Research Article A Time Scheduling Model of Logistics Service Supply Chain with Mass Customized Logistics Service

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1 Hndaw Publshng Corporaton Dscrete Dynamcs n Nature and Socety Volume 01, Artcle ID 48978, 18 pages do: /01/48978 Research Artcle A Tme Schedulng Model of Logstcs Servce Supply Chan wth Mass Customzed Logstcs Servce Wehua Lu, 1 Y Yang, 1 Xang L, Hatao Xu, 1 and Dong Xe 1 1 School of Management, Tanjn Unversty, Tanjn 30007, Chna College of Economc and Socal Development, Nanka Unversty, Tanjn , Chna Correspondence should be addressed to Wehua Lu, lwhlu@yahoo.com.cn Receved 9 July 01; Accepted 8 October 01 Academc Edtor: Xaochen Sun Copyrght q 01 Wehua Lu et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Wth the ncreasng demand for customzed logstcs servces n the manufacturng ndustry, the key factor n realzng the compettveness of a logstcs servce supply chan LSSC s whether t can meet specfc requrements wth the cost of mass servce. In ths case, n-depth research on the tme-schedulng of LSSC s requred. Settng the total cost, completon tme, and the satsfacton of functonal logstcs servce provders FLSPs as optmal targets, ths paper establshes a tme schedulng model of LSSC, whch s constraned by the servce order tme requrement. Numercal analyss s conducted by usng Matlab 7.0 software. The effects of the relatonshp cost coeffcent and the tme delay coeffcent on the comprehensve performance of LSSC are dscussed. The results demonstrate that wth the tme schedulng model n mass-customzed logstcs servces MCLSs envronment, the logstcs servce ntegrator LSI can complete the order earler or later than scheduled. Wth the ncrease of the relatonshp cost coeffcent and the tme delay coeffcent, the comprehensve performance of LSSC also ncreases and tends towards stablty. In addton, the tme delay coeffcent has a better effect n ncreasng the LSSC s comprehensve performance than the relatonshp cost coeffcent does. 1. Introducton In the face of growng demand for customzed logstcs servces, numerous logstcs enterprses are not only provdng customers wth mass servces, but are also begnnng to meet the demand for customzed servces and are consderng a change n ther logstcs servce modes. Specfcally, they try to provde mass customzed logstcs servces MCLS nstead of mass logstcs servces 1. MCLS represents a sgnfcant development n logstcs servces, and a

2 Dscrete Dynamcs n Nature and Socety logstcs company s capablty to offer MCLS s crucal to enhance ts market compettveness. In the MCLS envronment, to meet customzed servce demand and offer large-scale servces, several logstcs enterprses form a logstcs servce supply chan LSSC va unon and ntegraton, 3. LSSC s a new supply chan of whch logstcs servce ntegrator LSI s the core enterprse. The basc structure of LSSC s functonal logstcs servce provder FLSP LSI customer. FLSP s ntegrated by LSI when LSI bulds the ntegrated logstcs to customer. The man purpose of LSSC s to provde the flexble logstcs servce for manufacturng supply chan 3. As the core enterprse of a LSSC, the LSI ntegrates the advantages of the FLSPs, such as varous logstcs processes and logstcs servce functons and then provdes flexble logstcs servces to customers. In such an envronment, the key to mprove the LSSC s compettveness s ts capablty to offer customzed logstcs servces wth mass logstcs costs. An n-depth research on the tme schedulng of the LSSC s necessary to meet customers requrements. However, the exstng research on supply chan schedulng model has three defcences, whch are dscussed as follows. Frst, the exstng research on supply chan schedulng does not consder the feature that the operaton tme of supplers may be delayed or compressed. It also gnores the fact that the customer s order s flexble n many cases, and that the order completon tme may be delayed or compressed wthn an acceptable range. Thus, questons arse n expressng features of tme delay or compresson n model buldng and effects of tme delay or compresson on the comprehensve performance of LSSC. Second, n most studes on supply chan schedulng, cost control s regarded as the prmary schedulng goal. However, ths s not always the case for an LSSC n the MCLS envronment. The flexblty of the order completon tme and the satsfacton of FLSPs are also sgnfcant. Expressng these objectve functons n an optmzaton model and searchng for a more reasonable method of solvng ths model are pertnent questons. Thrd, the conclusons drawn from tradtonal manufacturng supply chan schedulng models may not be fully applcable to LSSC schedulng problems. Therefore, we wll determne how LSI can use the tme schedulng model proposed n ths paper to better manage ts LSSC. Ths paper s organzed as follows. Secton s the lterature revew n whch the exstng supply chan optmzaton schedulng models and methods are systematcally summarzed. Secton 3 focuses on model buldng, n whch a tme schedulng optmzaton model of LSSC n the MCLS envronment s establshed. Secton 4 descrbes the model soluton: a method of solvng the multobjectve programmng model. Secton 5 presents numercal analyss, ncludng a dscusson of the nfluence of relevant parameters on LSSC s schedulng performance. Secton 6 provdes management nsghts and recommendatons to mprove actual operaton of LSSC. The last secton presents the conclusons and future research drectons n ths feld.. Lterature Revew Most studes on supply chan schedulng have focused on the manufacturng ndustry and have acheved sgnfcant results. Many earler studes dscussed job shop schedulng wthn a sngle enterprse see, e.g., 4, 5. They are prmarly nterested n the arrangement of processng procedures and the order operaton sequence. Krepl and Pnedo 6 ntroduced what s plannng and what s schedulng and gave an overvew of the varous plannng and schedulng models n general. Several scholars wrote about the coordnaton of the assembly

