Dual-Route Distribution Strategy with Supply Chain Disruption

Transcription

1 Dual-Route Dstrbuton Strategy wth Supply Chan Dsrupton Sung Ho Hur, Dong-Kyu Km, Seung-Young Kho, and Chungwon Lee Unexpected dsruptons n the supply chan can drectly and ndrectly cause addtonal logstcs costs because of delayed delvery. Prevous studes have mnmzed the addtonal cost wth a networ desgn that used the concept of level of servce and unt delay cost; however, n cases of dsrupton n a regonal dstrbuton center (RDC), companes commonly must secure a bypass through another RDC and pay more to use a faster transportaton mode. The am of ths study s to develop a dual-route dstrbuton strategy to mnmze the logstcs costs that stem from the dsrupton n the RDC. The model addressed n ths study determnes the RDC allocaton and the freght dualzaton rato to establsh a bypass before a dsrupton occurs and to ensure the punctualty of delvery wthout losses due to late delvery. An applcaton of the model uses an actual company s networ data. The results of ths applcaton show that the dual-route dstrbuton strategy can be more advantageous than a sngle-route dstrbuton strategy. The model provdes a theoretcal bass for the use of the dual-route strategy to mnmze the drect and ndrect costs assocated wth the RDC dsrupton. Interest n unexpected dsruptons has ncreased sgnfcantly as the result of recent ncdents that have affected the supply chan, such as the terrorst attac on the Unted States on September 11, 21; the hurrcane that ht the U.S. Gulf Coast; and the great earthquae that occurred n east Japan. Dsruptons n a supply chan can cause an ncrease n a varety of logstcs costs, as mentoned by Zhang and Fglozz (1). Among them, the followng two costs tae up the majorty of the total cost: frst, the addtonal transportaton cost of usng a hgh-speed transportaton mode to avod late delvery, whch can be exorbtant, and, second, f a delvery delay occurs and affects the schedule at the demand sde, compensaton for shortages may be requred, and the credblty of the company could be damaged. In realty, to mnmze losses, companes mae varous alternatve plans n case dsruptons occur. After a dsrupton occurs, the tme between the start of the loss on the demand sde and the tme requred to secure a bypass and delver products s very mportant; the longer ths tme s, the greater a company s expenses wll be because of losses from late delvery. The company therefore pays more for a hgher-speed transportaton mode to decrease the delvery tme, or t secures another bypass to decrease the tme to fnd a S. H. Hur, Department of Logstcs Research, Dvson for Logstcs Technology and Maret Analyss, Korea Transport Insttute, 315 Goyangdaero, Ilsanseo-Gu, Goyang Cty, Gyeongg-Do , South Korea. D.-K. Km, S.-Y. Kho, and C. Lee, Department of Cvl and Envronmental Engneerng, Seoul Natonal Unversty, 1 Gwana-Ro, Gwana-Gu, Seoul, South Korea, Correspondng author: C. Lee, chungwon@snu.ac.r. Transportaton Research Record: Journal of the Transportaton Research Board, No. 2466, Transportaton Research Board of the Natonal Academes, Washngton, D.C., 214, pp DOI: / new bypass, whch delays the start of the loss on the demand sde. Most prevous studes were conducted wth lttle consderaton of these actual strateges n case a dsrupton occurs. In ths study, a dual-route strategy s consdered for the decson-mang process to secure a bypass when a dsrupton occurs and s compared wth the tradtonal sngle-route strategy. Among the varous threats to the supply chan, ths study focuses on regonal dstrbuton center (RDC) dsrupton. Ths study ams to apply the dual-route dstrbuton strategy to mnmze the logstcs cost, ncludng the cost rs assocated wth RDC dsrupton, and consequently to propose an optmzed freght dstrbuton strategy. Companes can recover from RDC dsrupton more rapdly than from a supply dsrupton, so the dstrbuton strategy also reacts more qucly. Ths dfference maes t dffcult to apply models developed n prevous studes because they usually focus on the general faclty locaton problem over the long term. So n ths study, the dstrbuton strategy decson problem s examned to consder a bypass through another avalable RDC for a short perod. The model s formulated as a nonlnear, mxed-nteger problem, and a partcle swarm optmzaton (PSO) algorthm s used to determne the soluton. An applcaton of the model s presented by usng an actual company s busness records. In terms of addtonal costs that stem from the dsrupton, most prevous studes used a constant unt delay cost or the decrease of the servce level. However, as mentoned earler, the company must pay addtonal transportaton costs and absorb the losses assocated wth delayed delveres n cases of dsrupton. Those two types of addtonal costs also are consdered n ths study. Lterature Revew The ncreased attenton on the supply chan reflects the ncreased nterest n dsasters and other ncdents that can cause dsruptons n supply chans. These studes also rase the ssue that the pursut of effectveness n a supply chan can expose the augmented rs n the supply chan (2). The defnton of threat n the supply chan has been studed n prevous research (3). Transportaton dsrupton, whch s one of the threats, has been characterzed snce t restrcts the movement of goods (4). Dfferent types of dsruptons also have been defned, such as dsruptons n supply, transportaton, communcatons, and demand; at facltes; and freght breaches (5). Varous studes on supply chan dsruptons have been conducted, and they focused on dfferent aspects, ncludng threats to the supply chan (3, 4, 6 12), dsruptons n the transportaton networs n the supply chan (2, 13 15), and locaton decson and safety stoc optmzaton problems (16 19). Studes on faclty locaton problems and locaton nventory problems, whch 12

