Open Access Optimal Configuration Algorithm for Mechanical Products Based on the Constraint of Carbon Footprint

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1 Send Orders for Reprnts to 32 The Open Mechancal Engneerng Journal, 2, 9, Open Access Optmal Confguraton Algorthm for Mechancal Products Based on the Constrant of Carbon Footprnt We Bo *,, L Renwang 2, Zheng Hu, Chen Gang and Zong Xanlang College of Mechancal Engneerng, Tanjn Unversty of Scence and Technology, Tanjn, 3222, P.R. Chna 2 Faculty of Mechancal Engneerng and Automaton, Zhejang Sc-Tech Unversty, Hangzhou, 38, P.R. Chna Abstract: The concept of carbon footprnt controllable product s proposed to assess carbon footprnt durng the stage of product development and confguraton. It s dfferent from carbon footprnt assessment afterwards. As a result, the control objectves can be quantfed accurately and realzed easly. Relatons among product characterstcs, whch nclude carbon footprnt, are uncertan. In order to obtan the optmal product confguraton scheme based on constrant of carbon footprnt, three-stage theory s proposed. These three stages refer to functonal confguraton, complance evaluaton of carbon footprnt, and optmal comprehensve evaluaton. Usng ths theory, functonal feasble soluton set, carbon footprnt conformng set and the optmal scheme are generated respectvely. Grey relaton analyss s verfed as an effectve method for comprehensve beneft evaluaton. Reducer desgn s used as a case study to llustrate the proposed concept. Keywords: Product confguraton, Carbon footprnt, Grey relaton analyss, Mult-objectve decson-mang.. INTRODUCTION Carbon footprnt (CFP) can be dvded nto four types: natonal carbon footprnt, enterprse carbon footprnt, personal carbon footprnt, and product carbon footprnt. Recently, more and more concerns and attenton have been pad to the last categorzaton,.e. product carbon footprnt. Carbon footprnt label s the manfestaton of product carbon footprnt to show the amount of greenhouse gas emssons durng all processes, ncludng producton, transportaton, sales stage, sometmes also ncludng use stage and fnal dsposal stage. One of the purposes of carbon footprnt label s to mae enterprses better communcate wth consumers about enterprse's efforts n energy conservaton and carbon emssons reducton, as well as carbon footprnt. Consequently, consumers are able to compare products among dfferent manufacturers. In recent years, low carbon product standards have developed rapdly. The trend has the potental to evolve nto a wde range of green trade barrers, ratonalty n surface, legalty n form, wdespread n content, and concealment n mplement. The concept of Carbon Footprnt Controllable Products s proposed to meet the eternal demands such as carbon tarffs, other nternatonal trade barrers, consumer preference, and government requrements. Ths concept can also help enterprses to ncrease consumng effcency of energy and resources, mprove producton process, and reduce cost etc., wth the prces of energy and raw materals rsng qucly. Because carbon footprnt s closely related to greenhouse emsson, more and more partners worldwde ncludng manufacturers, consumers, governments and envronmental groups put more attenton to product carbon footprnt. Many *Address correspondence to ths author at the College of Mechancal Engneerng, Tanjn Unversty of Scence and Technology, Tanjn, 3222, P.R. Chna; Tel: ; E-mal: webotj@63.com studes have been conducted n the related felds. The man progresses focus on:.. Low Carbon Manufacturng and Desgn Technology Rapd Manufacturng (RM) s regarded as the low carbon manufacturng technology of the future []. Scpon et al. have proposed a method, whch can dentfy man processes contrbutng to clmate change n enterprse producton and supply chan [2]. Rahmfard et al. have proposed a general conceptual and computatonal framewor for the effcency evaluaton of the manufacturng processes [3]. Alsaffar et al. hghlghted the mportance of reducng carbon footprnt through smultaneous consderaton of manufacturng processes and supply chan actvtes [4]. Bao