3 Dscrete Dynamcs n Nature and Socety 3 system n manufacturng enterprse see, e.g., 7. But n early studes, many researches emphases were focused wthn one manufacturng enterprse and dd not pay much attenton to the roles outsde the enterprse. As s known to all, customer s the most mportant role n the compettve market. Phlpoom 8 transferred hs attenton to the most mportant part, whch s the customers requrements and ther feelngs. The dlemma for the manufacturng manager when plannng the lead-tmes was dscussed. He took delvery relablty and tme as the vtal factors n schedulng. The dea of thnkng hghly of customer satsfactory s worthy of our research. A systematc study of the supply chan schedulng model had been establshed by Hall and Potts 9 and from then on plannng and schedulng problems began gettng more attenton. However, studes on the supply chan schedulng wth the mass-customzaton producton mode are a relatvely new development see, e.g., 10, 11. The contents of these studes ncluded the applcaton of postponement strategy, the postonng of customer order decouplng pont CODP, and the tme schedulng problem. In terms of the supply chan tme schedulng, several scholars examned the domnant contradctons analyss and ts optmzaton soluton of supply chan schedulng n mass customzaton see, e.g., 1, 13. Yao and Pu 13 ntroduced a dynamc and multobjectve optmzaton model to balance the contradcton between scale producton effect and customzed demand. They consdered the delay coeffcent but dd not gve out the tme delay punshment n mathematcal expresson. Other scholars studed the dfferences between the deal tmetables of the dfferent supply chan members and that of customer demand, and then explored ways to solve ths dscrepancy see, e.g., 14. From the perspectve of ntegrated supply chan producton plannng and schedulng process, Mshra et al. 15 desgned a mxed nteger programmng model. Moreover, n the schedulng of manufacturng supply chan, the man objectve of schedulng optmzaton s supply chan cost see, e.g., Most studes assumed that the order completon tme or the delvery tme of supplers was fxed. However, n a number of cases, as an ndex reflectng supply chan aglty, the order tme requrements may be changed see, e.g., Thus, consderng the nfluence of tme compresson or delay on the schedulng results s necessary. Smlar to studes on manufacturng supply chan, research on the servce supply chan manly focuses on servce process schedulng see, e.g.,, 3, order assgnment schedulng see, e.g., 3, 4, and so forth. Tme schedulng, although s a sgnfcant part of LSSC schedulng, has not receved suffcent attenton. Tme schedulng s a key aspect of the servce supply chan operaton. It s drectly related to whether the logstcs servce can be completed successfully based on customer requrements. Therefore, examnng tme schedulng of LSSC s necessary. Ths paper ams to address these ssues and to evaluate the tme schedulng model of LSSC n the MCLS envronment. The man contrbutons of ths study are lsted as follows. 1 The effects of tme delay and compresson of the customer order on LSSC s comprehensve performance are analyzed. Tme delay n the order requrements contrbutes to an ncrease n the satsfacton of FLSPs. However, ther satsfacton level remans stable after t reaches a certan value. Moreover, the extent of tme compresson s also lmted. The effect of the relatonshp cost coeffcent on the comprehensve performance of LSSC s dscussed. Wth the ncrease of LSI s relatonshp cost coeffcent, the comprehensve performance of LSSC also ncreases. Ths comprehensve performance cannot be nfntely enhanced, but remans stable upon reachng a certan value.

