and, such as formula (21).

$S_i=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ij}}---\left(21\right)$

Step 2: the eigenvalue of maximum λ calculating comparator matrix according to formula (22) _max.

${\mathrm{\&lambda;}}_{\max }=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{S}_i---\left(22\right)$

Step 3: utilize the consistance of the ratio C R of consistency check index CI and average homogeneity index RI to comparator matrix to judge.

$\mathrm{CI}=\frac{{\mathrm{\&lambda;}}_{\max }-n}{n-2}---\left(23\right)$

$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}---\left(24\right)$

Wherein, the value of average homogeneity index RI can be tried to achieve by the mode of tabling look-up, as shown in table 3.

Table 3 average homogeneity index table

Generally, as CR < 0.1, then can think that comparator matrix has good consistance, when CR >=0.1, then think that comparator matrix has larger inconsistency, need to adjust comparator matrix.

Complete after consistency check obtains having the comparator matrix of satisfactory consistency, just based on comparator matrix, can calculate the weight vectors of each criterion as follows:

Step 1: the numerical value of the every a line in comparator matrix is connected and takes advantage of, and open n power, shown in (25).

$c_i=\sqrt[n]{\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{A}_{\mathrm{ij}}}---\left(25\right)$

Step 2: the weight solving each criterion according to formula (26), (27).

$w_i=\frac{c_i}{C}---\left(26\right)$

$C=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_i---\left(27\right)$

Step 3: draw final weight vectors, shown in (28).

W＝{w _i|i＝1,2,...n} (28)

So far, the weight calculation of the interpretational criteria of Reconfigurable Manufacturing System evaluation method PROMETHEE algorithm is completed.

The selection of PROMETHEE preference function

When utilizing the parameter of index i to compare scheme a and scheme b, preference function can reflect the advantage size that scheme a has relative to scheme b.Because each index has different characteristics, thus need decision maker rule of thumb or actual conditions carry out the selection of preference function.Up to the present, six the most frequently used class preference functions cover most of situation.This six classes preference function is respectively:

1. common preference function

2. accurate judge preference function

3. linear preference function

4. level preference function

5. there is the linear preference function in irrelevance region

6. Gauss's preference function.

The definition of this six classes preference function presents in describing below.Before introducing this six classes preference function, need first to carry out some hypothesis and definition.

Preference function can reflect the advantage size (with the parameter of index i for foundation) that scheme a has relative to scheme b, therefore needs the deviation d of the index i of definition scheme a and scheme b _i(a, b), under normal circumstances, deviation d _ithe difference of the index i parameter that (a, b) is scheme a and scheme b, that is:

d _i(a,b)＝g _i(a)-g _i(b) (29)

Suppose d here _i(a, b)>=0, because work as g _i(b)>=g _itime (a), d can be used _i(b a) represents, for convenience of description, represents deviation d with variable x _i(a, b), that is:

x＝d _i(a,b) (30)

Six class preference functions are described below in detail.

Class1: common preference function

As can be seen from formula, when deviation is zero, namely when the parameter of the index i of scheme a and scheme b is equal, think that index i does not affect for the evaluation of scheme a and scheme b, namely the value of preference function is 0, once there is deviation, the value of preference function is 1, when namely only considering index i, strictly think that scheme a is better than scheme b.

Type 2: accurate judge preference function

As can be seen from formula, when deviation is no more than l, when namely the parameter difference of the index i of scheme a and scheme b is less than l, the value of preference function is 0, and when deviation is greater than l, the value of preference function is 1.

Type 3: linear preference function

As can be seen from formula, when deviation is no more than l, the preference of decision maker is linear increasing, and when deviation is more than or equal to l, the preference of decision maker reaches maximum 1, namely in the evaluation of index i, strictly thinks that scheme a is better than scheme b.

Type 4: level preference function

As can be seen from formula, when deviation is no more than l, think that criterion i does not affect for the evaluation of scheme a and scheme b, namely the value of preference function is 0, when deviation size is positioned between [l, l+s], think that scheme a is better than scheme b slightly, namely the value of preference function is 1/2, when deviation is greater than l+s, strictly thinks that scheme is better than scheme b.

Type 5: the linear preference function with irrelevance region

As can be seen from formula, when deviation is no more than l, think that index i does not affect for the evaluation of scheme a and scheme b, namely the value of preference function is 0, when deviation size is positioned between [l, l+s], think that scheme a linearly changes relative to the advantage of scheme b, namely the value of preference function is linear change, when deviation is greater than l+s, strictly thinks that scheme is better than scheme b.

Type 6: Gauss's preference function.

As can be seen from formula, when deviation is zero, preference function value is 0, and when deviation increases, preference function value changes according to Gaussian curve.