2 Hur, Km, Kho, and Lee 13 have focused especally on the networ desgn problem, have consdered the rs-poolng effect aganst stochastc unrelablty (15, 2 22). However, faclty locaton problems are a long-term decson problem, whereas decsons concernng dstrbuton strateges must be made rapdly n response to changes n the logstcal envronment. In the logstcal management sde, the number of dstrbuton centers and the decson concernng ther locaton have been researched to prevent uncertantes (16, 18). In these studes, a unt loss cost was appled for shortages, but n cases of actual dsrupton n a supply chan, addtonal costs are ncurred such as bypass transportaton cost and delay losses on the demand sde. Some studes used the concept of multroute networ desgn n order to be ready for a dsrupton. Weaver and Church generalzed the p-medan problem on th servces to prepare the cases n whch the closest faclty s not n servce (23). Snyder and Dasn developed the study by Weaver and Church wth the nonprespecfed fracton of demand served by each faclty (24). Prul and hs colleagues analyzed prmary and secondary supply facltes to prepare for supply dsruptons (25). L optmzed system cost wth a unformly appled expedted shpment cost to the shortage under the varable demand on sngle and multfaclty cases (26). Unle other studes on supply dsruptons (23, 26), ths study concentrates on RDC dsruptons that cause addtonal decson mang n the delvery process. Such RDC dsruptons cause the problems of ncreasng the transportaton cost to the suppler and delayng the producton schedule for the demand sde. In a short-term dstrbuton strategy, as n ths study, another route s necessary to connect supply and demand and to connect the rato of freght separaton for each road because t changes the dsrupton response tme, whch affects the emergency transportaton cost. In ths study, the problem assocated wth the decson concernng a dstrbuton strategy was assessed to mnmze the logstcs cost should RDC dsrupton occur. Problem Defnton In ths study, an optmal dstrbuton strategy s proposed to prepare for RDC dsrupton n a two-stage multmodal transportaton networ. A dual-route strategy s proposed to mnmze losses from the dsrupton by transportng a certan porton of the freght through a bypass that was secured n advance. If a dsrupton arses n the RDC, the amount of freght delvered through the bypass could delay the start of the loss that would have been caused by late delvery at the demand sde. Fgure 1 shows the concept of the dual-route delvery strategy. The subject of ths study s a long-dstance, two-stage, mass freght transportaton networ that generally conducts busness-tobusness delvery. The two-stage networ s composed of a supply node, demand nodes, and RDC nodes, and all freght s supposed to be delvered va dstrbuton centers. For the trun-lne transportaton from the supply to the RDCs, varous transportaton modes are used to ft the company s transportaton objectve, ncludng ar transportaton and sea transportaton. For the feeder-lne from the RDCs to the demand, transportaton by truc s used, as s generally the case. As mentoned earler, the am of ths study s to decde the short-term dstrbuton strategy; accordngly, the constructon of the dstrbuton center s not dscussed because t nvolves a long-term decson factor. The demand quantty s supposed to be random accordng to the specfed probablty dstrbuton under uncertanty, and each RDC node holds some stoc n reserve to be prepared for any uncertantes n the demand. Also, dsruptons on each RDC node are assumed to be mutually exclusve; ths assumpton means that the occurrence of a dsrupton at an RDC does not affect the probablty that a dsrupton wll occur at another RDC. The concurrent dsrupton of more than two RDCs s not consdered n ths study. Also, t s assumed that the demand node holds some buffer stoc n order to be prepared when delvery s uncertan, and the replenshment cycle of stoc at demand s a wee. Model Formulaton A mxed-nteger, nonlnear problem s formulated to determne the RDC that s used, the prmary route freght rato (PRFR), and demand RDC allocaton as a part of the dstrbuton strategy to mnmze the logstcs cost assocated wth the dsrupton rs. The logcal process that reflects the probablty of each case and the logstcs Prmary route Secondary route (one part of the dualzed freght volume delvered) (a) Emergency route (n dsrupton) Secondary route (total freght volume delvered n dsrupton case) (b) FIGURE 1 Concept of dual-route delvery strategy.