4 4 Dscrete Dynamcs n Nature and Socety 3 LSI can mprove the comprehensve performance of LSSC by both the relatonshp cost coeffcent and tme delay. However, compared wth the relatonshp cost coeffcent, usng tme delay s a superor way to mprove the comprehensve performance. 3. Tme Schedulng Model of LSSC 3.1. Model Assumptons and Varables A two-echelon LSSC s assumed to consst of one LSI and several FLSPs. The logstcs servce comprses multple servce processes. Every servce process s completed by many cooperatve FLSPs. Each FLSP s servce capablty s dfferent from that of the others; dfferent FLSPs have varyng normal completon tmes for the same work. Table 1 presents the notatons of the model. The other assumptons of the model are as follows. 1 The 1 th servce process cannot begn untl the th servce process s fnshed. In each servce process, the quantty of servce orders assgned by LSI to FLSP s assumed gven. FLSP can only complete these orders based on the order quantty assgned by LSI. The servce cost of FLSP s equal to the servce cost per unt tme multpled by servce tme. 3 The normal servce tme of FLSP refers to the typcal length of tme needed to complete a task usng ts capablty wthout consderng any tme delay or compresson. Whle workng wthn the normal tme, the satsfacton of FLSP s at ts hghest, and the FLSP does not have to pay any addtonal cost. 4 In each servce process, tme delay or compresson to complete an order produces addtonal costs. The costs of tme delay or compresson per unt tme are the same. 5 All the servce processes are outsourced to FLSPs by LSI and are completed by the former. The model does not consder the operaton cost of LSI. 6 The assgnment of the servce orders s fnshed. And the CODP has been decded. The model does not consder the locaton problem of the CODP. 7 T means the normal servce tme of the jth FLSP n the th servce process, whch s a parameter decded by the technology of the correspondng FLSP and dffers from each other. In the secton of numercal analyss see Secton 5, t s a defntve parameter. In practce, the normal servce tme of fnshng a specfc order s usually defntve, but not stochastc. 3.. Model Buldng Consderng multple goals n LSSC tme schedulng s necessary. To mnmze the total cost ncurred n LSSC, to mnmze the dfference between the expected and the actual tme of completng the servce order, and to maxmze the satsfacton of FLSPs, ths paper establshes a tme-schedulng model that s constraned by the servce order tme requrement. The modelng process s as follows.

5 Dscrete Dynamcs n Nature and Socety 5 Notatons C p ext T T ext U φ β T U 0 R Z 1 Z Z 3 Z mn 1 Z mn Z mn 3 Z max Z max 3 Table 1: Notatons for the model. Descrpton The normal servce cost per unt tme of the jth FLSP n the th servce process, whch s 1,, 3,...,I 0, j 1,, 3,...,J 0, the same as below The addtonal servce cost per unt tme of the jth FLSP n the th servce process When the th servce process s delayed, the delay cost per unt tme ncurred n the 1 th servce process When the tme of the th servce process s compressed, the tme compresson cost per unt tme ncurred n the 1 th servce process The normal servce tme of the jth FLSP n the th servce process The addtonal servce tme of the jth FLSP n the th servce process The expected operaton tme for the th servce process set by LSI The satsfacton of the jth FLSP n the th servce process Weghts of the jth FLSP s satsfacton n the th servce process Tme delay coeffcent for the th servce process set by LSI The upper lmt of tme delay or compresson ncurred n the 1 th servce process, whch can be endured by the th servce process The lower lmt of the satsfacton of the jth FLSP n the th servce process The adjustment coeffcent of the tme delay or compresson, n whch R > 0meansthat the operaton tme s delayed. R< 0 ndcates that the operaton tme s compressed The total cost of LSSC The total delvery tme of all processes n LSSC The total satsfacton of FLSPs n LSSC The mnmum of the objectve functon Z 1 when the objectve functons Z and Z 3 are not consdered The mnmum of the objectve functon Z when the objectve functons Z 1 and Z 3 are not consdered The mnmum of the objectve functon Z 3 when the objectve functons Z 1 and Z are not consdered The maxmum of the objectve functon Z when the objectve functons Z 1 and Z 3 are not consdered The maxmum of the objectve functon Z 3 when the objectve functons Z 1 and Z are not consdered C The relatonshp cost coeffcent of the LSI, C>1 Z K 1 K F The objectve functon syntheszed by Z and Z 3, whch s also called the comprehensve performance of LSSC Weght coeffcents of the objectve functon Z n the comprehensve performance of LSSC Weght coeffcents of the objectve functon Z 1 n the comprehensve performance of LSSC The jth FLSP n the th servce process

