Incorporating Location, Routing and Inventory Decisions in Dual Sales Channel - A Hybrid Genetic Approach

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1 Incopoating Location, Routing and Inventoy Decisions in Dual Sales Channel - A Hybid Genetic Appoach Chia-lin Hsieh 1, Shu-hsien Liao 2, Wei-chung Ho 2 1 Depatment of Statistics and Actuaial Science, Aletheia Univesity, New Taipei City, Taiwan 2 Gaduate Institute of Management Science, Tamkang Univesity, New Taipei City, Taiwan (au1328@ .au.edu.tw) Abstact - In this study, we pesent a thee-echelon dual sale channel supply chain netwok including a single vende, multiple distibution centes (DCs), also physical etailes and online customes. In the poposed business model, the vende eceives odes eithe fom physical etailes o online customes, then assigns specific DCs to fulfill these odes. The pupose of this poblem is to detemine the numbe and locations of DCs which assign both physical etailes and online customes. These decisions ae vey citical policy that the vende is esponsible fo managing inventoy eplenishment at specific DCs. Since the fomulated poblem is consisting of LIP (Location-Inventoy Poblem) and LRP (Location-Routing Poblem) issues, we develop a genetic algoithm by incopoating a thee-phase heuistic appoach to solve both LIP and LRP. The expeimental esults demonstate tade-off cost elations which impact on the numbe of potential DCs to be opened unde the obective of minimizing total supply chain cost. Keywods - dual sale channel, genetic algoithm, integated supply chain design, location-inventoy poblem, location-outing poblem I. INTRODUCTION In supply chain and logistics management, the distibution netwok design is one of the most impotant poblems because it offes a geat potential to educe costs and to impove sevice quality. The location-outing poblems (LRP) poblem simultaneously is developed [1]. Howeve, the combination of the location-allocation and the vehicle outing poblems is suely difficult. The advent of e-commece (EC) has made etailing moe complicated and moe competitive. It is within this business context that it is focing many taditional bicks-and-mota companies to econside how to efficient etofit thei existing infastuctue which offeing multiple complementay channels povides a geate and deepe mix of custome sevice [2]. On the othe hand, deliveing poducts to customes is also a citical activity in any business. Especially, B2C envionment has voluminous, unpedictable, and dynamically changing custome odes. On-time delivey elies heavily on effective vehicle outing. The vehicle outing poblem is much moe complicated in B2C envionment. Unfotunately, thee is little eseach specifically addessing etail/e-tail opeations and how the addition of an online sales channel should affect a fim s supply chain netwok design [3]. Ou eseach contibutes to fill this gap and to examine stategies that etaile/e-tailes can employ to leveage synegies between online channels and bicks locations. The location-outing poblem (LRP) [4] is an integated supply chain eseach within locational analysis, with the distinguishing popety of paying special attention to undelying issues of vehicle outing. Most of them ([5] [6] [7]) ae elated to a simple distibution netwok with two layes (depots and customes). Only few exceptional studies addessed moe complex distibution netwok design poblems. [8] developed a fou-tie integated LRP made up of fou layes (plants, cental depots, egional depots and customes), with the aim of defining the numbe and the location of the diffeent types of facilities fo designing a new distibution netwok o fo impoving an existing netwok. [9] also consideed fou laye supply chains The solution of the supply chain netwok design can be defined as one that consists of the location and vehicle outing poblems of plants and depots which have to be solved simultaneously. In LRPs, thee ae vey limited eseaches addessing the etail/e-tail opeations in dual sale channel. [10] and [11] ageed that the need of having a quick-esponse vehicle dispatching system that handles dynamic demands of consumes is much geate in the B2C envionment than in B2B. [12] solved a thee-tie location-outing poblem that embace the clicks-andbicks stategy in thei etail opeations to minimize the total supply chain cost. In this pape, we addess moe complex distibution netwok design poblems, which have so fa eceived limited attentions, and which involve