3 14 Transportaton Research Record 2466 cost were derved from Snyder s capactated relablty fxed-charge locaton problem model (14), and the storage and shortage costs assocated wth the probablstc demand were taen from wor by Starr and Mller (27). Notaton n the formulaton s shown n the followng sectons. Sets and Parameters I = set of RDC node ( I); J = set of demand node ( j J); TC = unt transportaton cost from supply to RDC by basc transportaton mode; TC = unt transportaton cost from RDC to demand; RHC = RDC holdng cost; SHC = stoc holdng cost; DLC = delay loss cost; ETC so = hgh-speed transportaton mode unt transportaton cost wth shortage of RDC ; ETC j dr = hgh-speed transportaton mode unt transportaton cost wth dsrupton of RDC to delver demand j on th route; SO = expected shortage quantty on RDC ; SL = servce level on RDC, whch s coeffcent to standard devaton of f(x ); S max = maxmum number of RDCs on servce; d = dstance from supply node to RDC node ; d j = dstance from RDC node to demand node j; e = emergency factor; = order of prorty of delvery route, whch ncludes prmary and secondary route ( K{1,2}); p = probablty of no dsrupton; p = probablty of dsrupton occurrence on RDC ; q m = transportaton mode factor; t b = delvery tme by basc transportaton mode; t s(m) = delvery tme by transportaton mode m; x = freght quantty from supply to RDC ; x j = freght quantty from RDC to demand j on th route (x j ); z max = maxmum number of RDCs on servce; f(x ) = probablty dstrbuton functon of demand x ; β = buffer stoc rato on demand node; µ j = mean value of demand on demand node j; r = nventory quantty on RDC ncludng delvery stoc and safety stoc; and σ j = standard devaton of demand on demand node j. Decson Varables y j = 1 f freght s delvered from RDC to demand node j on th route, otherwse; α = demand quantty rato through th route of whch prmary route passes va RDC ( α 1); and z = 1 f RDC on servce, otherwse. The objectve functon s composed of the transportaton cost, fxed cost, storage cost, shortage cost, and rs cost. Decson varables are RDC used, PRFR, and demand node allocaton to RDCs. The problem s establshed as follows: ( j ) ( ) ( ) mn p TC d + TC d x + RHC z I j J K SO ( ) + SHC r x f x dx + d ETC TC I r I dr ( ) ( ) + ( ETCj + TC ) r x r f x dx p d d x I j J K I, y + p DLC δ x j j I j J K subject to j j I j j x = y α µ, j, (1) j j j yj 1 j, (2) α = 1 (3) K y α j = 1 j (4) y max S z, j (5) j max z z (6) p + =1 (7) p 2 r = SL y α σ + x (8) j j J K x = x j j J K j SO = ( ) ( x r f x dx (1) r ( tsm ( ) j ) δ = max + mft dat dst,, j, (11) j The frst term of the objectve functon s transportaton cost, whch s the cost to delver the freght from the supply node to the demand node through an RDC node n a normal case. The cost s calculated by multplyng the cost of transportaton from supply to demand by the probablty that a dsrupton wll not occur. The second term s fxed cost, whch s the basc cost to use the RDC, so t s not dependent on the amount of freght that s passng through. The cost s only proportonal to the number of RDC nodes used, so t s calculated by multplyng the unt RDC holdng cost by the number of RDC nodes used. The thrd and fourth terms are storage and shortage costs, respectvely. Each RDC can hold some amount of addtonal stoc to prepare for uncertantes n the demand. Demand s assumed to follow a certan probablty dstrbuton, and the storage and the shortage costs refer to Starr and Mller s model (27). The unt shortage cost s the dfference between hgh-speed (9)