6 6 Dscrete Dynamcs n Nature and Socety We set that f x max{0,f x }. Then mn Z 1 mn Z max Z 3 I 0 J 0 1 j 1 C T I 0 J0 mn j 1 1 I 0 J0 mn j 1 1 I 0 J 0 1 j 1 [ [ T ext ) I 0 J0 max j 1 1 ) ] T T ext p ext, [ T T ext ] ) 3.1 ) ] T T ext, 3. T T 1 C T T C T ext )φ, 3.3 subject to T T ext 1 β R ), T T ext T 1, T T 1 C T T C T ext ) U In 3.1, the objectve functon Z 1 s made to mnmze LSSC total operaton cost. The frst part of 3.1 represents the total operaton cost of all processes n the LSSC. The second part of 3.1 represents the tme delay cost ncurred n the next process, whch s caused by the prevous process. The thrd part of 3.1 represents the cost of tme compresson ncurred n the next process, whch s caused by the prevous process too. In 3., the objectve functon Z makes the servce order completed on tme as much as possble. In 3.3, the objectve functon Z 3 s made to maxmze the weghted satsfacton of all FLSPs. Ths ndcator conssts of two parts: one s the satsfacton wth operaton tme and the other s related to the cost. In Z 3, the frst part 1 T /T represents the proxmty degree between the normal operaton tme and the order expected tme of the jth FLSPs n the th servce process, whch represents the satsfacton n the tme aspect. The second part T C / T C T ext means the proporton of the normal operaton cost n the total cost of the jth FLSP n the th servce process, whch represents the satsfacton n the cost aspect. In 3.4, the frst constrant represents the requrements of FLSP s order completon tme proposed by the LSI. Specfcally, t requres that the actual completon tme must be less than a certan multple of the expected tme. Ths multple s determned by the product of β and R, whch represents the lmts that LSI can endure the tme delay or compresson. The second constrant means that the dfference between the actual order completon tme and the expected tme cannot exceed the upper lmt of the tme varaton tme compresson or delay

7 Dscrete Dynamcs n Nature and Socety 7 ncurred n the 1 th servce process, whch can be endured by the th servce process. Ths s a strong constrant that must be observed because durng the entre servce provson process, the contnued lnk of operaton tme exsts between the upstream and downstream servce processes. The startng tme of each process should meet certan tme requrements. The thrd constrant means that the satsfacton of each FLSP must be more than the lower lmt that they can accept. 4. Model Soluton 4.1. Smplfyng the Multobjectve Programmng Model The model descrbed has three objectves and three constrants. It s a typcal multobjectve programmng problem. Multobjectve programmng problems have numerous mature solutons, such as the evaluaton functon method ncludng lnear weghtng method, reference target method, maxmn method, goal programmng method, delamnatng sequence method, nteractve programmng method, and subordnate functon method. For the specfc ssues, t s necessary to choose an approprate soluton method to solve the practcal problems. Ths paper s based on the MCLS envronment, so we should consder not only the cost target but also the customzed target. In tme schedulng, LSI tends to conform to the customzed tme requrements and set correspondng requrements related to order completon tme for ther FLSPs. Each FLSP s satsfacton wll drectly determne the qualty and the possblty of order completon. Thus, order completon tme and FLSPs satsfacton are two crtcal goals. Operaton cost s often not the prmary consderaton. Completng logstcs servce orders wth the mnmum cost s not requred; the total cost of LSSC must be mantaned wthn a certan range. Besdes, to buld and mantan a good relatonshp wth FLSPs, LSI s usually wllng to make a certan amount of cost concessons. Consderng these actual stuatons, we ntroduce the followng parameter called the relatonshp cost coeffcent C C >1 nto our model and use t to represent the cost augmentaton lmts 4.1. Z 1 <Z mn 1 C. 4.1 Thus, 4.1 can be regarded as a new constrant and be combned wth 3.4 to form the new constrants. The orgnal model then becomes a twn-goal programmng problem. Gven that a certan degree of conflct and ncommensurablty occurs among the targets n multobjectve decson-makng problems, determnng an absolute optmal soluton s dffcult. In ths paper, we choose the commonly used lnear weghtng method to solve our model, and attempt to transform ths multobjectve programmng model nto a sngleobjectve programmng model. The objectve functon Z and the objectve functon Z 3 mean to make the servce order completed on tme as much as possble and to maxmze the satsfacton of FLSPs, respectvely. Therefore, each of them has to be normalzed. Z and Z 3 are thus dvded by the possble maxmum value Z max and Z max 3, respectvely, and ther correspondng results are added up. The syntheszed objectve functon s as follows: max Z K Z 3 Z max 3 K 1 Z Z max. 4.

8 8 Dscrete Dynamcs n Nature and Socety In 4., K 1 and K represent the weghts of Z and Z 3, respectvely, whch are determned by the lnear weghtng method. Consder the followng: max Z K Z 3 Z max 3 K 1 Z Z max, subject to T T ext 1 β R ), T T ext T 1, T T 1 C T T C Z 1 <Z mn 1 C. T ext ) U 0, 4.3 Here, Z 1 Z Z 3 C T I 0 J 0 1 j 1 I 0 J0 mn j 1 1 I 0 J0 mn j 1 1 I 0 J 0 1 j 1 [ [ T ext ) I 0 J0 max j 1 1 ) ] T T ext p ext, ) ] T T ext, T T 1 C T T C [ T T ext T ext )φ. ] ) Usng the Genetc Algorthm to Solve the Multobjectve Programmng Problem The genetc algorthm GA s an effectve method of searchng for the optmal soluton by smulaton of the natural selecton process. It uses multple startng ponts to begn the search; t has global search capablty. Smlar to the natural evolutonary process, the computatonal process of genetc algorthms s teratve, whch means that t ncludes selecton, crossover, and mutaton. For reference, GA s descrbed n Numercal Analyss Ths secton frst llustrates the valdty of the model va a numercal analyss, and then explores the nfluence of relevant parameters on tme schedulng results. Addtonally, some effectve recommendatons are gven for use n the actual operaton-based on numercal analyss.