Method of the present invention is as follows:

Step 1: decision maker is before carrying out decision-making, work out evaluation of programme, each evaluation of programme includes several evaluation indexes, characteristic according to evaluation index selects different preference functions respectively, utilize each evaluation index to evaluate each scheme more respectively, calculate corresponding preference function value:

d _i(a,b)＝f _i(a)-f _i(b)；

{f ₁(a),f ₂(a),...,f _n(a)|a∈A}；

Wherein, f _ia () represents the parameter of the index i in scheme a, f _ib () represents the parameter of the index i in scheme b, A represents the set of possibility, d _i(a, b) represents the deviation of the index i of scheme a and scheme b, p _i(a, b) represent when only considering index i, scheme a relative to the preference value of scheme b, 0≤p _i(x, y)≤1, G _irepresent the preference function that decision maker selects for the characteristic of index i;

Step 2: the calculating of preference function.By the comparative result of n evaluation index of two schemes (the scheme a in such as step 1 and scheme b) that compares, (comparative result of i-th index of such as scheme a and scheme b is p _i(a, b)) weight vectors of convolution (28) calculates according to formula (40), thus draws the preference function of a scheme relative to another scheme, is defined as π (a, b).

$\mathrm{\&pi;}(a,b)=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{p}_i(a,b)}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i}---\left(40\right)$

Wherein, 0≤π (a, b)≤1.When π (a, b) more close to 1 time, illustrate compared with scheme b, decision maker is preference scheme a more.

Step 3: preference function π (a, x) simply show other schemes in scheme a and possibility set A between two relatively after preference relation, how is the total preference relation of other schemes so in scheme a and possibility set A? Here it is, and we need the evaluation of estimate of scheme a in all schemes determined further, and using this evaluation of estimate as the index of schemes ranking, shown in (41), (42).

${\mathrm{\&phi;}}^{+}\left(a\right)=\underset{x\&Element;A}{\mathrm{\&Sigma;}}\mathrm{\&pi;}(a,x)---\left(41\right)$

${\mathrm{\&phi;}}^{-}\left(a\right)=\underset{x\&Element;A}{\mathrm{\&Sigma;}}\mathrm{\&pi;}(x,a)---\left(42\right)$

Wherein, φ ⁺(a) represent compared with other schemes, decision maker for the preference of scheme a, φ ⁺a (), more close to 1, illustrates that decision maker more tends to selection scheme a, otherwise the selected possibility of scheme a will be very low, be even zero; φ ^-a () represents compared with other schemes, decision maker is for the detest degree of scheme a, and namely decision maker is more prone to the degree of other schemes, works as φ ^-(a) more close to 0 time, illustrate that decision maker more tends to selection scheme a, otherwise illustrate and select, scheme a will be a very bad decision.

Step 4: schemes ranking rule.Provide the partial ordered index of each scheme in step 3, so, how according to these indexs, all schemes to be sorted? now, need to formulate ordering rule, shown in (43), (44).

Wherein, P ⁺, P ^-expression scheme a has superiority more relative to scheme b, and namely decision maker more prefers to scheme a; I ⁺, I ^-do not have dividing of obvious quality between expression scheme a and scheme b, namely decision maker does not have preference for these two schemes.

Ordering rule according to definition carries out integrated ordered to scheme, shown in (45).

Wherein, P ^Ιrepresent decision maker more preference scheme a, namely as (φ ⁺(a) > φ ⁺(b) & φ ^-(a) < φ ^-(b)) or (φ ⁺(a) > φ ⁺(b) & φ ^-(a)=φ ^-(b)) or (φ ⁺(a)=φ ⁺(b) & φ ^-(a) < φ ^-(b)) time, scheme a has superiority than scheme b; I ^Ιit doesn't matter, namely as (φ to represent two schemes ⁺(a)=φ ⁺(b) & φ ^-(a)=φ ^-(b)) time, which probability decision maker select be the same; R represents that scheme a and scheme b cannot compare, and has such as occurred that certain scheme is very large relative to the advantage of other schemes, just cannot compare, i.e. (φ when inferior position is also very large ⁺(a) > φ ⁺(b) & φ ^-(a) > φ ^-(b)).

Step 5: step 4 can complete most schemes ranking, but when certain scheme is very large relative to the advantage of other schemes, just cannot compare when inferior position is also very large, i.e. (φ ⁺(a) > φ ⁺(b) & φ ^-(a) > φ ^-(b)).So consider that the index φ (a) that sorts completely makes up the deficiency of partial ordered index, shown in (46), the index that but sorts completely can lose the information of some details, so decision maker will take into account two sequence indexs when carrying out decision-making.

φ(a)＝φ ⁺(a)-φ ^-(a) (46)

The ranking results drawn according to the index φ (a) that sorts completely is such as formula shown in (47).

