Fuzzy Task Assignment Model of Web Services Supplier in Collaborative Development Environment

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1 , pp Fuzzy Task Assget Model of Web Servces Suppler Collaboratve Developet Evroet Su Ja 1,2, Peg Xu-ya 1, *, Xu Yg 1,3, Wag Pe-e 2 ad Ma Na- 4,2 1. College of Autoato, Harb Egeerg versty, Harb; 2. Ceter of Iforato ad Network, Helogag versty of Scece ad Techology, Harb; 3. College of Scece, Helogag versty of Scece ad Techology, Harb; 4. College of Iforato& Coucato Egeerg, Harb Egeerg versty, Harb; [email protected],[email protected], @qq.co, @qq.co, @qq.co Abstract I vew of collaboratve developet evroet web servces suppler ablty, cost, te suppler relatos ad copoet relevace forato uder ucertaty probles. The fuzzy ult-obectve task assget odel of web servces are bult a collaboratve developet evroet. sg cut sets ad exteso prcple to splfy the fuzzy ult-obectve assget ode, we get the soluto of splfed assget odel va the Geetc ad sulated-aealg algorth. I vew of the odel soluto sets are fuzzy ad ucerta ebershp fucto, a ew cetrod defuzzfcato ethod s used for the odel soluto. Thus the optzato allocato of copoet suppler s fuzzy task s realzed collaboratve developet evroet. Fally, the sulato results verfy the feasblty of the proposed ethod, whch ca esure the supplers taskg successve software proect collaboratve developet evroet. Keywords: collaboratve developet, fuzzy task assget, cetrod defuzzfcato 1. Itroducto I the process of collaboratve software developet based o web servces, software desgers ad aageet persoel wll cosder the collaboratve developet of web servces provders. By gvg full play to the provders capablty ad advatage of desg ad developet, they wll esure the servces qualty, reduce the overall cost of developet ad eve shorte the developet cycle. I spte of those advatages, there are soe probles such as how to assg tasks for the supplers the collaboratve developet ad how to select suppler scetfcally wth ucerta forato. Therefore, t s ecessary to put forward a scetfc ad reasoable ethod ad establsh a fuzzy task assget odel for web servces uder the collaboratve developet evroet. Sce supplers volveet s a portat lk the process of developet ad ovato collaboratve product developet, R&D eterprses are payg ore atteto to collaborato of ore supplers. Eve the supplers collaboratve developet has bee a subect aog ay research sttutos ad lteratures whch are dedcated to researchg ad explorg the theory fro several aspects. The lterature * Correspodg author. Tel.: E-al address: [email protected] ISSN: IJNESST Copyrght c 2015 SERSC