9 Dscrete Dynamcs n Nature and Socety 9 BY logstcs company FLSP FLSP FLSP FLSP FLSP F11, F1, F13 F1, F, F3 F31, F3, F33 F41, F4, F43 F51, F5, F53 Shenyang Cty, Chna Hghway transportaton Ralway transportaton Martme transportaton Package and Process Dstrbuton Tanjn Cty, Chna Fgure 1: The logstcs servce process of one order of BY Company Numercal Data Descrpton and Basc Results BY s a logstcs company based n northern Chna. It s a logstcs ntegrator that has ntegrated several thrd-party logstcs frms. Ths company has receved an order requrng t to delver goods from Shenyang Cty to Tanjn Cty. Durng delvery, fve servce processes are needed: road transportaton, ral transportaton, martme transportaton, packagng and processng, and dstrbuton. The CODP has been decded and t wll be at the 4th servce process whch s packagng process. Obvously, the processes before the CODP are provded wth mass operatons and the processes after the CODP are provded wth customzed operatons. Each servce process s to be completed by three FLSPs see Fgure 1. The servce capablty of each FLSP s dfferent from that of the others because the normal operaton tmes T vary when dfferent FLSPs complete the same order. BY company, the LSI, has set an expected operaton tme for each order n every process. The parameters of each process and of each FLSP are dfferent Tables and 3. We assume that be the servce process, 1,, 3, 4, 5, j represents the number of FLSPs n each process, so that j 1,, 3. C represents the normal servce cost per unt tme of the jth FLSP n the th process. In the model solvng, genetc algorthms and Matlab 7.0 software are used. Assumng the genetc populaton to be 00, the heredtary algebra to be 400, the adjustment coeffcent R 1, and the relatonshp cost coeffcent C 1., then the calculaton result of comprehensve performance Z s equal to The tme parameters of each FLSP n every process are shown n Table 4. We can fnd that among the 15 FLSPs, seven completed the order wth tme compres- < 0, and eght completed the order wth tme delay > 0. son 5.. The Effect of Tme Delay Coeffcent on LSSC Schedulng Results In practce, respondng rapdly to customzed demand s one of the man features of the masscustomzed LSSC. It s often the case that the LSI requres ts FLSPs to compress ther servce tme frequently to respond to the customer s demand. Therefore, the order s completed ahead of the expected tme, whch s reflected n the model as β R<0. In some cases, f the tme requrement of the order s not that urgent, LSI may permt ts FLSPs to delay ther work. That s, the completon tme s later than the expected tme, whch s reflected n the model as β R>0. The permtted order completon tme s drectly related to the dffculty faced by FLSPs n completng the order. It has a drect mpact on the cost of these FLSPs. To descrbe

10 10 Dscrete Dynamcs n Nature and Socety Table : Basc data 3.1. C j 1 j j j 1 j j T j 1 j j U 0 j 1 j j φ j 1 j j p ext Table 3: Basc data p ext 1 p ext p ext 3 p ext 4 p ext β β 1 β β 3 β 4 β T T T 3 T 4 T 5 T the two stuatons, we dscuss the nfluence of the tme delay or compresson coeffcent on the satsfacton of LSSC and on the order completon tme. We use the syntheszed objectve functon Z to denote the comprehensve performance of LSSC. Keepng the model parameters unchanged and changng only the value of adjustment coeffcent R, we obtan the calculaton results of Z. The results are presented n Table 5. When the calculaton results n Table 5 are plotted, a curve s shown n Fgure.

11 Dscrete Dynamcs n Nature and Socety 11 Table 4: Calculaton results. Process F The total operaton tme of each FLSP F F F F F F F F F F F F F F F Table 5: The effect of tme delay compresson coeffcent on the comprehensve performance of LSSC. R Z Analyss of the Overall Change Trend From Fgure, we can observe that along wth the ncrease of R from negatve to postve values, the syntheszed objectve functon Z rses gradually, whch ndcates that the satsfacton of LSSC ncreases and remans stable after reachng a certan value. The slope n the delay part s smaller; usng the tme delay strategy, the margn of ncrease n the LSSC s comprehensve performance s slow. However, the slope of the curve n the tme compresson part s bgger than that n the tme delay part. Hence, the nfluence on the comprehensve performance of LSSC s greater. It s due to that along wth the ncrease of R, these FLSPs can get tme relaxaton, but they are requred to pay the delay cost at the same tme. In addton, ther addtonal tme s occuped by the order, thus they could not use t to fnsh other servce orders. And the more tme relaxaton s offered, the effect descrbed above s larger. Therefore, Z value s shown margnal decrease wth the ncreasng of adjustment