facility location, inventoy and outing decisions. Ou eseach addesses a thee-echelon duel sale channel supply chain netwok configuation consisting of a single vende, distibution centes (DCs), and two type of customes (etaile/etailes). The goal of ou model is to choose, locate and allocate a set of DCs, to detemine the inventoy policy and to schedule vehicles outes to meet customes demands such that the total cost is minimized. Ou model focuses on some specific functions: (1) dispatch of vehicles to delive poducts fo duel sales channel, (2) allocation of e-tailes to DCs, (3) inventoy odeing and allocation policy with isking pool. This pape is oganized as follows. Section II illustates ou eseach poblem and fomulates the mathematical model of ou dual-channel based integated supply chain model. Section III details the solution methodology fo solving the poblem. Computational esults ae epoted in Section VI. Conclusion and futue diections ae discussed in the last Section V /13/$ IEEE

2 II. PROBLEM STATEMENT AND FORMULATION A. Poblem Desciption and Assumptions We conside a thee-echelon integated supply chain netwok system (in Fig. 1) that consists of a supplie with a waehouse at the top echelon, multi-dcs in the middle echelon and the etailes fom dual sales channels (eithe taditional o Intenet-enabled channel) at the bottom echelon. Dual sales channels ae explained below. The supplie uses both a taditional etail stoe (etaile) and an Intenet-enabled channel (e-taile) to distibute poducts via its own DCs. Demand fom etailes at the etaile is met with the on-hand inventoy fom the bottom echelon while odes placed though the e-tailes ae satisfied diectly with the on-hand inventoy fom the top echelon but distibuted fom its own DCs. A single poduct whee the poduct quantity tanspoted to any etaile must cove the demand is consideed. Single DC supplies one etaile. The poduct is always available to customes thoughout two channels. Also, the poduct pice is the same fo both channels. The system eceives odes fom two custome segments accoding to thei pefeences. The custome in eithe channel has uncetain demand that follows an identically independent nomal distibution. Vendo managed inventoy (VMI) mode is consideed whee the supplie is esponsible fo the safety stock pooled at diffeent DCs. Each DC follows a (, R) inventoy policy, i.e., when the inventoy level at DC lowes a eode point R a fixed quantity, is odeed by the supplie. Each DC possesses two types of vehicles capacities fo dual sale channels. The capacities in the same channel ae the same, and fleet type is homogeneous. B. Mathematical Models Befoe pesenting the model, we depict the notation used thoughout the pape. Indices. i is an set of etailes (i I). is an index set of potential DCs ( J). n is an index set fo E-tailes (n N). is an index set of all outes (vehicles) ( R). Fig. 1. Thee-echelon supply chain netwok with dual sale channels Ou poblem incopoates VRP that can be descibed as the poblem of designing least cost outes fom one depot (say DC) to a set of geogaphically scatteed points of e-etailes. The outes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time inteval; all outes stat and end at the DC, and the total demands of all e-etailes on one paticula oute must not exceed the capacity of the vehicle. In addition, fo each DC thee ae two diffeent delivey policies. In the taditional etaile channel, a point-to-point policy is adopted fo the shipment between DCs and etailes; in the e-taile channel, the DCs have to quickly esponse the online custome s equiements. A home delivey sevices guaanteed that shipment should aive duing designated time window. The obective of this study is to find a solution that will minimize the sum of the outing cost, expected annual inventoy cost, and the fixed opening and opeating cost. The outing cost is dependent on the distance between the two selected points (clustes). The expected annual inventoy cost includes woking inventoy and safety stock costs. The fixed and opeating cost fo opening distibution centes will be incued when these DCs ae used. The following assumptions ae used thoughout the whole pape: Supplie and DCs stoage capacities ae unlimited. The inte-dispatch shipping is pohibited. Each ode is fulfilled by only a specific DC. The e- taile/etailes assignment to the DC is known a pioi. Decision Vaiables. is the aggegate economic ode quantity fo DC shipped fom the supplie. Y =1 if