2 [1] ot oly defes for supplers volveet ew product developet ad assesses ts theory foudato, but also akes a proposal that we should vte supplers at the early stage of ew product developet, ad take advatage of the supplers desgg potetal order to boost the success rate of ew product developet. The lterature [2] troduces a exaple of early suppler volveet the product developet of a teratoal electroc copay ad further proves the vtal sgfcace of a resposble ad capable suppler s collaborato the process of ew product developet. The lterature [3] assesses partcpats collaboratve developet evroet ad establshes evaluato odel, coductg -depth aalyss for the developet process of a large proect, ad declares the assesset odel has a valuable referece ters of collaboratve developet proects. The above lteratures aly focus o explorg the ecessty ad fucto of supplers volveet collaboratve product developet, ad ts prcples ad ecessty also ca be used the collaboratve product developet based o web servces. Despte these acheveets, there reas a lack of correspodg theoretcal bass ad practcal applcato the suppler volveet product desg ad task allocato. I the process of supplers collaboratve developet based o web servces, the assesset of suppler s developet capacty, cost ad delvery te wll play a key role the success of software proect. Due to the ucertaty of developet cost, the lterature [4] uses sestvty aalyss ethod to solve assget proble uder fuzzy evroet. Moreover, t also copares the three kds of sestvty aalyss ethod ad gves correspodg solutos respectve evroet. The lterature [5] troduces preferece factor of decso akers choosg a suppler ad set up a fuzzy ult-task odel dealg wth supplers lowest cost, hghest stablty ad shortest delvery te, the covert t to a covex fuzzy sgle obectve odel. By dog that we ca fully preset ay fluetal factors betwee decso arkers ad supplers. The lterature [6] proposes a geeral odel of collaboratve desg that cotas the ethod fraework, coceptual fraework ad techology fraework. The user wll fsh the overall collaboratve task desg, task assget ad overall assesset. But the odel s ust a theoretcal fraework, rather a atheatcal odel correspodg to collaboratve task assget. The lterature [7] puts forward the dstrbuted collaboratve software developet odel that descrbes the relatoshp betwee the developet tea ad the task of foral cocept, ad troduces SMP (Stable Marrage Proble) ethod for task assget. The lterature [8] utlzes the partcle swar optzato algorth to solve the proble of ult-suppler volveet collaboratve product task assget, ad costructs the total te odel. The lteratures [4, 5] are based o fuzzy ult-obectve odel wth fuzzy forato of supplers ad o accout of supplers task assget collaboratve evroet. Eve though the lteratures [7, 8] solve the task assget proble collaboratve evroet by a ult- obectve optzato odel, they do ot preset how to assg tasks o the codto of fuzzy suppler forato. Through the research lteratures above, we fd that ost lteratures cocerg supplers' volveets product developet aly focus o the sequet terests brought by supplers ad assessets of supplers' forato, wth lttle forato of task assget collaboratve developet evroet, especally the feld of software proect developet. The collaboratve software developet process, based o web servces, ca reduce the coplexty of the software proect ad developet rsks. But there are stll two probles to be solved the process of software proect developet. O oe had, whe supplers are volved the developet, how to guaratee the coordato of the developet process, ad ake the developet te short. O the other had, we eed to take accout of the supplers' ucerta forato ad establsh a scetfc ad ratoal odel whe the supplers' developet ablty, collaboratve developet te ad cost forato are fuzzy. I vew of the above probles, the followg work has bee doe ths paper. I the 200 Copyrght c 2015 SERSC

3 odel costructo process, we fully cosdered the ablty of web servces suppler, cooperatve developet te ad cost forato the collaboratve developet evroet. The fuzzy ult-obectve task assget odel of web servces suppler s proposed collaboratve developet evroet, whch eet the supplers eed of hgh relablty, low cost ad short te the process of software proect developet ad provde the task optzato assget for software developet eterprses, whch ca guaratee the collaboratve developet evroet software supplers volved the successful copleto of the proect. I the process of pleetato the odel, we splfy the coplex fuzzy ult-obectve proble by the sets ad the exteso prcples ad set up sgle obectve optzato odel decoposed wth geetc ad sulated-aealg algorth. The odel soluto sets are fuzzy, the troducto of a ew ethod of ceter of gravty defuzzfcato of fuzzy sets are operated. Fally, we prove the effectveess of the ethod proposed ths paper by exaples. 2. Model Costructo Assug that the software aker has a large software proects deadg hgh relablty, low cost, the shortest te to arket. The arker wll decopose the proect to several web servces ad choose soe web servces supplers to partcpate the proect developet, order to ake full use of ther techology ad resources. Assug that the proect decoposto has bee copleted, the uber of web servce s, the uber of web servces suppler volved the software developet s. There s a te sequece the web servces developet process, so te process developet s w. the web servces developet tasks, ; the web servces supplers, ; :the :the x :0-1 varables,the p :the ablty of web servces s assged to the suppler developet of rage s [0,1]; developet sequece,the t o : the o WEB servces of the te,as a fuzzy uber rage s [0,1]; web servces; t :the logest developet te of the q o : the o developet sequece,the start te of the suppler; web servces,as a fuzzy uber web servces supplers developet the web servces, o1.. w c :the costs of suppler developet of web servces,as a fuzzy uber rage s [0,1]; e k :degree of forato depedece betwee the servces,as a fuzzy uber rage s [0,1]; d :the coordato degree betwee the, f ( k ) web servces ad the suppler ad bear servces suppler f( k ),as a fuzzy uber rage s [0,1]; Durg the web servces suppler collaboratve software developet process, t s essetal to detere the collaboratve workg te of each WEB servces suppler. Each WEB servces copleto te depeds o the three parts: web servces started collaboratve te, each suppler to the WEB servces ad WEB servces betwee developet te. By usg the ethods etoed the lterature [9], there are depedeces aog the web servces, so the collaboratve te suppler requred the developet of the web servces ca be expressed as: the k k ; web web Copyrght c 2015 SERSC 201

