《系统工程》课程教学资源（英文文献）Modeling of Robust Design of Remanufacturing Logistics Networks

Modeling of Robust Design of Remanufacturing LogisticsThe uncertainty of time, quantity and quality of recycling products leads to the bed stability andflexibility of remanufacturing logistics networks, while general design only covers the minimizinglogistics cost, so robust design is presented to solve it. The mathematical model of remanufacturinglogistics networks is built on the stochastic distribution of uncontrollable factors, and robustobjectives are presented. The basic elements of robust design of remanufacturing logistics areredefined,and eachpart of mathematicalmodelisexplainedindetail aswell.Robustdesignofremanufacturing logistics networks is a problem of multi-objective optimization in essence.Keywords: Remanufacturing Logistics network, Modeling,Robust designIntroductionRemanufacturing is a process of bringing an assembly to like-new condition through replacing andrefurbishing component/parts at least to current specification It is being driven by environmentalconcerns,legislationand economics.Remanufacturingnormallyinvolvestheremoval oftheused product by the customer and its return to a specialized facility for disassembly, salvage orreprocessing and replacement ofcomponent material The product is then reassembled and tested priortoresaleorreturntothecustomer.Manifold examples of remanufacturing have been presented, encompassing a variety of products,actors, drivers, and business processes. One of the common elements across all of these casesconcerns the need for an appropriate logistics infrastructure' =.3.s.e.9) Just as in traditional supplychains, logistics network design is commonly recognized as a strategic issue ofprime importance. Thelocations of production facilities, storage and transportation strategies are major determinants ofsupply chain performance. Analogously, setting up an appropriate logistics network has a fundamentalimpact on the economic viability of remanufacturing. In order to successfully exploit the opportunitiesof recovering value from used products, companies need to design a logistics structure that facilitatesthe arising goods flows in an optimal way. To this end, decisions need to be taken on where to locatethe various processes of remanufacturing;, how to design the corresponding transportation links andwhat size to design the facilities.The structure ofremanufacturing logistics network is illustrated inFig.1.The main problems facing the remanufacturing logistics networks design appear to be associated

Modeling of Robust Design of Remanufacturing Logistics The uncertainty of time, quantity and quality of recycling products leads to the bed stability and flexibility of remanufacturing logistics networks, while general design only covers the minimizing logistics cost, so robust design is presented to solve it. The mathematical model of remanufacturing logistics networks is built on the stochastic distribution of uncontrollable factors, and robust objectives are presented. The basic elements of robust design of remanufacturing logistics are redefined, and each part of mathematical model is explained in detail as well. Robust design of remanufacturing logistics networks is a problem of multi-objective optimization in essence. Keywords: Remanufacturing Logistics network, Modeling,Robust design Introduction Remanufacturing is a process of bringing an assembly to like-new condition through replacing and refurbishing component/parts at least to current specification. It is being driven by environmental concerns, legislation and economics. Remanufacturing normally involves the removal of the used product by the customer and its return to a specialized facility for disassembly, salvage or reprocessing and replacement of component material. The product is then reassembled and tested prior to resale or return to the customer. Manifold examples of remanufacturing have been presented, encompassing a variety of products, actors, drivers, and business processes. One of the common elements across all of these cases concerns the need for an appropriate logistics infrastructure' =.3.s.e.9} .Just as in traditional supply chains, logistics network design is commonly recognized as a strategic issue of prime importance. The locations of production facilities, storage and transportation strategies are major determinants of supply chain performance. Analogously, setting up an appropriate logistics network has a fundamental impact on the economic viability of remanufacturing. In order to successfully exploit the opportunities of recovering value from used products, companies need to design a logistics structure that facilitates the arising goods flows in an optimal way. To this end, decisions need to be taken on where to locate the various processes of remanufacturing; how to design the corresponding transportation links and what size to design the facilities. The structure of remanufacturing logistics network is illustrated in Fig. 1. The main problems facing the remanufacturing logistics networks design appear to be associated