et al. constructed a mult-constraned objectve optmzaton model to obtan the most reducton of carbon emsson through low-carbon desgn mprovement of ey modular unts []..2. Low Carbon Supply Chan To brng carbon footprnt management nto supply chan, the tradeoff among cost, servce, qualty and carbon emsson must be acheved by coordnaton of supply chan n product, process, nformaton and captal [6]. A mult-objectve med nteger programmng model s used to ntegrate carbon emssons and the total cost of logstcs supply chan nto desgn process, the effects of carbon tradng rght to supply chan desgn are also taen nto account[7]. Ingram and Dewayne acqure product carbon footprnt data through applyng EPC to supply chan of enterprse product, tracng and montorng the products carbon emssons from producton, storage, dstrbuton, transport and consumpton [8]..3. Verfcaton of Product Carbon Footprnt A large number of research have focused on carbon footprnt calculaton and verfcaton methods for specfc prod- 874-X/ 2 Bentham Open

2 Optmal Confguraton Algorthm for Mechancal Products The Open Mechancal Engneerng Journal, 2, Volume 9 33 Fg. (). The collaboratve research and development framewor of CFP controllable product. ucts n many dfferent felds such as plastc, wood, and hotel [9-2]. In fact, carbon footprnt over product lfe cycle only represents one attrbute of a product. Only after enterprses consder all aspects ncludng cost, qualty and many other factors durng product desgn and confguraton, can they mae the rght decson. Especally, reducng carbon footprnt may deterorate other ndcators, such as cost, due to the nherent relatons among these factors. Hence, as a whole, carbon footprnt of products s not the smaller the better. Core enterprses should match carbon footprnt wth other relevant ndcators, and control carbon footprnt at a reasonable level, such product can be called carbon footprnt controllable products. Product carbon footprnt plannng s a multobjectve decson problem based on constrant of carbon footprnt. 2. CONFIGURATION STRATEGY AND ALGO- RITHM OF CFP CONTROLLABLE PRODUCT Tradtonal product confguraton only needs to meet functonal requrements from customers. Now the confguraton scheme must also control product carbon footprnt. Carbon footprnt controllable product requres quantfable carbon emsson evaluaton durng desgn stage accordng to the specfed standard. Hence, carbon footprnt of the fnal product can be realzed wthn an acceptable margn of error. Certanly, t s necessary to mae a tradeoff among factors such as cost, qualty, delvery tme, etc. 2.. Collaboratve R&d Framewor of CFP Controllable Product From the vewpont of Lfe Cycle Assessment (LCA), product carbon footprnt conssts of mported carbon footprnt from supply chan (raw materals and components), carbon footprnt from core manufacturng enterprse, logstcs carbon footprnt, carbon footprnt from consumng and EOL (End of Lfe). Fg. () llustrates collaboratve research and development framewor of CFP controllable product. Carbon footprnts from transportaton, consumng, EOL are nfluenced by many uncertan factors. Relevant accurate databases are hard to obtan. Usually, what core enterprses are able to control nclude choosng raw materals, selectng supplers, and controllng manufacturng processes. Therefore, confguraton algorthm s essental to the proposed carbon footprnt controllable product development. As shown n Fg. (), the confguraton process ncludes three stages: functon confguraton, carbon complance evaluaton, and comprehensve beneft evaluaton. The functon feasble soluton set, carbon footprnt conformng set and optmal scheme are generated after the above-mentoned three stages. How to set a reasonable target for product carbon footprnt? If clents have requrements for carbon footprnt, t should be satsfed as much as possble. If clents have not come up wth specfc requrements, the ndustry standard should be followed nstead. In addton, core enterprses can also set a compettve carbon footprnt standard usng a topdown or bottom-up method to embody ther socal responsblty, to fulfll the preferences of envronmental conscous customers as well. Why s t emphaszed that the above-mentoned processes are on a collaboratve development platform? The net secton of ths paper s based on the premse that core enterprses can obtan suppler s real-tme nformaton such as prce, qualty, delvery tme, carbon footprnt ndees convenently, for nstance, through Internet. Supported by suppler ratng system, core enterprses can create an nde database of product components and parts. Ths database s vtal for sub-