12 1 Dscrete Dynamcs n Nature and Socety 0.8 Synthess of the objectve functon Z Adjustment coeffcent R Fgure : Curve of Z changed wth R. coeffcent R. Based on these facts, t can be nferred that n practce, before the LSI requres ts FLSPs to operate wth tme compresson to shorten ther operaton tme n fnshng the same order, t s necessary to carefully wegh the advantages and dsadvantages. Furthermore, followng certan measures such as offerng cost compensaton to mnmze the declne n the FLSPs satsfacton s necessary. To further analyze the nfluence on the LSSC performance caused by the tme delay or tme compresson coeffcent, Secton 5.. and Secton 5..3 cover the relevant conclusons drawn from the dfferent parts of Fgure Analyss of the Tme Compresson Part Fgure 3 shows the curve of Z changed wth R when operaton tme s compressed. When R<0, the LSSC s n the operaton status of tme compresson. Fgure 3 ndcates that wth the ncrease of the absolute value of R, Z decreases, whch means that the performance of LSSC s declnng. In the part of R decreasng from 0 to 0.9, from the slope of the curve Fgure 3, thez value decreases by a much larger margn from 0.67 to Thus, f FLSPs are requred to operate n the tme compresson state, ther total satsfacton wll declne sharply. Moreover, a greater ncrease n tme compresson ndcates a greater declne n the satsfacton of FLSPs. In our numercal example, f R< 0.9, no soluton n the model occurs, whch means LSSC has collapsed and can no longer operate. Ths also shows that n practce, the order completon tme of FLSP cannot be compressed nfntely. Upon reachng a certan pont, the FLSP s operaton tme can no longer be compressed. When workng wthn ths lmtaton tme, the comprehensve performance of LSSC s at ts lowest Analyss of the Tme Delay Part Fgure 4 shows the curve of Z changed wth R when operaton tme s delayed. When R>0, LSSC s n the operaton status of tme delay. Fgure 4 ndcates that along wth the ncrease of R, Z also ncreases. That s, the comprehensve performance of LSSC contnues to ncrease. However, when R>0, Z only ncreases slghtly. The range of ncrease of Z s far less than the range of ts declne when operaton tme s delayed or compressed at the same extent. Ths occurs because n the case of tme delay, FLSPs must pay the penalty cost. In addton, the same wth that n Fgure, the Z value s shown that margnal decrease wth the ncreasng of adjustment coeffcent R, the more tme relaxaton s offered, the more the servce capactes

13 Dscrete Dynamcs n Nature and Socety Synthess of objectve functon Z Adjustment coeffcent R Fgure 3: Curve of Z changed wth R when operaton tme s compressed. Synthess of objectve functon Z Adjustment coeffcent R Fgure 4: Curve of Z changed wth R when operaton tme s delayed. of FLSPs are occuped and cannot be used to complete other servce orders. For the reasons mentoned, FLSPs are generally unwllng to delay ther completon tme. Fgure 4 llustrates that Z remans unchanged after R >, whch shows that the tme delay has reached the upper lmt. Increasng the tme delay coeffcent s of no use to mprove the Z value anymore. In other words, Z has reached the maxmum at R. It also explans that n practce, the servce tme cannot be delayed nfntely. In summary, allowng the FLSPs to delay the order completon tme to a certan extent wll contrbute to LSCC performance. However, constraned by the tme connectons between the upstream and downstream servce processes, the LSSC s performance mprovement faces an upper lmt The Effect of Relatonshp Cost Coeffcent of LSI on LSSC Schedulng Results The relatonshp cost coeffcent s ntroduced nto the model solvng approach, and the cost of LSI s allowed to ncrease approprately. In ths part, we explore the effect of the LSI s relatonshp cost coeffcent on LSSC schedulng results to provde a theoretcal bass for the LSI s decson-makng.