with high uncertainty and high risk, since it is impossible to determine in advance the time, quantityand quality of the incoming products[l-9] Such uncertainty has significant implications for scheduling,capacity planning and logistics networks design. Therefore, the ability to plan for uncertainty and tomakeminimumlogistics costand itsfluctuating iscrucialto theremanufacturer.It turns out that most of the currently available models rely on mixed integer linearprogramming(MILP).To date, almost all of the remanufacturing logistics network design modelstake a stationary, single-period perspective'sl235.69]Although this approach allows for large scalemathematical optimization deriving general insights associated with the impacts of variousparameters is difficult. Most literatures pointed out that uncertainty of time, quality and quantity ofrecycling products is a distinctive distribution characteristic Different from traditional networks;however above literatures models models are take onlythe In general, the minimizing the little wascovered by optimum objectives above logistics cost, and the (big) fluctuation of logistics cost in acertain period into account little, and the parameters of mathematical models do not reflect a highlevel of uncertainty completely.Consequently,robustness ofthe logistics network design with respectto variations in flow volumes and composition appears to be particularly important. Above all, it needsto build the robust model of remanufacturing logistics networks,and therobust model reflects theuncertain factors Robust Design of Remanufacturing Logistics NetworksRobust designof remanufacturing logistics networksinvolves two processes: one is modeling of remanufacturing logistics networks; the other is modelingof robustdesign.1Modelingofremanufacturing logistics networksThe logistics cost of remanufacturing in a certain period is composed of two parts, namelytransportation cost and fixed cost,the latter involves depreciation expenses of cleaning.disassembling and testing equipment, and depreciation expenses of building remanufacturingcenters) and storages points.1.1AssumptionsUnder the existing distributing network, several assumptions based on engineering background andexistingdistributionstatus weremade,theassumptions areasfollows:(1) Recycling channels chiefly include main users and wholesalers. Main users are the users whosepurchasing goods is up to a certain quantity and is directly delivered by manufacturer. Main users orwholesales may lie at local cities or local capital cities. In the distribution networks, all of products are

with high uncertainty and high risk, since it is impossible to determine in advance the time, quantity and quality of the incoming products[1-9] .Such uncertainty has significant implications for scheduling, capacity planning and logistics networks design. Therefore, the ability to plan for uncertainty and to make minimum logistics cost and its fluctuating is crucial to the remanufacturer. It turns out that most of the currently available models rely on mixed integer linear programming(MILP).To date, almost all of the remanufacturing logistics network design models take a stationary, single-period perspective's[1,2,3,5,6,9] .Although this approach allows for large scale mathematical optimization, deriving general insights associated with the impacts of various parameters is difficult. Most literatures pointed out that uncertainty of time, quality and quantity of recycling products is a distinctive distribution characteristic Different from traditional networks; however above literatures models models are take only the In general, the minimizing the little was covered by optimum objectives above logistics cost, and the (big) fluctuation of logistics cost in a certain period into account little, and the parameters of mathematical models do not reflect a high level of uncertainty completely. Consequently, robustness of the logistics network design with respect to variations in flow volumes and composition appears to be particularly important. Above all, it needs to build the robust model of remanufacturing logistics networks, and the robust model reflects the uncertain factors Robust Design of Remanufacturing Logistics Networks Robust design of remanufacturing logistics networks involves two processes: one is modeling of remanufacturing logistics networks; the other is modeling of robust design. 1 Modeling of remanufacturing logistics networks The logistics cost of remanufacturing in a certain period is composed of two parts, namely transportation cost and fixed cost, the latter involves depreciation expenses of cleaning, disassembling and testing equipment, and depreciation expenses of building remanufacturing centers) and storages points. 1.1 Assumptions Under the existing distributing network, several assumptions based on engineering background and existing distribution status were made, the assumptions are as follows: (1) Recycling channels chiefly include main users and wholesalers. Main users are the users whose purchasing goods is up to a certain quantity and is directly delivered by manufacturer. Main users or wholesales may lie at local cities or local capital cities. In the distribution networks, all of products are