3 34 The Open Mechancal Engneerng Journal, 2, Volume 9 Bo et al. sequent evaluaton for product confguraton schemes. Therefore, product development process of core enterprse s actually a collaboratve development process accompaned by contnuous nformaton echange wth supplers Confguraton Algorthm Grey Relatonshp Analyss (GRA) ams at analyzng the relatonshps n behavor, posture, and boundary. Dfferent from tradtonal mathematcal analyss, GRA provdes a smple scheme to analyze the seres relatonshps or the system behavor, even f the gven nformaton s nsuffcent. In fact, t s a holstc comparson method wth reference system [3]. In the early stage of product desgn and development, product s attrbutes, ncludng carbon footprnt, are fuzzy. Therefore, an acceptable result can be drawn usng GRA. Defnton : Product characterstc (ndcator) seres. Characterstc nformaton of an object part can be epressed as : = ( (), (2), L, ( )) ' ' ' ' therefore, commonly used ndcators for mechancal product suppler evaluaton, cost (C), qualty (Q), on-tme delvery rate (T), purchase cost savng rate (H), credt (M), plus carbon footprnt, form a seres to descrbe parts characterstcs (ndcators) of suppler as follows: = (( CFP), C, Q, T, H, M, L ) ' Defnton 2: Scheme-characterstc (ndcator) matr. The matr that descrbes all characterstcs (ndcators) of a product s functon confguraton for a scheme s, ( CFP) ( CFP) 2 ( CFP) 3 C C2 C n Q Q2 Q n T T2 L Tn H H2 H n M M2 Mn L L In the above matr, each row represents a characterstc (ndcator), each column represents the characterstc (ndcator) set for a confguraton scheme. The frst step s functonal confguraton and carbon complance evaluaton. Because supplers are bascally equvalent n product functonal requrements fulfllment, product functonal confguraton s smplfed nto a problem of permutaton and combnaton. Usng ehaustve method or relevant computer software and procedures, an deal result can be found. The second step s comprehensve beneft evaluaton. As Fg. () llustrates, at ths stage, secondary apprasal targets should be comprehensvely evaluated ecept for carbon footprnt. The man steps are shown as follows: Accordng to scheme-characterstc (ndcator) matr, we can form scheme pattern seres: = ( C, Q, T, H, M ) ( =,2, L, n) And s the scheme number. To form the characterstc (ndcator) pattern seres ( ), and s the number of product s characterstcs (ndcators). Here s. For nstance, cost seres () = ( C, C2, C3, C4, C, C6), qualty seres (2) = ( Q, Q, Q, Q, Q, Q ). Intalzng the characterstc (ndcator) pattern seres ( ) INIT '( ) = ( ) For cost seres (), C C C C C C C C C C C C () = (,,,,, ) Therefore, the characterstc (ndcator) pattern seres of scheme s = (,,,,), and the others are: C Q T H M =(,,,, ) ( =2,3, L, n) C Q T H M The nflu of ndcator s polartes s: Q(2), T(3), H(4), M() P (ma) ( ) C P (mn) OL The ndcator s domnatng data and ther ntalzed values are shown n Table. Table. OL Domnatng data and ther ntalzed values. Domnatng Data Intalzed Values C() C mn={c, C 2,, C 6} C mn/ C Q() Q ma={q, Q 2,, Q 6} Q ma/ Q T() T ma={t, T 2,, T 6} T ma/ T H() H ma={h, H 2,, H 6} H ma/ H M() M ma={m, M 2,, M 6} M ma/ M Accordng to the polartes of seres and by means of Domnatng Prncple n grey theory, the reference seres s obtaned. = ( C(), Q(2), T(3), H(4), M()) = C Q T H M C Q T H M mn ma ma ma ma (,,,, ) By tang dfference as Δ ( ) = ( ) ( ),we thus have the followng dfference seres Δ ( =,2,3, L, n) : C Q T H M Δ = mn ma ma ma ma ( C, Q, T, H, M ) C Q T H M!(mn) = mn!(ma) = ma mn! ()! () ma Calculatng all schemes grey relatonal coeffcent and grade.