Wherein, P ^Πrepresent decision maker more preference scheme a; I ^Πrepresent that decision maker does not have preference to two schemes.

Since then, just complete/achieve the evaluation procedure of Reconfigurable Manufacturing System.

Advantage of the present invention:

(1) Reconfigurable Manufacturing System (RMS) was pursued and make response to turn of the market within the fastest time: the various production requirement proposed according to client, assay is carried out to existing system, determine whether manufacturing system satisfies the demands fast, if do not meet, then need to adjust software and hardware facilities, rebuild out the production function and productive capacity that meet production requirement.The evaluation of Reconfigurable Manufacturing System (RMS) is starting point and the terminal of system reconfiguration link, is significant to manufacturing system production cycle smooth transition.

(2) six symbolic characteristics of Reconfigurable Manufacturing System are taken into full account based on Reconfigurable Manufacturing System (RMS) evaluation method of PROMETHEE, comprise scalability, convertibility, diagnosticability, modularization, integration, customization, and from the angle of decision maker, utilize experience and the real data of decision maker, in conjunction with preference function (preference function), Reconfigurable Manufacturing System is reasonably evaluated.Evaluate clear thinking, in order, the implementation process of evaluation is easy to operate, has larger realistic meaning.

(3) the six large features for Reconfigurable Manufacturing System (RMS) have carried out comprehensive analysis, make to have taken into full account the reconstitution of system in system evaluation process, thus the evaluation of Reconfigurable Manufacturing System and the evaluation of other manufacturing systems are made a distinction.

(4) PROMETHEE algorithm is evaluated from the angle of decision maker Reconfigurable Manufacturing System Design scheme, make evaluation result meet decision-making requirements, and evaluation procedure is clear, specifically implements simple to operation.

(5) the Importance of Attributes table of grading utilizing Satty to propose and the weight of analytical hierarchy process to different indexs calculate, and compensate for the defect that decision maker rule of thumb carries out subjective assignment.

(6) for the preference function that different classes of choose targets is different, to make in decision process more closing to reality, thus obtain evaluation result more accurately.

The above is only to better embodiment of the present invention, not any pro forma restriction is done to the present invention, every any simple modification done above embodiment according to technical spirit of the present invention, equivalent variations and modification, all belong in the scope of technical solution of the present invention.

The present invention will be described to enumerate specific embodiment below:

Embodiment 1:

Quantitative formula (1)-(20) according to Reconfigurable Manufacturing System evaluation index quantize Reconfigurable Manufacturing System main points feature, in order to fully demonstrate the feature of PROMETHEE algorithm, avoid accidentalia to the interference of result of calculation simultaneously, design 5 evaluations of programme to compare, the key feature quantized result of these 5 schemes is as shown in table 4, and this quantized result of this quantification is the enforcement starting point of PROMETHEE algorithm: evaluate form.

The key feature quantized result of table 4 scheme to be evaluated---evaluate form

After completing the quantification of key feature, carry out the weight calculation of index, by the importance rate in the feature of analysis of key feature and the importance associative list 2 in manufacturing system, importance assignment is carried out to these six features, draw index importance comparator matrix as shown in table 5 according to table 2.

Table 5 index importance comparator matrix

Based on table 5, calculate six evaluation index { retractilities according to formula (21) (22) (23); Convertibility; Diagnosticability; Modularization; Integration; Customize } weight, draw weight vectors W={0.135; 0.218; 0.219; 0.187; 0.113; 0.126}.

The achievement data trend comparison that can analyze these 5 schemes according to the data of table 4 is similar, in order to simplify calculating, might as well all select common preference function.

After completing above-mentioned work, just can implement PROMETHEE algorithm, according to formula (37)---the index calculate result calculating schemes ranking that the computing method of (46) carry out being correlated with is as shown in table 6.

Table 6 schemes ranking index calculate result

Carry out partial ordered (PROMETHEE Ι) according to table 6 pair scheme and sort (PROMETHEE Ι Ι) completely, the result of sequence as shown in Figure 2,3.Scheme 4 is the poorest schemes as can be seen from Figure 2, but due to scheme 10 Φ+, Φ-value is all greater than scheme 1, i.e. with the obvious advantage relative to other schemes of scheme 10, but inferior position equally clearly, so just cause and cannot compare scheme 10 and scheme 1, this is also partial ordered shortcoming, not enough in order to make up this, complete sort method is adopted to draw result as Fig. 3, can find out that scheme 1 is better than scheme 10, scheme 4 is still the poorest scheme, although sort method can provide the sequence of all schemes completely, but also lost the detailed information of some schemes, the advantage of such as scheme has much, inferior position has much, so in specific implementation process, preferably partial ordered method and complete sort method are combined use, consider the quality of scheme.