4 e k T k co ( ) e d k f ( ) k 1, f ( k ) dcates the degree of forato depedece betwee the (1) web servces ad the web servces, but the web servces forato depedece s dffcult to represet specfc quattatve data, so there are expressed by fuzzy ubers. represets the d, f ( k ) coordato degree betwee the suppler ad the suppler. Related to teroperablty betwee supplers, the exchage of forato betwee the degree of suppler, the collaborato degree vares aog dfferet suppler. Sce the specfc quattatve crtera are coplex, we use the fuzzy uber as the evaluato data. Whe, the coordato degree of up to 1. Each suppler to the web servces f ( k) developet te s expressed as t o t te ad each suppler to the copoet, the te of all web servces ca be expressed as : e T ( ) ( ( q t t ) ( )) w k total o o f ( ) o1 k 1 d, f ( k ). Accordg to the copoet of developet suppler to develop collaboratve developet Because of the exstece of forato depedece betwee dfferet web servces the process of web servces developet, there s a procedure proble whe the web servces assg tasks for supplers. The overall te of software proect developet eeds the copleto of each web servces, so t evtably depeds o the total te of supplers who take the ost developet te cocurret developet process. Therefore, software proect developet te shortest s seekg a al odel. The total te that each suppler to coplete the assget of web servces requred, all ther supplers to the u te of cosupto s zed, expressed as: ( Ttotal ( )) 1.. The fuzzy ult-obectve task assget odel of web servces s bult a collaboratve developet evroet, whch should cosder web servces perforace optzato, collaboratve developet wth the shortest te ad lowest cost. Fuzzy task assget proble of web servces suppler collaboratve developet evroet ca be descrbed as a fuzzy ult-obectve assget proble as follows: 1 G ( p x ) G ( c x ) 1 1 e G ( ( ( q t t ) ( ) x ) 1 w k o o 1,.., f ( ) o 1 k 1 d, f ( k ) s. t. x 1, 1,.., ; q t t q, o 1,.., w; 1,.., ; 1,.., ; o o o, 1 x 0 3. Model Soluto or 1, 1,.., ; 1,.., Fuzzy task assget odel of web servces suppler collaboratve developet evroet s a ult-obectve proble wth fuzzy syste, so t s dffcult to get a (2) (3) (4) (5) (6) 202 Copyrght c 2015 SERSC

5 accurate soluto. Accordg to the sets ad the exteso prcple, coprehesve aalyss of the lterature [9-11]. et ad as the target (4) of the upper ad lower bouds, ad G t G c ad G c G p G p as the target (5) of the upper ad lower bouds, G t as the target (56) of the upper ad lower bouds, the ult-obectve fuzzy assget odel s decoposed to two lear goal prograg odel(fmoap_1 ad FMOAP_2): MODE FMOAP_1: Z ( ( x) ( x) ( x)) st.. ( x) p ( x) c p c t ( p ) x Gp 1 1 Gp Gp c ( ) 1 1 Gc Gc G c x, w ( e ) k Gt ( ( ( o ( o ) ) ( )) ) 1,.., f ( ) q t t o x 1 k 1 ( d, f ( k )) t ( x) G G 1 x 1, 1,.., ; o o o, 1 t t q ( t ) t q, o 1,.., w; 1,.., ; 1,.., ; x 0 or 1 MODE FMOAP_2: 1, 1,.., ; 1,.., ; Z ( ( x) ( x) ( x)) st.. ( x) p ( x) c p c t ( p ) x Gp 1 1 Gp Gp c ( ) 1 1 Gc Gc G c x, w ( e ) k Gt ( ( ( o ( o ) ) ( )) ) 1,.., f ( ) q t t o x 1 k 1 ( d, f ( k )) t ( x) G G 1 x 1, 1,.., ; o o o, 1 t t q ( t ) t q, o 1,.., w; 1,.., ; 1,.., ; (7a) (7b) Copyrght c 2015 SERSC 203