4 Optmal Confguraton Algorthm for Mechancal Products The Open Mechancal Engneerng Journal, 2, Volume 9 3 Defnton 3: Grey relatonal coeffcent s a comparatve measure between ponts. (mn) + ζ (ma) γ ( ( ), ( )) = Δ + ζ (ma) Where parameter n (mn) = mn mn Δ ( ) s lower envronment LY, and envronment parameter n gr (ma) = ma ma Δ ( ) s upper gr LY. ζ [,], dstngushng coeffcent, usually accordng to the prncple of mnmum nformaton, ζ =.. Set (mn) = a (ma) = b then, grey relatonal coeffcent a+. b γ( ( ), ( )) = = ξ( ) Δ +. b Defnton 4: By focusng the γ ( ( ), ( )) at utter ponts, the algorthm on grey relatonal grade s as follows: γ(, ) = γ( ( ), ( )) n = The grey correlaton grade s a comparatve measure among seres. Scheme s evaluated based on grey correlaton grade; the scheme wth the mamum value s regarded as the best. 3. CASE STUDY A small reducer enterprse adopts the above-mentoned mechancal products optmal confguraton algorthm based on the constrant of carbon footprnt to verfy the effectveness. The assembly BOM s shown n Fg. (2). Fg. (2). BOM of the reducer. Among the parts, F s manufactured by the enterprse, and E, G, H, I are provded by supplers. The matchng numbers of supplers for them are 3, 2, 3, 2 respectvely. The nde sequences for each suppler are shown n Table 2. Stage of functon confguraton. Because each suppler s parts are standard n functon and nterface, there are no Fg. (3). Combnaton of supplers. Table 2. The nde sequence lsts of dfferent supplers. Parts Num Supplers Inde Sequence E 3 S3-E S3-E S32-E 26,24,.99,.9,26,.99,.96 3,38,.99,.94 F 2 manufactured 6, 8,.99,.96 G 3 H 4 I 4 S4-G S4-G S-H S-H S2-H S2-I S2-I 27,3,.99,.96 24,37,.99,.96 78, 6,.99,.9 7, 68,.98,.96 73, 66,.99,.9 43,,.99,.97 38,,.99,.98

5 36 The Open Mechancal Engneerng Journal, 2, Volume 9 Bo et al. Fg. (4). Partal results screenshot by software. constrant conflcts. Theoretcally, t s a problem of permutaton and combnaton. Obvously, there are =36 functonal feasble schemes. Fg. (3) llustrates the combnaton of supplers. Stage of complance evaluaton for carbon footprnt. To fnd the schemes whch meet the carbon footprnt requrement from functon feasble scheme set, namely the schemes whose total CFP satsfy CFP p. Descrpton of the problem: The assembly BOM has four varables, a, b, c, and d, representng four alternatve carbon footprnt values, respectvely. It s assumed that a has three optons, b has two optons, c has three optons, and d has two optons. Accordng to the requrement, carbon footprnt of the products should be less than g, and the carbon footprnt of F (2) s 3g ( 6 2 ). As a result, the total carbon footprnt of other four parts cannot be more than 42g, a+b+c+d p, and p s 42 g. For smplcty, CFP, C, Q, T are consdered frstly. { } { } { } { } a= 78,7,73 b= 43,38 s.t c = 26,,3 d= 27,24 a+ b+ c+ d p; Fg. (4) shows partal results screenshot by software calculatng. Accordng to the above result calculated, there are 6 schemes conformng to carbon footprnt constrant. They are [28,2,34,62][292,2,34,62][28,72,34,62], [32,2,34,62][292,72,34,62][28,72,378,62]. Usng [28,2,34,62] as an eample, whch corresponds to scheme, eplaned as follows: the scheme s confgured by, S-H(7,68,.98,.96), S2-I(38,,.99,.98), S3-E(,26,.99,.96), S4-G(24,37,.99,.96), and manufactured part F6,8,.99,.96. Where a=7b=38c=d=24. So, for scheme, Total CFP =9g Total cost =22yuan Total qualfed rato =.8469 Total On-Tme Delvery Rate (ODR) =.8367 Usng the same method to calculate the remanng data of other fve schemes, addng purchase cost savng rate (H) and credt (M), the nde lst of carbon footprnt conformed set s shown n Table 3. At ths stage, carbon footprnt constrant has been satsfed, therefore no longer nvolved n the net comprehensve evaluaton subsequently. The stage of optmal comprehensve evaluaton. From Table 3, we can form the scheme pattern seres: Scheme : = ( C, Q, T, H, M ) = (22,.8469,.8367,.7,.89)