14 14 Dscrete Dynamcs n Nature and Socety Synthess of objectve functon Z Relatonshp cost coeffcent C Fgure 5: Curve of Z changed wth C. Table 6: The effect of C on Z. C Z The relatonshp cost coeffcent s made by LSI. Its sze wll have a drect nfluence on the FLSP s satsfacton and on the overall performance of LSSC. To explore the relatonshp between the syntheszed objectve functon and the cost relatonshp coeffcent, we assgn dfferent values to C, and then obtan the correspondng Z Table 6 and Fgure 5. Fgure 5 shows the curve of Z changed wth C. It ndcates that along wth the ncrease of C, Z also ncreases and ultmately tends to stablze at Along wth the ncrease of the LSI s relatonshp cost coeffcent, the comprehensve performance of LSSC ncreases as well. However, ths mprovement s not unlmted. Instead, t remans stable after reachng a certan value due to the mandatory requrement on servce tme that FLSPs must meet. As mentoned, the servce tme cannot be delayed or compressed wthout lmt. Thus, when the cost augmentaton ncreases to a certan level, contnung to ncrease the cost does not contrbute to the mprovement of the LSSC s comprehensve performance. In the actual tme schedulng, LSI may consder usng the relatonshp cost coeffcent strategy to mprove the comprehensve performance of LSSC, but ths mprovement s lmted Comparson of the Effects of Dfferent Parameters on LSSC Schedulng Results Followng the precedng analyss, LSI can use both the relatonshp cost coeffcent and the tme delay coeffcent to mprove the comprehensve performance of LSSC. Indeed, these two strateges are often used by LSIs n actual tme schedulng. To compare the effects of these two strateges, we respectvely set C 1. andr 1. as benchmarks and fgure out the proporton of the varatons of Z wth R and C. The results are shown n Table 7. Plottng the data n Table 7 nto a lne chart, we obtan Fgure 6. Fgure 6 shows the comparson of the performance changes caused by C and R. It clearly shows the followng. 1 The slope of the curve of Z% vared wth R% s bgger than that of Z% vared wth C%. Therefore, compared wth the cost augmentaton, tme delay s better n mprovng the comprehensve performance of LSSC.

15 Dscrete Dynamcs n Nature and Socety 15 Table 7: Influence on the comprehensve performance of LSSC caused by tme delay and cost ncrease. R Z R% Z% %.9% % 0.37% % 0.00% % 1.63% % 1.77% %.1% %.81% C Z C% Z% % 0.15% % 0.07% % 0.06% % 0.00% % 0.07% % 0.10% % 0.13% % 0.13% % 0.13% % 0.15% Change n the objectve functon value Z %) Change n the ndependent varables C or R %) Z% vares wth R% Z% vares wth C% Fgure 6: Comparson of the performance changes caused by C and R. In terms of the curve of Z% vared wth R%, when R% s less than 0, the slope of the curve s bgger. Thus, f FLSPs operate n the tme-compressed state and then the LSI allows some tme delay, the mprovement n the comprehensve performance of LSSC s much more sgnfcant. By contrast, f FLSPs operate n the tme delay state, and then the LSI allows more tme delay, the mprovement n the comprehensve performance of LSSC s not substantal. 6. Man Conclusons and Management Insghts Based on the precedng analyss, the followng conclusons can be made. 1 Along wth the ncrease of R from negatve to postve value, the syntheszed objectve functon Z rses gradually, whch shows that the overall satsfacton of

16 16 Dscrete Dynamcs n Nature and Socety LSSC ncreases and remans stable upon reachng a certan value wth the tme delay. Furthermore, tme compresson decreases the satsfacton level of FLSPs, whereas delayng the completon tme ncreases ther satsfacton. Along wth the ncrease n the LSI s relatonshp cost coeffcent, the comprehensve performance of LSSC ncreases as well. The effect on mprovng the comprehensve performance s relatvely slow and mprovement s lmted and remans unchanged upon reachng a certan value. 3 Both tme delay and the LSI s relatonshp cost can mprove the LSSC s comprehensve performance to a certan degree. However, compared wth the cost augmentaton, tme delay s better n mprovng the comprehensve performance of the LSSC. Based on ths result, LSI should address the tme schedulng problem reasonably and try to reduce unnecessary tme compresson requrements to prevent the sharp declne of the LSSC s comprehensve performance. If the comprehensve performance of LSSC has to be mproved, LSI should prortze the use of the tme delay strategy. 4 The results of numercal analyss ndcate that the tme schedulng model tends to reduce the operaton tme dfference among varous FLSPs that are n the same servce process and always tres to brng the actual servce tme close to the expected servce tme. Thus, t s strongly recommended that the LSI could try ts best to choose FLSPs wth normal completon tmes that are close to one another s to mnmse the dfference n the tme of order completon. What the best case scenaro s, the normal completon tmes of those FLSPs are the same as the expected workng tme. Furthermore, the tme schedulng model ndcates that wth flexble schedulng, we could reach the goals of makng the operaton tme to be compressed or to be delayed n accordance wth customer s needs. Tme flexblty s a qute mportant characterstc of flexble supply chan. All the ponts mentoned prevously contrbute to make the 3rd-party logstcs more relable to customers, especally the manufacturers. It s helpful to release outsourcng pressure of the manufacturng ndustry. 5 Through the model establshed n ths paper, t ndcates that t s possble to get an optmzed schedulng plan of the FLSPs operaton tme f LSI could get the parameters used n the tme schedulng model. Ths model s sutable for the stuaton whch s under the MC background and the CODP has been decded n advance. LSI could use ths model to choose a better tme delay coeffcent and relatonshp cost coeffcent, thus better manage hs FLSPs. 7. Research Lmtatons and Future Work After revewng the lterature on the LSSC schedulng model to mnmze the total cost ncurred n the LSSC, mnmze the dfference between the expected and actual tmes of completng the servce order, and maxmze the satsfacton of FLSPs, ths paper has establshed a tme schedulng model of LSSC that s constraned by the servce order tme requrement. Numercal analyss has been conducted by usng the Matlab 7.0 software. The effects of the relatonshp cost coeffcent and the tme delay coeffcent on the LSSC s comprehensve performance have been dscussed. Fnally, the man conclusons and management nsghts have been presented.