6 x 0 or 1 1, 1,.., ; 1,.., ; To solve the odel FMOAP_1 ad FMOAP_2, upper ad lower bouds of each obectve fucto value ust be detered. We ca solve each obectve fucto(ot cosderg the obectve fucto) correspodg to the set u values.,, respectvely represet preferece of the suppler ablty, cost, developet te, ad the experts charge gve the value of preferece accordg to the actual stuato. It s value s the rage of [0, 1], ad eet. Because the coeffcets of obectve fucto are gve fuzzy uber, ad the values are obtaed by cut sets s fuzzy. Therefore the dfferet values, whch obtaed accordg to the specfc requreets of decso akers or usg the defuzzfcato ethod to cofr results. 4. Algorth Desg 0 of the u ad 1 Accordg cut sets ad exteso prcple, we have decoposed the fuzzy ult-obectve task assget odel to a lear goal prograg odel. The assgets of web servces suppler the collaboratve developet are teractve, therefore t s ecessary to select sutable heurstc algorth. By usg the geetc ad sulated-aealg algorth to solve the task assget odel, the basc process of solvg algorth are as follows: (1) Descrbe the algorth paraeters : the uber of web servces; : the uber of suppler; :tal teperature; W :utato rate; T Ge :the uber of geerato cycle; (2) Algorth descrpto 1) Code sg bary code (0 represet the suppler s ot assged, 1 represet the suppler s assged), the legth of the strg s the uber of web servces; 2) The tal populato Radoly geeratg the requred uber of populato, the legth of each populato for the web servces uber s. The populato of odes are represeted by bary, each dvdual the populato represets whether the suppler should be assged to coplete the correspodg web servces; 3) Select operato Geeratg the offsprg group fro the paret group, the radoly select dvdual of ad both fro the paret ad offsprg group, the ad s copettve to the ext geerato of probablty for: f ( ) f ( ) exp( ) T 4) Crossover operato The rado part structure of two paret dvdual s replaced ad reorgazed ad the geerates ew dvdual by usg the ult-pot crossover operator. 5) Mutato operato The rado uber 0-1 ad the coparso betwee the ways of utato, f the rado uber s less tha W, the selected paret populato by rado utato to geerate ew populato. 204 Copyrght c 2015 SERSC

7 5. Sulato Aalyss Assue that the software developer plas to desg a set of software syste whch s decoposed to 12 web servces. There are 8 caddate web servces supplers. Although each web servces suppler has dfferet forato (developet ablty, the developet cost, developet cycle), we eed to select the ost proper suppler collaboratve developet evroet. The codto s: the shortest developet cycle, the hghest relablty ad u cost. For the sake of clarty, we assue the sae developet te of dfferet supplers dealg wth the sae web servces at dfferet stages Because the suppler basc forato s fuzzy, we use the trapezodal fuzzy ubers to represet the dfferet degree of fuzzy forato, as show table 1. Table 1. Trapezodal Fuzzy Nuber Relatoshp ablty cost te web servces Suppler relatoshp relatoshp fuzzy uber A weakest owest shortest weakest weakest 0,0,0.1,0.2 B weak ow Short weak weak 0.1,0.2,0.2,0.3 C weaker lower Shorter weaker weaker 0.2,0.3,0.4,0.5 D oderat oderat oderat e e e oderate oderate 0.4,0.5,0.5,0.6 E stroger Hgher oger stroger stroger 0.5,0.6,0.7,0.8 F strog Hgh og strog strog 0.7,0.8,0.8,0.9 G stroges t hghest logest strogest strogest 0.8,0.9,1.0,1.0 The followg three Tables 2-4 respectvely represet the suppler (S1-S8) fuzzy evaluato value of desg web servces (C1-C12) capacty, cost ad developet te. Table 2. Suppler Developet Ablty ablty C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 S1 F B B B F E D B F B F F S2 E G F B F F G D B B B C S3 D F E D B F F F B C C B S4 B D F A F E B G F F F F S5 B D B G E G B B C F E E S6 D B G F C B B C C F B F S7 D B F B B B F C E D C G S8 F D E C F D F F F G E B Table 3. Suppler Developet Cost cost C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 S1 D B A E D D C D D F D C S2 D F D C C D D C D C D F S3 E F F C D F E E C C F E S4 C E D B E B F C C B F C S5 B D B F E E C D B C B B Copyrght c 2015 SERSC 205