delivered to many local areas,and there is one local capital city in each area. which rules anddistributes products to its local cities;(2) Considering the integration of distributing process and recycling process, we define therecycling products in each recycling point are sent to the belonging local cities, then the recyclingproducts are gathered to local capital cities, finally all recycling products in local capital cities are sentto remanufacturing center(s)(see Fig 2).The above method can take advantage ofexisting distributingnetworks and reduce investment cost,(3) Considering the convenience of management and the reduction of investment cost, we assumeremanufacturing centers can only bebuilt in local capital cities; the locations ofcleaning/disassembling testing only lie in the local cities or local capital cities; and the sizes ofstorages are built based on the quantity of recycling products in the areas. There are two types ofstorages: one is to take advantage of existing distributing storages when the quantity of recyclingproducts is small, which can reduce the investment cost; the another is the special storages which arebuilt when the quantity are large;(4) The constructing cost of remanufacturing centers) and storages have linear relations with thequantity of recycling products. The local land price, the constructing and labor expense also hasinfluence on the constructingcost,(5)Transportation cost is a function of the transportation distance and weight;(6) The investment cost of cleaning/disassembling/testing equipment has linear relations with thequantity of recycling products;(7) All the assets of building remanufacturing logistics networks decrease according to straight linedepreciation method, and the life)pan of latter example is 20 years;(8) The quantity of recycling products of each main user/wholesaler and the weight of useful partsof each recycling product in a certain period are both stochastic variables of some type of distributionsThe parameters and maybe the types of the distributions are different and can be obtained from theprocess ofcollectingdata and proof-testing,(9) During the process of modeling, the transportation expense of recycling products within therecycling city is neglected, because it is very small in contrast to the transportation expense betweentwo recycling cities, and the expense exists in spite ofthe structure types ofremanufacturing logisticsnetwork;(10) During the process of modeling, transportation expense and landfill cost of waste are neglected

delivered to many local areas, and there is one local capital city in each area, which rules and distributes products to its local cities; (2) Considering the integration of distributing process and recycling process, we define the recycling products in each recycling point are sent to the belonging local cities, then the recycling products are gathered to local capital cities, finally all recycling products in local capital cities are sent to remanufacturing center(s)(see Fig. 2).The above method can take advantage of existing distributing networks and reduce investment cost; (3) Considering the convenience of management and the reduction of investment cost, we assume remanufacturing centers can only be built in local capital cities; the locations of cleaning/disassembling testing only lie in the local cities or local capital cities; and the sizes of storages are built based on the quantity of recycling products in the areas. There are two types of storages: one is to take advantage of existing distributing storages when the quantity of recycling products is small, which can reduce the investment cost; the another is the special storages which are built when the quantity are large; (4) The constructing cost of remanufacturing centers) and storages have linear relations with the quantity of recycling products. The local land price, the constructing and labor expense also has influence on the constructing cost; (5)Transportation cost is a function of the transportation distance and weight; (6) The investment cost of cleaning/disassembling/testing equipment has linear relations with the quantity of recycling products; (7) All the assets of building remanufacturing logistics networks decrease according to straight line depreciation method, and the life}pan of latter example is 20 years; (8) The quantity of recycling products of each main user/wholesaler and the weight of useful parts of each recycling product in a certain period are both stochastic variables of some type of distributions. The parameters and maybe the types of the distributions are different and can be obtained from the process of collecting data and proof-testing; (9) During the process of modeling, the transportation expense of recycling products within the recycling city is neglected, because it is very small in contrast to the transportation expense between two recycling cities, and the expense exists in spite of the structure types of remanufacturing logistics network; (10) During the process of modeling, transportation expense and landfill cost of waste are neglected

the reasons are the same as(9);(1l) We only consider logistics cost during modeling, which includes transportation expense,building cost of storages and equipment fixed cost, because all of the cost can be controlled, whileother cost such as the expense of reclaiming products, the cost during remanufacturing process, areindependent ofthe design of remanufacturing networks, so they are uncontrollable and neglected. Theredistribution of remanufacturing products can take advantage of existing distribution logisticsnetworks, so the process is also neglected;(12) The management expense of inventory per day is neglected, because the expense is very small,and the management can be finished by the workers who are in charge of the inventory ofdistribution,1. 2 Transportation costTransportation cost is composed of two parts:(1) the transportation cost from local cities to thelocal capital cities;(2) the transportation expense from local capital cities to the remanufacturingcenters).So the computingformula of transportationcost is defined as followN,TCost(D) =Ec(Pjkm, (t), T) + Ec(Qjm, (t), T)nI=Xw×((TL+min/T,L/ ×(a(-H+H))N2(t), T)+ZN(Qn(t), T)>C(Pn2=1×(w×(a(1-H)+H))×min(TL)(1)The formula shows when the number of remanufacturing centers is 1, the transportation costin a certain period is TCost(I).The definitions ofeach notation are as follows:jsubscript for local capital cityksubscript for general city belong to some capital citym,subscript for the wholesaler at general citymFsubscript for the wholesaler at local capital cityn,subscript for the main user at general citynFsubscript for the main user at local capital city1the number ofremanufacturing centersa,positionof cleaning/disassembling/testing site,J=l,2,,J