6 Optmal Confguraton Algorthm for Mechancal Products The Open Mechancal Engneerng Journal, 2, Volume 9 37 Table 3. Inde lst of CFP conformed set. X X2 X3 X4 X X6 C() Q(2) T(3) H(4) M() Scheme 2: = ( C, Q, T, H, M ) = (244,.882,.839,.2,.92) Scheme 3: = ( C, Q, T, H, M ) =(232,.74,.8282,.9,.83) Scheme 4: ' = ( C, Q, T, H, M ) = (24,.882,.828,.2,.87) Scheme : = ( C, Q, T, H, M ) = (224,.8644,.89,.4,.8) Scheme 6: = ( C, Q, T, H, M ) =(248,.83,.89,.6,.8) Characterstc(ndcator) pattern seres: Cost seres: () = ( C, C, C, C, C, C ) = (22,244,232,24,224,248) Qualty seres: (2) = ( Q, Q, Q, Q, Q, Q ) = (.8469,.882,.74,.882,.8644,.83) ODR seres: (3) = ( T, T, T, T, T, T ) = (.8367,.839,.8282,.828,.89,.89) Purchase cost savngs rate seres: (4) = ( H, H, H, H, H, H ) = (.7,.2,.9,.2,.4,.6) Credt seres: () = ( M, M, M, M, M, M ) = (.89,.92,.83,.87,.8,.8) Intalzng the characterstc (ndcator) pattern seres ( ), therefore () = (,.9969,.992,.993,.989,.978) (2) =,.489,.886,.489,.28,.987 (3) = (4) = () = Hence, the characterstc (ndcator) pattern seres of scheme s = (,,,,), and the others are: = (.9969,.489,.2,.76,.34) = (.992,.886,.9898,.8,.933) = (.993,.489,.9896,.23,.978) = (.989,.28,.979,.824,.9) = (.978,.987,.979,.94,. 899) The nflu of ndcator s polartes are as follows: Q(2), T(3), H(4), M() P (ma) C() POL(mn) The ndcator s domnatng data and ther ntalzed values are lsted n Table 4. Table 4. OL Domnatng data and ntalzed values. Domnatng Data Intalzed Values C() Q() T() H().2.23 M() Accordng to the polartes of seres and by means of Domnatng Prncple n grey theory, the reference seres s obtaned. = ( C(), Q(2), T(3), H(4), M()) = (.9779,.4888,.22,.23,.34) By tang dfference as Δ ( ) = ( ) ( ),we thus have the followng dfference seres Δ ( =,2,3, L, n) :

7 38 The Open Mechancal Engneerng Journal, 2, Volume 9 Bo et al Δ = (.282,.4888,.22,.23,.34) Δ = (.28,,,.29,.6) 2 Δ = (.238,.6237,.37,.7,.) 3 Δ = (.23,,.393,,.6) 4 Δ = (.724,.293,.42,.4,.24) Δ = (,.683,. 42,.294,.3) 6 Δ (mn) = mn mn Δ ( ) = Δ (ma) = ma ma V ( ) =.29 Calculatng all schemes grey relatonal coeffcent and grade. The grey relatonal coeffcent a+. b γ ( ( ), ( )) = =ξ( ) Δ +. b Where a=b=.29. ξ = (.47468,.477,.4834,.3462,.4698) ξ ξ ξ ξ 6 = (.47737,.,.,.2,.49439) = (.4846,.3827,.4726,.4944,.4984) = (.47872,.,.47238,.,.424) = (.9388,.92669,.8673,.396,.6882) ξ = (,.82,.8673,.4739,.6628) The grey correlaton grade n γ(, ) = γ( ( ), ( )) n = ξ γ(, ) =.449 ξ γ(, ) = ξ γ(, ) = ξ γ(, ) = ξ γ(, ) =.7672 ξ γ(, ) = That s to say, γ(, ) > γ(, ) > γ(, ) > γ(, ) > γ(, ) > γ(, ) Accordng to the value of grey correlaton grade, the ranng of schemes from good to bad s: Scheme 6, scheme, scheme 4, scheme, scheme 2, scheme 3 Therefore, based on constrant of carbon footprnt, the optmal confguraton scheme s scheme6 [28,72,378,62], that means the proper supplers are: S-H(7,68,.98,.96),S2-I(43,,.99,.97), S3-E(26,24,.99,.9),S4-(24,37,.99,.96). 