8 S6 C F D E D G E D B D B C S7 C F D B D F D F E E B D S8 F C E F B D E F F D E D Table 4. Suppler Developet Te te C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 S1 A E F C F D B E B F A B S2 C A B F A D A F F E G F S3 E C C E F B D B D D F F S4 G B D G B F D A A B B E S5 F B D A B C F D E C B C S6 D D A B D F D F D D F B S7 D E B F G E C C F D D A S8 C F B F F D B C B A D B After the decoposto of proect, the forato depedece degrees of each web servces are gve Table 5. The forato depedecy atrx s syetrc, the sae web servces ad the o depedece forato degree of web servces s 0. Table 5. Iforato Depedece of Web Servces C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C1 0 F G C B B C C2 0 0 E F F 0 B C F 0 C C 0 0 C F 0 C C 0 C F 0 C B 0 C6 0 0 B F C C 0 C7 0 0 F F C 0 C8 0 0 F F D C9 0 F D B C10 0 F E C11 0 F C The coordato degrees of dfferet supplers are showed the Table 6, whch the hghest degree of coordato betwee supplers s oe. At the sae te the hgher degree of coordato, the coordato sped less te. Table 6. Degree of Coordato Betwee Supplers S1 S2 S3 S4 S5 S6 S7 S8 S1 1 F B F B E D B S2 1 B D B D E B S3 1 B B D B C S4 1 B F F B S5 1 B D B 206 Copyrght c 2015 SERSC

9 S6 1 F D S7 1 F S8 1 The web servces for the logest te 20],the web servces process o t s followg Table 7: : Te= [ Table 7. Web Servces Process o Accordg to the SGSA algorth the MATAB prograg, put paraeter =1000, =0.35, Ge =1000. Suppler capacty, cost, developet te s respectvely 0.2,0.3,0.5. sg =0,0.1,0.2,..,1)ca be calculated for each set of solutos of,,, Z. The soluto sets Table 8, the correspodg ebershp fucto dstrbuto s show Fgure 1. T G 1 W G 2 G 3 cuts( Table 8. G 1, G 2, G 3, Z Fuzzy Sets ( P) ( P) ( C) ( C) ( T) ( T) ( Z) ( Z) Copyrght c 2015 SERSC 207

10 Fgure 1. G 1, G 2, G 3 Mebershp Fucto Dstrbuto It ca be see fro Fgure 1 after calculatg suppler ablty, cost ad te as a fuzzy uber. The calculato results are dfferet for dfferet cut sets, ad the calculated results for the rage are dfferet (.e. as a fuzzy uber). It wll eed to be defuzzfed to a real uber, whch provde a accurate assget schee for decso akers. Z 6. The Cetrod Defuzzfcato Method Several defuzzfcato ethods have bee developed the fuzzy cotrol area, such as the cetrod, the ceter of a ethod, ad the ea of a ethod [13]. Aog the, the cetrod defuzzfcato ethod s ofte used, ad ths ethod s defed as follows: x ( A) 0 d a d a x ( x) dx A ( x) dx A Z (8) The odel (FMOAP_1 和 FMOAP_2) ca be defuzzfed to a real uber by Forula (8), that the fuzzy ebershp fucto ust be kow. But t s dffcult to cofr the fuzzy ebershp fucto of the odel (FMOAP_1 和 FMOAP_2). I ths paper, usg the ethod etoed the lterature [12], we copute uder the left ad rght boudary value by set. By usg set defuzzfcato, we get Table 9. sg the data of Table 9 to forula (9) gettg, fally get the task assget schee are gve Table 10 ad developet process followg Fgure 2. Z( A) (( z) ( z) ) 2 (( z) ( z) ) (( z) ( z) ) 2 (( z) ( z) ) (( z) ( z) ( z) ( z) ) 1 Z( A) 3 Table 9. The Soluto of Cetrod Defuzzfcato Method ( z) ( z) ( z) ( z) 2 2 ( z) ( z) 1 Z ( z) ( z) (9) Copyrght c 2015 SERSC