4 Hur, Km, Kho, and Lee 15 transportaton cost and normal transportaton cost. The hgh-speed transportaton cost can be decded as follows: ETC SO TC where sat+ rst tb = qtc where t sat + rst t... qmtc where ts( m 1) sat+ rst 1 b s() 1 As shown n Fgure 2, the term sat refers to the tme between the occurrence of an nventory shortage and the scheduled nventory replenshment, and rst refers to the tme between scheduled nventory replenshment and next expected occurrence of an nventory shortage, consderng the quantty of the nventory shortage. The ffth and sxth terms are rs costs. They are composed of the addtonal transportaton cost and the delay loss cost stemmng from the late delvery. The addtonal transportaton cost s the supplementary expense for the bypass, mostly by hgh-speed transportaton, whch s more expensve. It s calculated from the probablty of RDC dsrupton and the cost of hgh-speed transportaton. The delay loss cost s the compensaton for shortages and the damage to the credblty of the company when the shortage occurs on the demand sde. It can be calculated by multplyng the terms dsrupton probablty (p ), unt delay loss cost (DLC), freght quantty (x j), and shortage occurrence rato (δ j). If a dsrupton occurs at RDC, the x j should be delvered through the other RDC ; the freght on the prmary route through RDC should be detoured through the secondary route, and vce versa. So the addtonal transportaton cost s calculated by multplyng the terms choce of the bypass (y j ), freght quantty to be delvered (xj), dr and unt transportaton cost (ETC j d + TCd j). The dr term ETC j s the trun lne transportaton cost of the unt amount for the unt dstance when a dsrupton occurs. The cost s calculated by multplyng the terms emergency factor e, transportaton mode factor q m, and basc transportaton cost TC, as follows: ETC dr j e TC where dat + dstj mft tb = eqtc where tb dat dstj + mft t... eq mtc where ts( m 1) dat + dstj mft 1 s() 1 The transportaton mode m s decded by comparng the tme from the dsrupton to the start of the shortage at the demand sde (dat) plus the tme from the expected freght arrval tme to the expected start of the shortage at demand (dst j) and the tme to secure a bypass (mft) plus the tme for delvery from supply to demand (t b or t s(m) ). The term dst j can be calculated as dst j = 1 + β α j from Fgure 3, and δ j s when the freght s delvered before the occurrence of the shortage. Otherwse t can be calculated as δ j = t s(m) + mft dat dst j from Fgure 3. Constrant 1 determnes the quantty of freght to demand node j through RDC on the th route. Constrant 2 requres that each demand node be allocated to only one RDC node on the th route. Constrant 3 holds the total amount of dualzed freght. Constrant 4 allocates the dualzed freght for demand node j to the RDCs. Constrant 5 prevents allocaton of the demand node to an RDC that s not n use. Constrant 6 lmts the maxmum number of RDCs n use. By Constrant 7, the sum of probabltes of every dsrupton case becomes 1. Constrants 8 to 11 are used to smplfy the notaton. Constrant 8 defnes the stoc at RDC, ncludng the mean demand nventory and safety stoc proportonal to the standard varaton of the demand. Constrant 9 defnes the freght quantty from supply node to RDC node. Constrant 1 defnes the shortage quantty accordng to the probablty functon of demand. Constrant 11 determnes the shortage occurrence rato. Soluton Algorthm The formulaton of the problem s smlar to the uncapactated faclty locaton problem (UFLP), whch has been dentfed as NP-hard. Cornuejols et al. and Prul derved the most lely soluton of the UFLP by heurstcs methods n a reasonable tme (28, 29). Yapcoglu et al. and Bozorg-Amr et al., n partcular, used a PSO algorthm to solve the UFLP (3, 31). The PSO algorthm s one of the populaton-based optmzaton technques nspred by nature. It smulates the socal behavor of a swarm, such as a floc of brds or a school of fsh. In a PSO algorthm, each sngle soluton, called a partcle, s consdered as a brd, and the group becomes a swarm (populaton). The search space s the area to RDC nventory SO x r x SO Tme sat rst FIGURE 2 Concept of SO, sat, and rst.