17 Dscrete Dynamcs n Nature and Socety 17 However, certan lmtatons reman n ths paper. For example, the model solvng and analyss are only n accordance wth a real numercal example, whch cannot represent all actual stuatons. Besdes, we consder the normal servce tme for a specfc order T s certan, but n some cases, ths parameter s stochastc. In the future, we could contnue ths research consderng the stochastc factors. Furthermore, n ths paper, t s assumed that the upstream servce capablty matches the downstream servce capablty wthout consderng the unmatched cases. In the future, we can buld a tme schedulng model n whch the capablty s matched and the tme flexblty s consdered. Ths paper also assumes that mutual trust and collaboraton have already been establshed among the partcpants n LSSC. However, actual schedulng problems ndcate asymmetrc nformaton, whch should be examned n future research. Acknowledgments Ths research s supported by the Natonal Natural Scence Foundaton of Chna Grant no The suggestons of the revewers are also gratefully acknowledged. References 1 C. Chandra and J. Grabs, Managng logstcs for mass customzaton: the new producton fronter, n Proceedngs of the 6th Bannual World Automaton Congress Image Processng, Bomedcne, Multmeda, Fnancal Engneerng and Manufacturng Internatonal Forum on Multmeda Image Processng, IFMIP WAC 04), vol. 18, pp , July 004. K. L. Choy, C. L. L, S. C. K. So, H. Lau, S. K. Kwok, and D. W. K. Leung, Managng uncertanty n logstcs servce supply chan, Internatonal Journal of Rsk Assessment and Management, vol.7,no.1, pp. 19, W. H. Lu, X. C. Xu, Z. X. Ren, and Y. Peng, An emergency order allocaton model based on multprovder n two-echelon logstcs servce supply chan, Supply Chan Management, vol. 16, no. 6, pp , C. Y. Lee, S. Pramuthu, and Y. K. Tsa, Job shop schedulng wth a genetc algorthm and machne learnng, Internatonal Journal of Producton Research, vol. 35, no. 4, pp , Y. H. Lee, C. S. Jeong, and C. Moon, Advanced plannng and schedulng wth outsourcng n manufacturng supply chan, Computers and Industral Engneerng, vol. 43, no. 1-, pp , S. Krepl and M. Pnedo, Plannng and schedulng n supply chans: an overvew of ssues n practce, Producton and Operatons Management, vol. 13, no. 1, pp. 77 9, Z.-L. Chen and N. G. Hall, Supply chan schedulng: conflct and cooperaton n assembly systems, Operatons Research, vol. 55, no. 6, pp , P. R. Phlpoom, The choce of dspatchng rules n a shop usng nternally set due-dates wth quoted leadtme and tardness costs, Internatonal Journal of Producton Research, vol. 38, no. 7, pp , N. G. Hall and C. N. Potts, Supply chan schedulng: batchng and delvery, Operatons Research, vol. 51, no. 4, pp , X. G. Xu and X. Y. L, Customer order decouplng pont selecton model n mass customzaton based on MAS, Journal of Wuhan Unversty of Technology, vol. 8, no. 1, pp , X. G. Xu, Poston of customer order decouplng pont n mass customzaton, n Proceedngs of the 6th Internatonal Conference on Machne Learnng and Cybernetcs ICMLC 07), pp , August J. Yao and L. Lu, Optmzaton analyss of supply chan schedulng n mass customzaton, Internatonal Journal of Producton Economcs, vol. 117, no. 1, pp , J. M. Yao and Y. Pu, A supply chan schedulng optmzaton model n mass customzaton, Systems Engneerng, vol. 3, no. 8, pp , 005 Chnese. 14 M. Dawande, H. N. Gesmar, N. G. Hall, and C. Srskandarajah, Supply chan schedulng: dstrbuton systems, Producton and Operatons Management, vol. 15, no., pp , N. Mshra, A. K. Choudhary, and M. K. Twar, Modelng the plannng and schedulng across the outsourcng supply chan: a chaos-based fast Tabu-SA approach, Internatonal Journal of Producton Research, vol. 46, no. 13, pp , 008.

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