11 Table 10. Task Assget Schee web servces suppler Coclusos Fgure 2. The Developet of Task Process Because there s o certa relevat forato of copoet supplers ablty, cost, te, suppler relatos ad web servces collaboratve developet evroet, we put forward the fuzzy ult-obectve task assget odel of web servces ths paper. I ths way, we ot oly realze the dead of hgh relablty, low cost ad short te of web servces the process of software developet proects, but also provde a task optzato assget for software Developet Copay. I the process of solvg the odel optal soluto, we splfy the coplex fuzzy ult-obectve proble to a sgle obectve optzato proble usg set ad exteso of the prcple, get the splfed sgle obectve optzato odel wth the Geetc ad sulated-aealg algorth, ad fally verfy ts good covergece by sulato. Besdes, respose to the fal odel soluto sets are fuzzy ad ucerta ebershp fucto, we troduce a ew cetrod ethod o fuzzy sets to be defuzzfed ad get the fal soluto, whch ca reasoably ad effectvely assg the correspodg supplers the decoposed web servces ad arrage further procedures. Therefore, ths paper ca support task assget for dfferet supplers volved software developet collaboratve developet evroet both theory ad practce. Ackowledgeets The authors wsh to ackowledge the fudg support fro The Educato Departet of Helogag provce scece ad techology research proects o Copyrght c 2015 SERSC 209

12 Refereces [1] T. E. Johse, Suppler volveet ew product developet ad ovato: Takg stock ad lookg to the future, Joural of Purchasg& Supply Maageet, vol. 15, o. 3, (2009), pp [2] R. McIvor, P. Huphreys ad T. Cadde, Suppler volveet product developet the electrocs dustry: A case study, J.Eg.Techol Maage, vol. 23, o. 4, (2006), pp [3] Z. Kha, D. udlow ad S. Caceres, Evaluatg a collaboratve IT based research ad developet proect, Evaluato ad Progra Plag, vol. 40, (2013), pp [4] C.-J.,.-P. We ad P.-Y., Advaced sestvty aalyss of the fuzzy assget proble, Appled Soft Coputg, vol. 11, o. 8, (2011), pp [5] F. Arka, A fuzzy soluto approach for ult obectve suppler selecto, Expert Systes wth Applcato, vol. 40, o. 6, (2013), pp [6] J. Gallardo ad C. Bravo, A odel-drve developet ethod for collaboratve odelg tools, Joural of Network ad Coputer Applcatos, vol. 35, o. 3, (2012), pp [7] A. Sgh, A collaboratve software developet odel based o foral cocept aalyss ad stable atchg, Iteratoal Coferece o Iforatcs, Electrocs ad Vso, (2013) October 15-19, Doggua, Cha. [8] Z. Wa-Ju,. We ad Z. Z-Ja, Task assget for supplers partcpato collaboratve product developet, Coputer Itegrated Maufacturg Sysytes, vol. 15, o. 6, (2009), pp [9]. H. Che, A fuzzy odel for explotg qualty fucto deployet, Matheatcal ad Coputer Modellg, vol. 38, o. 5-6, (2003), pp [10] C. Kao, Fuzzy effcecy easures data evelopet aalyss, Fuzzy Sets ad Systes, vol. 113, o. 3, (2000), pp [11]. A. Zadeh, Fyzzy sets as a bass for a theory of possblty, Fuzzy Sets ad Systes, vol. 100, o. 1, (1999), pp [12] Y.-M. Wag, Cetrod defuzzfcato ad the zg set ad zg set rakg based o alpha level sets, Coputers & Idustral Egeerg, vol. 57, o. 1, (2009), pp [13].-H. Che ad M.-C. Weg, A evaluato approach to egeerg desg QFD processes usg fuzzy goal prograg odels, Europea Joural of Operato Research, vol. 172, o. 1, (2006), pp Author Su Ja, he s a doctoral studet College of Autoato, Harb Egeerg versty, Harb, Cha. Hs research terests focus o Web servces, syste tegrato. 210 Copyrght c 2015 SERSC