the reasons are the same as(9); (11) We only consider logistics cost during modeling, which includes transportation expense, building cost of storages and equipment fixed cost, because all of the cost can be controlled, while other cost such as the expense of reclaiming products, the cost during remanufacturing process, are independent of the design of remanufacturing networks, so they are uncontrollable and neglected. The redistribution of remanufacturing products can take advantage of existing distribution logistics networks, so the process is also neglected; (12) The management expense of inventory per day is neglected, because the expense is very small, and the management can be finished by the workers who are in charge of the inventory of distribution; 1. 2 Transportation cost Transportation cost is composed of two parts:(1) the transportation cost from local cities to the local capital cities;(2) the transportation expense from local capital cities to the remanufacturing centers).So the computing formula of transportation cost is defined as follow: The formula shows when the number of remanufacturing centers is 1，the transportation cost in a certain period is TCost(I).The definitions of each notation are as follows: j subscript for local capital city k subscript for general city belong to some capital city m , subscript for the wholesaler at general city m= subscript for the wholesaler at local capital city n , subscript for the main user at general city n= subscript for the main user at local capital city I the number of remanufacturing centers a; position of cleaning/disassembling/testing site, J=1, 2, } , J

q=0 shows the position is to build cleaning/ disassembling/testing pointq=1 shows the position is not to build point, andremanufacturing center to build onlycleaning/d isassembling/testing po intJthe number ofall local capital cities in the distribution networksWweight of each recycling product, the unit of weight is tonladisassembly coefficient, it reflects quatity ofrecycling product on the reuse theparts/components in this recycling product, namely the percentage of the weight of reuseparts/components accounting for the weight of whole product, the range of value is 0%100%T;ktransportation cost per km ton from general cityk to the local capital city jL;kdistancefromgeneral cityktolocal capitalcityjT,transportation cost per km ton from local capital city j to remanufacturing centerLj distance from local capital cityj to remanufacturing center1Pjkm(t) distribution function ofrecycling quantity of wholesaler m, at general cityk,local capitalcityjQkn(t)distribution function of recycling quantity of main user n, at general city k, local capitalcityjPjm2(t) distribution function of recycling quantity ofwholesaler m= at local capital cityjQjm2(t)distribution function of recycling quantityof main user n= at local capital cityjCO function ofrecycling quantity in a certain periodm in(T; L,)minimum function to search the smallest expense from local capital cityj to oneofremanufacturingcenters)The transportation map is illustrated with Fig, 2k1LyLiTikKVLocal cityLocal capital cityRenanufacturing centerK, M, N,, M=, N= are defined as follows:K=max(C, C=.-C}) Cm CzC, present respectively the number of localcities whichevery local capital city has, subscript J is the same as latter definition ofappendixM,=maxZGC,,GC=,..GC,}}J, GC,,GC=, ., GC,}} present respectively the number of

q=0 shows the position is to build cleaning/ disassembling/testing point q=1 shows the position is not to build point, andremanufacturing center to build only cleaning/disassembling/testing point J the number of all local capital cities in the distribution networks w weight of each recycling product, the unit of weight is ton la disassembly coefficient, it reflects quatity ofrecycling product on the reuse the parts/components in this recycling product, namely the percentage of the weight of reuse parts/components accounting for the weight of whole product, the range of value is 0%一 100% T;k transportation cost per km ton from general city k to the local capital city j L;k distance from general city k to local capital city j T,; transportation cost per km ton from local capital city j to remanufacturing center Ljj distance from local capital city j to remanufacturing center 1 Pjkm(t) distribution function of recycling quantity of wholesaler m, at general city k，local capital city j Qjkn(t)distribution function of recycling quantity of main user n, at general city k，local capital city j Pjm2(t) distribution function of recycling quantity of wholesaler m= at local capital city j Qjm2(t) distribution function of recycling quantity of main user n= at local capital city j C() function of recycling quantity in a certain period m in ( T,; L,; ) minimum function to search the smallest expense from local capital city j to one of remanufacturing centers) The transportation map is illustrated with Fig. 2 K, M,，N,，M=, N= are defined as follows: K=max(C, C=.一 C}}} Cm Cz.一 C, present respectively the number of local cities which every local capital city has; subscript J is the same as latter definition of appendix. M,=maxZGC, GC=,.GC,}}J, GC, GC=, .; GC,}} present respectively the number of