5 16 Transportaton Research Record 2466 Stoc on demand node y j µ j j µ j Buffer stoc µ j Dsrupton Tme dat dst j t s (m) mft t s(1) t b (a) Stoc on demand node y j µ j j µ j Buffer stoc µ j Dsrupton Tme Shortage = j x j dat dst j mft (b) t s (m) FIGURE 3 Changes of transportaton mode because of occurrence of RDC dsrupton: (a) freght delvered before occurrence of shortage and (b) freght delvered after occurrence of shortage. explore. Each partcle has a ftness value calculated by a ftness functon and a velocty of flyng toward the optmum (32). Dfferent from a genetc algorthm, a PSO does not produce a new partcle, but all partcles change ther postons to fnd a better ftness value. Ths acton s possble because each partcle remembers ts prvate best poston, pbest, and the populaton s global best poston, gbest. Elbeltag et al. and Sevl and Guner showed that a PSO algorthm performs better than a genetc algorthm for some NP-hard problems (33, 34). In ths study, the logstcs cost was set to the ftness, so the partcles moved for the lower logstcs cost n ths case. The poston of the partcle s composed of the decson varables RDC used, PRFR, and demand node allocaton to RDCs. Ths study used the MATLAB7 PSO toolbox developed by Brge (35). The applcaton of the PSO algorthm to the model s shown n Fgure 4. Numercal Experments Input Varables and Basc Condtons The nput varables and basc condtons n ths study were estmated on the bass of the actual expenses from a real busness-to-busness, logstcal case study n Chna. The nput varables are shown n Table 1. Three types of trun lne transportaton costs were used n ths case, and the unt delay loss cost was assumed to be the same as that n Table 1, consderng, for example, logstcs cost, actual sales, and long-term order condton. It was assumed that there was a unform dstrbuton of dsrupton occurrences, so the tme from a dsrupton to the tme of the next expected freght arrval was assumed to be 3.5 days, whch

6 Hur, Km, Kho, and Lee 17 TABLE 1 Input Parameters Parameter Value Trun lne transportaton cost Basc transportaton mode (TC ) 2 CNY/unt m Hgh-speed transportaton, Mode 1 (e q 1 TC ) 5 CNY/unt m Hgh-speed transportaton, Mode 2 (e q 2 TC ) 22 CNY/unt m TC 6 CNY/unt m SHC 588 CNY/unt RHC 6 CNY DLC 36 mllon CNY/unt Trun lne transportaton tme Basc transportaton mode (t b ) 7 days Hgh-speed transportaton, Mode 1 [t s(1) ] 4 days Hgh-speed transportaton, Mode 2 [t s(2) ] 2 days dat 3.5 days β p.1% Note: CNY = Chnese yuan (1 CNY = US$.16 n June 213). s a suppler of electronc components. Also, the demand was generated on the bass of the actual demand quantty wth the assumpton that t was normally dstrbuted. Comparson of Sngle-Route and Dual-Route Strateges FIGURE 4 Flowchart of PSO algorthm. s the average of one cycle. The buffer stoc level was set at zero, whch s neutral. And the dsrupton probablty was set at.1%; ths value means that about one dsrupton occurs n a 2-year perod of tme. The networ conssted of 1 orgn node, 5 RDC nodes, and 15 demand nodes from the actual delvery records of the company, whch Table 2 shows the results of the expected logstcs costs of the sngle-route strategy and the dual-route strategy. The expected logstcs cost for the sngle-route strategy represented n Fgure 5a was found to be 5,858, Chnese yuan (CNY) (1 CNY = US$.16 n June 213), and the cost from the dual-route strategy represented n Fgure 5b was found to be 5,839, CNY; thus, the cost for the dual-route strategy has a beneft of 19, CNY (approxmately.3%), and the dual-route strategy can be a reasonable choce n the gven envronment. The PRFRs are 1. for RDC 1 and.95 for RDCs 2 and 4. RDCs 3 and 5 were not used. In terms of the cost for each scenaro, when there s no dsrupton n any RDC, the sngle-route strategy s logstcs cost was 186, CNY less than that of the dual-route strategy. When there s a dsrupton n RDC 1, the sngle-route strategy s logstcs cost was 852, CNY less than the dual-route strategy s cost. But when a dsrupton occurs n RDCs 2 and 4, the dual-route strategy s TABLE 2 Expected Logstcs Cost by Strategy Dsrupton on Case No Dsrupton RDC 1 RDC 2 RDC 3 RDC 4 RDC 5 Sngle-route strategy a Actual logstcs cost ncurred 5,58 54,821 14,476 5,58 135,375 5,58 Logstcs cost reflectng probablty 5, Dual-route strategy b Actual logstcs cost ncurred 5,765 55,673 19,29 5,765 16,945 5,765 Logstcs cost reflectng probablty 5, Note: Values are n CNY thousands. Probablty of no dsrupton s.995 and probablty of dsrupton s.1. PRFR of RDC 1, RDC 2, and RDC 4 s 1.,.95, and.95, respectvely. a Expected logstcs cost s 5,858. b Expected logstcs cost s 5,839.