4. CONCLUSION Through comprehensve evaluaton of carbon footprnt of product, core enterprses can reasonably plan product carbon footprnt based on eternal carbon footprnt constrants, accordng to ther technology and management level. The carbon footprnt controllable product means controllng carbon emssons durng product development and confguraton stage. It s dfferent from tradtonal end-of-ppe control methods. Therefore, the control objectves can be quantfed accurately and realzed easly. The conclusons from ths study are summarzed as follows. The collaboratve research and development framewor of CFP controllable product s proposed based on LCA theory. Product confguraton s the most mportant lfe cycle stage for reducng carbon footprnt. A new three-stage theory under the constrant of carbon footprnt has been proposed. Grey correlaton analyss s verfed to have a good effect n terms of comprehensve beneft evaluaton for carbon footprnt controllable product. CONFLICT OF INTEREST The author confrms that ths artcle content has no conflct of nterest. ACKNOWLEDGEMENTS The wor was fnancally supported by the Natonal Natural Scence Foundaton of Chna (Grant No ) and the Scence Research Foundaton of Tanjn Unversty of Scence and Technology (Grant No.223). REFERENCES [] G. Hague, ATKINS: Manufacturng a Low Carbon Footprnt. Southborough Unversty, UK, 2. [2] A. Scpon, M. Mastrobuono, A. Mazz, Voluntary GHG management usng a lfe cycle approach A case study, Journal of Cleaner Producton. vol. 8, pp , 2. [3] S. Rahmfard, Y. Seow, T. Chlds. Mnmzng Emboded Product Energy to support energy effcent manufacturng, CIRP Annals- Manufacturng Technology, vol. 9, pp. 2-28, 2 [4] A.J. Alsaffar, K.R. Haapala, K.-Y. Km, K. Oudan, E. Gül, A process-based approach for cradle-to-gate energy and carbon footprnt reducton n product desgn, ASME 22 Internatonal Manufacturng Scence and Engneerng Conference Collocated wth the 4 th North Amercan Manufacturng Research Conference and n Partcpaton wth the Int. Conf., MSEC 22, 22, pp. 4-. [] B. Hong, L. Guangfu, W. Ja. Optmal desgn of products wth low-carbon based on carbon footprnt analyss, Journal of Computer-Aded Desgn and Computer Graphcs, vol. 2, pp , 23. [6] B. Karen, G. Detmar, H. Jeffrey. Masterng Carbon Management Balancng Trade - offs to Optmze Supply Chan Effcences. IBM Global Busness Servces, [7] T. Abdallah, A. Dabat, D. Smch-Lev. Sustanable supply chan desgn A closed-loop formulaton and senstvty analyss, Producton Plannng and Control, vol. 23, pp. 2-33, 22.

8 Optmal Confguraton Algorthm for Mechancal Products The Open Mechancal Engneerng Journal, 2, Volume 9 39 [8] D.L. Ingram. Lfe Cycle Assessment to Study the Carbon Footprnt of System Components for Colorado Blue Spruce Feld Producton and Use, Journal of the Amercan Socety for Hortcultural Scence, vol. 38, pp. 3-, 23. [9] L. Peng, H. J-hua, M.O. Yan-fen, Carbon Footprnt Calculaton and Analyss of Accommodaton Servces n Four-star Hotels of Kunmng, TOURISM TRIBUNE, vol. 2, pp , 2. [] C. Jan-hu, L. Xue-mn, Z. Xue-ru. Demarcaton Problems and the Correspondng Measurement Methods of the Urban Carbon Accountng, Chna Populaton Resources and Envronment, vol 24, no. 4, pp. 9-2, 24. [] C. Sha, L. Y-pe, C. Le. Data qualty analyss wth combnaton uncertanty and senstvty for carbon footprnt assessment of products, Chna Envronment Scence, vol. 34, pp , 24. [2] A. Dormer, D.P. Fnn, P. Ward, J. Cullen, Carbon footprnt analyss n plastcs manufacturng, Journal of Cleaner Producton, vol., pp. 33-4, July, 23. [3] D. Julong, The Prmary Methods of Grey System Theory, Wuhan, Hube provnce: Huazhong Unversty of Scence and Technology Press, 2, pp Receved: May 26, 2 Revsed: July 4, 2 Accepted: August, 2 Bo et al.; Lcensee Bentham Open. Ths s an open access artcles lcensed under the terms of the Creatve Commons Attrbuton-Non-Commercal 4. Internatonal Publc Lcense (CC BY-NC 4.) ( whch permts unrestrcted, non-commercal use, dstrbuton and reproducton n any medum, provded that the wor s properly cted.