wholesalers at each local city,thedefinition ofsubscript W is W-ofN,=max(GU,.GU=,.，GU、/.GU,)),thenumberataremainusersGU..GU=, ..,each local city respectively.M==maxZCC,.CC=,.. CC,J, CC,.CC=,.; CC, are the number of wholesalers at eachlocal capital city respectively.N==maxZCU, CU=, ., CU,J, CU,.CU=, ., CU, are the number of main users at eachlocal capital city respectively.So we build the restriction as follows:ForVCE{Ci,C2, ..,Cr),if C,<K, forVkE(C,+1,Cr+2,,K),C(Pjkm,(t),T)=0,C(Qjkn,(t),T)=0,Lik=0,Tu=0,l=1,2,JVGC,E/CC1, GC2,., GCw), if GCI< M1,ForforVm E{GC+ 1, GC)+ 2, ", M), C(Pjkm,(t),T) = 0.ForVGU,E(GUi,GU2,.,GUw),ifGUI<Ni,forVn E{CU+1, GUI+ 2, ., Ni), C(Qin,(t),T) = 0.ForVCC, E{CC1, CC2, .., cC,), if CC,< M2,forVm2(CC,+ 1,CC, +2, .", M2),C(Pjm,(t)T) = 0.ForvCU,E{CU1,cU2,.",CU),ifCUI<N2,forVn2E[CU,+1,CU,+2,**N2),C(Qmz(t),T) = 0.Ofcourse,J,K,M,,N,,M=,N=arenon-negativeParameters1.3Fixed costFixed cost is composed of three parts, namely(1) Deprec iation expenses ofbuilding storage points(2)Depreciationexpensesof building cleaning/disassembling/testing sites)(3)Depreciationexpenses of remanufacturing centers)The fixed cost is defined as follows:

wholesalers at each local city; the definition of subscript W is W= N,=max(GU,.GU=, ., GU 、 /.GU,}}, are the number of main users at GU,.GU=, .,each local city respectively. M==maxZCC,.CC=, .} CC,J, CC,.CC=, . ; CC, are the number of wholesalers at each local capital city respectively. N==maxZCU, CU=, ., CU,J, CU,.CU=, .; CU, are the number of main users at each local capital city respectively. So we build the restriction as follows: Of course, J, K, M,，N,，M=, N= are non-negative Parameters 1. 3 Fixed cost Fixed cost is composed of three parts, namely: (1) Depreciation expenses of building storage points (2) Depreciation expenses of building cleaning/disassembling/testing sites) (3) Depreciation expenses of remanufacturing centers)The fixed cost is defined as follows:

CIRCost,tFCost()=ICost,+i=E(1-a)×DCostj+>ZRMCost;DRCost;+(2)Fost(I)depreciation expenses in a certain period for building 1 remanufacturing centers)ICostjdepreciation expenses in a certain period for building recycling inventory at j localcapital cityIRCostj depreciation expenses in a certain period for building recycling inventory at iremanufacturingcenterDCosjt depreciation expenses in a certain period building cleaning/disassembling testing sitelocalcapitalcityDRCost depreciation expenses in a certain period building cleaning/disassembling testing siteremanufacturingcenterRMCost, depreciation expenses in a certain period for building iremanufacturing centerICost, 1RCost,RMCost, have linear recycling products, and expense such as laborsrelations are defined as DCost, DCost, DRCost, and relationswith the quantity oftheyalsohave relation with other and expand clue and so on.Their relations are defined as follows:

Fost(I)depreciation expenses in a certain period for building 1 remanufacturing centers) ICostj depreciation expenses in a certain period for building recycling inventory at j local capital city IRCostj depreciation expenses in a certain period for building recycling inventory at i remanufacturing center DCosjt depreciation expenses in a certain period building cleaning/disassembling testing site local capital city DRCost depreciation expenses in a certain period building cleaning/disassembling testing site remanufacturing center RMCost，depreciation expenses in a certain period for building i remanufacturing center ICost，1 RCost，RMCost，have linear recycling products, and expense such as labors relations are defined as D Cost，D Cost，DRCost，and relations with the quantity of they also have relation with other and expand clue and so on. Their relations are defined as follows:

0Cap, > Col,(1) ICostj =Capj<ClL(A,×Col+B,)/LSCol;Average quantity of recycling products in a certainperiodinjlocal capital cityCol, = → ZcolsjiSSMN7Ec(Pjmn (0), T) +c(Colj =T=mi="=M2N2Ec(Qim2(t),CC(PPjmz(t)，T)+T

Stimesofmathematical simulation,choosing themaximum between simulation times meeting the1colColsjfollowingformulaS+SAandS=1000 setting constant, the value is smallLSlife-span of equipment and otherassets,namelydepreciation timeAj,B,defined coefficients, they are associated withother expense such as labors,land-value,andconstructingCap jdefined critical stocks,if the quantity ofrecycling products is small, the storage point ofdistribution is used to reduce the fixed cost; or anewstoragepointis built(2)IRCost,=(AR,×CoIR,+BR,)/LSARi,BR,Defined constructing coefficients,they areassociated with other expense such as labors,land-valueand constructingexpenditureColR;Average quantityof recycling products in acertain period in i remanufacturing center,colRs,Sisthesamas foregoinColR,= SSdefinitionMIN,AZ2Ec(Pam,(t), T)+ Zc(Qjm, (t), T)ColR,=2R,=1>a(),T)+Ec(Qm(t),COP12=JiThe number of local capital cities in the charge of iJremanufacturingcenter,J=-(3)DCostj=(AD×ColD,+BD)/LSADj,BD,Defined constructing coefficients, they are

e(P o. )+ 2c( (0, + 22cPm(0. )+ 2a0, 0. COIDRa, J,are the same as foregoing definitions(5)RMCost,=(ARM,×CoIRM,+BR,)/LSADR,BDR,Definedconstructing coefficients,theyareassociatedwith other expense suchas labors,land-value and constructing expenditureColRM,Averagequantityofrecyclingproducts in a certainperiod in i remanufacturing center, ColRM,ColR,1.4Modelofremanufacturing logistics networkAffer the transportation cost and fixed cost are defined, we build the mathematical model ofremanufacturing logistics networks as follows:(3)Y=F(X,Z)= TCost(I)+FCost(I)YThe logistics cost whenI remanufacturing centers are built, and it is a function ofX and ZX, zThe aggregate of design parameters, uncontrollable factor(noise factor)2 Robust design of remanufacturing logistics networks2. 1 The basic elements of robust designIt is necessary to define basic elements of robust design of remanufacturing logistics networks,whichissimilartorobustdesignofproduct.Thebasicelementsareasfollows:Signal factors(Input factors):YoDesign parameters: X-(xi,x2,..,n)Noise factors(Uncontrollable factors):Z=(zi,Z2.,Zm)TOutput factors(System characteristic):Y=F(X, Z):Signal factors(lInput factors)areto meet the objective value ortechnical criterion duringthe robustdesign of products,whilethey refer tothe structure of remanufacturing logisticsnetworks in this study, Design parameters are the aggregate of controllable parameters, while herethey refer to the aggregate of all the parameters of structure of networks such as the size and numberof storages, the position and number of remanufacturing center and so on, Noisefactors(Uncontrollable factors) are the aggregate of uncontrollable and stochastic variables, while

1. 4 Model of remanufacturing logistics network After the transportation cost and fixed cost are defined, we build the mathematical model of remanufacturing logistics networks as follows: Y The logistics cost when I remanufacturing centers are built, and it is a function of X and Z X, Z The aggregate of design parameters, uncontrollable factor(noise factor) 2 Robust design of remanufacturing 1ogistics networks 2. 1 The basic elements of robust design It is necessary to define basic elements of robust design of remanufacturing logistics networks, which is similar to robust design of product. The basic elements are as follows: Signal factors(Input factors):Y0 Design parameters: X=(x1,x2,.,xn) T Noise factors(Uncontrollable factors):Z=(z1,z2,.,zm) T Output factors(System characteristic):Y=F(X, Z): Signal factors(Input factors) are to meet the objective value or technical criterion during the robust design of products, while they refer to the structure of remanufacturing logistics networks in this study; Design parameters are the aggregate of controllable parameters, while here they refer to the aggregate of all the parameters of structure of networks such as the size and number of storages, the position and number of remanufacturing center and so on; Noise factors( Uncontrollable factors) are the aggregate of uncontrollable and stochastic variables, while