7 18 Transportaton Research Record 2466 Lattude FIGURE Longtude (a) Lattude Orgn RDC Demand Orgn RDC Demand RDC allocaton for (a) sngle-route strategy and (b) dual-route strategy Longtude (b) Prmary route Secondary route 128 logstcs cost was less than that of the sngle-route strategy by 85,447, and 118,43, CNY, respectvely; these costs are large enough to put a busness at rs. Senstvty Analyss The nput varables n ths study can be changed accordng to changes n the envronment. Ths study amed to choose an approprate freght dstrbuton strategy under a gven crcumstance. Decson changes for the sngle- and dual-route strateges, therefore, were observed as functons of changes n the unt delay loss cost and the buffer stoc rato. Frst, decson changes from the unt delay loss cost varaton were analyzed. When the product s relatvely more valuable compared wth the transportaton cost and ts maret s more senstve to the delay, the unt delay loss cost ncreases. In the dualroute strategy, the PRFR value was used for the demand nodes en bloc by ther man RDC. That s, the demand nodes wth same prmary RDC were dualzed on the same rato. The expected dfferences n the logstcs costs for the dfferent strateges are shown n Fgure 6a. When there s no dsrupton, the dual-route strategy costs more than the sngle-route strategy, as shown n Fgure 6b, because of the longer transportaton dstance through the bypass. In the case of the dsrupton on RDC 1, the dual-route strategy s advantageous over the unt delay loss cost of 43,2, CNY, whch s the pont at whch the dual-route strategy should begn to be used at RDC 1 (Fgure 6c). In the case of RDCs 2 and 4, t s advantageous over 32,4, CNY and 36,, CNY (Fgure 6, d and e). The same analyss was conducted for buffer stoc varaton as shown n Fgure 7. A just-n-tme system can be represented wth zero buffer stoc. When the buffer stoc level s less than.5, the dual-route strategy costs less than the sngle-route strategy. The dfference of the expected logstcs cost decreased to zero as the buffer stoc ncreased. Expected logstcs cost (1, CNY) 6, 5,95 5,9 5,85 5,8 5,75 5,7 5,65 5,6 5,55 Sngle route 18, 21,6 25,2 28,8 32,4 36, 39,6 43,2 46,8 5,4 54, Unt delay loss cost (1, CNY) (a) FIGURE 6 Expected and actual logstcs costs for each case wth unt delay loss cost varaton: (a) expected logstcs costs wth model. (contnued)

8 Hur, Km, Kho, and Lee 19 Expected logstcs cost (1, CNY) 5,85 5,8 5,75 5,7 5,65 5,6 5,55 5,5 5,45 18, 21,6 25,2 28,8 32,4 36, 39,6 43,2 46,8 Sngle route 5,4 54, Expected logstcs cost (1, CNY) 8, 7, 6, 5, 4, 3, 2, 1, 18, 21,6 25,2 28,8 32,4 36, 39,6 43,2 46,8 Sngle route 5,4 54, Unt delay loss cost (1, CNY) (b) Unt delay loss cost (1, CNY) (c) Expected logstcs cost (1, CNY) 16, 14, 12, 1, 8, 6, 4, 2, 18, 21,6 25,2 28,8 32,4 36, 39,6 43,2 46,8 Sngle route 5,4 54, Expected logstcs cost (1, CNY) 25, 2, 15, 1, 5, 18, 21,6 25,2 28,8 32,4 36, 39,6 43,2 46,8 Sngle route 5,4 54, Unt delay loss cost (1, CNY) (d) Unt delay loss cost (1, CNY) (e) FIGURE 6 (contnued) Expected and actual logstcs costs for each case wth unt delay loss cost varaton: (b) actual cost wth no dsrupton, (c) actual cost wth dsrupton on RDC 1, (d) actual cost wth dsrupton on RDC 2, and (e) actual cost wth dsrupton on RDC 4. Expected logstcs cost (1, CNY) 6,4 6,3 6,2 6,1 6, 5,9 5,8 5,7 5,6 5,5 5,4 Sngle route Buffer stoc rato (a) FIGURE 7 Expected and actual logstcs costs for each case wth buffer stoc varaton: (a) expected logstcs costs wth model. (contnued on next page)