Claims (4)

1., based on a Reconfigurable Manufacturing System evaluation method of PROMETHEE, it is characterized in that carrying out according to following steps:

Step 1: decision maker is before carrying out decision-making, work out evaluation of programme, each evaluation of programme includes several evaluation indexes, characteristic according to evaluation index selects different preference functions respectively, utilize each evaluation index to evaluate each scheme more respectively, calculate corresponding preference function value;

Step 2: the calculating of preference function; By the comparative result of all evaluation indexes of two schemes that compares in conjunction with weight vectors according to formula

$\mathrm{\&pi;}(a,b)=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{p}_i(a,b)}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i}$

Calculate, thus draw the preference function of a scheme relative to another scheme, be defined as π (a, b), wherein, 0≤π (a, b)≤1, as π (a, b) more close to 1 time, illustrate compared with scheme b, decision maker is preference scheme a more;

The total preference relation of other schemes in step 3: scheme a and possibility set A is as follows:

${\mathrm{\&phi;}}^{+}\left(a\right)=\underset{x\&Element;A}{\mathrm{\&Sigma;}}\mathrm{\&pi;}(a,x)---\left(41\right)$

${\mathrm{\&phi;}}^{-}\left(a\right)=\underset{x\&Element;A}{\mathrm{\&Sigma;}}\mathrm{\&pi;}(x,a)---\left(41\right)$

Wherein, φ ⁺(a) represent compared with other schemes, decision maker for the preference of scheme a, φ ⁺a (), more close to 1, illustrates that decision maker more tends to selection scheme a, otherwise the selected possibility of scheme a will be very low, be even zero; φ ^-a () represents compared with other schemes, decision maker is for the detest degree of scheme a, and namely decision maker is more prone to the degree of other schemes, works as φ ^-(a) more close to 0 time, illustrate that decision maker more tends to selection scheme a, otherwise illustrate and select, scheme a will be a very bad decision;

Step 4: schemes ranking Rulemaking;

Wherein, P ⁺, P ^-expression scheme a has superiority more relative to scheme b, and namely decision maker more prefers to scheme a; I ⁺, I ^-do not have dividing of obvious quality between expression scheme a and scheme b, namely decision maker does not have preference for these two schemes;

Ordering rule according to definition carries out integrated ordered to scheme:

Wherein, P ^Ιrepresent decision maker more preference scheme a, namely as (φ ⁺(a) > φ ⁺(b) & φ ^-(a) < φ ^-(b)) or (φ ⁺(a) > φ ⁺(b) & φ ^-(a)=φ ^-(b)) or (φ ⁺(a)=φ ⁺(b) & φ ^-(a) < φ ^-(b)) time, scheme a has superiority than scheme b; I ^Ιit doesn't matter, namely as (φ to represent two schemes ⁺(a)=φ ⁺(b) & φ ^-(a)=φ ^-(b)) time, which probability decision maker select be the same; R represents that scheme a and scheme b cannot compare, i.e. (φ ⁺(a) > φ ⁺(b) & φ ^-(a) > φ ^-(b));

Step 5: definition completely sequence index φ (a) makes up the deficiency of partial ordered index:

φ(a)＝φ ⁺(a)-φ ^-(a) (46)

Ranking results according to the index φ (a) that sorts completely draws:

Wherein, P ^Πrepresent decision maker more preference scheme a; I ^Πrepresent that decision maker does not have preference to two schemes.

2. according to the Reconfigurable Manufacturing System evaluation method based on PROMETHEE a kind of described in claim 1, it is characterized in that: described 6 evaluation indexes are respectively: retractility (S, Scalability), convertibility (C _v, Convertibility), diagnosticability (D, Diagnosability), modularization (M, Modularity), integration (I, Integrability), customize (C _m, Customisation).

3., according to the Reconfigurable Manufacturing System evaluation method based on PROMETHEE a kind of described in claim 1, it is characterized in that: described preference function comprises:

1. common preference function;

2. accurate judge preference function;

3. linear preference function;

4. level preference function;

5. there is the linear preference function in irrelevance region;

6. Gauss's preference function.

4., according to the Reconfigurable Manufacturing System evaluation method based on PROMETHEE a kind of described in claim 1, it is characterized in that: the computation process of described weight vectors is:

Step 1: the numerical value of the every a line in comparator matrix is connected and takes advantage of, and open n power, shown in (25):

$c_i=\sqrt[n]{\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{A}_{\mathrm{ij}}}---\left(25\right)$

Step 2: the weight solving each criterion according to formula (26), (27):

$w_i=\frac{c_i}{C}---\left(26\right)$

$C=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_i---\left(27\right)$

Step 3: draw final weight vectors:

W＝{w _i|i＝1,2,...n}。