9 2 Transportaton Research Record 2466 Expected logstcs cost (1, CNY) 6,2 6,1 6, 5,9 5,8 5,7 5,6 5,5 5,4 5,3 Sngle route Buffer stoc rato (b) Expected logstcs cost (1, CNY) 16, 14,1 12, 1, 8, 6, 4, 2, Sngle route Buffer stoc rato (c) Expected logstcs cost (1, CNY) 3, 25, 2, 15, 1, 5, Sngle route Buffer stoc rato (d) Expected logstcs cost (1, CNY) 4, 35, 3, 25, 2, 15, 1, 5, Sngle route Buffer stoc rato (e) FIGURE 7 (contnued) Expected and actual logstcs costs for each case wth buffer stoc varaton: (b) actual cost wth no dsrupton, (c) actual cost wth dsrupton on RDC 1, (d) actual cost wth dsrupton on RDC 2, and (e) actual cost wth dsrupton on RDC 4. Conclusons The development of a nonlnear, mxed-nteger model s reported on to choose a freght delvery strategy n preparaton for a possble dsrupton at an RDC. The model specfed the rs cost, whch s caused by the dsrupton n two components: addtonal transportaton cost and the delay loss cost stemmng from the late delvery. A case study was conducted wth a partcle swarm algorthm usng an actual company s freght delvery data and the best soluton was determned n a reasonable tme. A senstvty analyss was also conducted wth unt delay loss cost and buffer stoc level changes. The applcaton results showed that ths model could provde numercal references to decde the freght delvery strategy to prepare for an RDC dsrupton. It was found that the dual-route delvery strategy s more advantageous than the sngle-route strategy when the unt delay loss cost s hgh and the buffer stoc at the demand node s low. The results ndcated that there exsts a pont at whch the dual-route strategy starts to cost less than the sngle-route strategy. The proposed model could be mproved through further research. Frst, more than one transportaton mode could be appled on feederlne transportaton to enhance the practcal use of the model. Second, the ln capacty constrant could be appled n the model to enlarge the model s adaptablty n supply chan studes. Thrd, the model could be modfed to create a dynamc analyss model, whch would enhance ts accuracy wth dynamc transportaton data. Fourth, control of the reorder pont level and the frequency of delvery also could be consdered an addtonal strategy to recover from the dsrupton. Last, the mprovement n effcency and accuracy of the PSO algorthm would contrbute to enhancng the accuracy and relablty of the proposed model. Ths study can be utlzed benefcally n the followng ways. It can provde expected logstcs costs of delvery strateges under the rs of dsrupton occurrence. Moreover, t can provde the prmary route freght rato so that the expected logstcs cost can be mnmzed. Acnowledgment Ths research was supported by a grant from the Jung Seo Logstcs Foundaton, South Korea. References 1. Zhang, Z., and M. A. Fglozz. A Survey of Chna s Logstcs Industry and the Impacts of Transport Delays on Importers and Exporters. Transport Revews, Vol. 3, No. 2, 29, pp Snyder, L. V., Z. Bulut, P. Peng, Y. Rong, A. J. Schmtt, and B. Snsoysal. Supply Chan Dsruptons: A Revew. Worng Paper. Lehgh Unversty, Bethlehem, Pa., Mtchell, V. W. Organzatonal Rs Percepton and Reducton: A Lterature Revew. Brtsh Journal of Management, Vol. 6, No. 2, 1995, pp Chopra, S., and M. M. S. Sodh. Supply-Chan Breadown. MIT Sloan Management Revew, Rce, J. B., and F. Canato. Buldng a Secure and Reslent Supply Networ. Supply Chan Management Revew, Vol. 7, No. 5, 23, pp Steele, P. T., and B. H. Court. Proftable Purchasng Strateges: A Manager s Gude for Improvng Organzatonal Compettveness Through the Slls of Purchasng. McGraw-Hll School Educaton Group, New Yor, La Londe, B. J. Supply Chan Management: Myth or Realty? Supply Chan Management Revew, Vol. 1, No. 1, 1997, pp. 6 7.

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