DC is open (=0, othewise). X i =1 if DC seves etaile i (=0, othewise). W n =1 if e-taile n is assigned to DC (=0, othewise). V n =1 if node pecedes node n in oute (=0, othewise). Model Paametes. B is the numbe of e-tailes contained in set N, i.e. B = N. d i is the mean of annual demand at etaile i. u n is the mean of annual demand at e-taile n. δ i is the standad deviation of annual demand at etaile i. δ n is the standad deviation of annual demand at e-taile n. f is the annual fixed cost fo opening and opeating DC. c is the unit tanspotation cost between the supplie and DC. tc i is the unit tanspotation cost between DC and etaile i. vc n is the unit tanspotation cost between node and node n;, n J N. a n is the ealiest time of oute to seve e-taile n. b n is the latest time of oute to seve e-taile n. t n is the specified aival time of oute fo e- taile n. s is the inventoy holding cost pe unit time (annually) at DC. o is the inventoy odeing cost pe ode to the supplie fom DC. ζ is the aveage lead time in days to be shipped to DC fom the supplie. z α is the left α-pecentile of standad nomal andom vaiable. In ou model, the supply chain cost is decomposed into the following items: (1) Facility Opeating Cost (FC), which incued the annual fixed cost of opeating the open DCs, (ii) Woking Inventoy Cost (WIC), which incued the expected annual cost of placing odes and the annual cost of caying woking inventoy, Safety Stock Cost (SSC), which captued the cost of holding sufficient inventoy to ensue safety stock is maintained to povide the specified sevice level, (iv) Tanspotation Cost (TC), which is the annual tanspotation cost including the

3 outbound outing costs fom the DCs to eithe etaile o e- taile channels and the inbound tanspotation cost fom the supplie to DCs. Thus, the total cost will be FC WIC SSC TC, as in (1). Z= J (i) f Y (ii) ( di X i un W n) i I n N ( o ) s ( Y ) 2 J J [15] (iv) s [ z α ( δ ζ X δ ζ W )] tc i di X i 1 i i n n J i I n N (iv) J i I vc n V n c ( di X i un W n) I J n I J R J i I n N We adapted the EO-appoximation pocedue of [13]. The optimal ode quantity * at DC can be obtained by diffeentiating eq.(1) with espect to and equaling to zeo to minimize the total cost Z. We obtain the optimal solution of as follows: * = 2 o ( d X u W ) i i n n i I n N By substituting (2) in tems of (1), the poblem is fomulated as follows. Min f Y [ 2 o ( )] s di Xi un Wn J J i I n N tc i d i X i vc n V n J i I R J N s c ( di X i un W n) (3) s.t. J i I n N X i = 1, i I (4) X i Y, i I, J (5) V = 1, n N (6) R J N n M l M n ( B Vn ) B 1, J, l, n N, R (7) V V = 0, R, (8) J n n n J N n J N Vn 1 R J n N Wn ( Vu Vun ) 1, u J N an W n tn bn W n (1) (2), (9) J, n N, R (10), J, n N, R (11) 0,1 0,1 0,1 V 0,1 (12) X { } Y { } W { } { } i n The model minimizes the total expected cost. Constaints (4) estict a etaile to be seviced by a single DC. Constaints (5) make sue that etailes can only be assigned to open DCs. Constaints (6) ensue that each e- taile is placed on exactly one vehicle oute. Constaints (7) ae the sub-tou elimination constaints which guaantee each tou must contain a DC fom which it n oiginates, i.e. each tou must consist of a DC and some e- tailes [14]. Constaints (8) ae flow consevation constaints saying that wheneve a vehicle entes an e- taile o DC node, it must leave again and ensuing that the outes emain cicula. Constaints (9) imply that only one DC is included in each oute. Constaints (10) link the allocation and the outing components of the model: the e- taile n is assigned to the DC in oute, which visits the e-taile n, stats its tip fom the DC. Constaints (11) ensue the DC delivey sevice fo the E-taile can aive duing the designated time window. Constaints (12) enfoce the integality estictions on the binay vaiables. III. SOLUTION METHODOLOGY Ou poposed model combines the location-allocation poblem (LAP) and the multi-depot vehicle outing poblem (VRP) in dual sales channel envionments that esults in a lage and moe complex poblem. A heuistic method which decomposed it into constuctive and impovement stages is developed. In the constuctive stage, the physical etaile allocation phase andomly geneates open DCs and the initial allocation of physical etailes to specific opening DCs is pefomed. In the impovement stage, we have two phases: online E-taile cluste phase and online E-taile outing phase. The fome mainly clustes the online e-tailes based on open DCs, the latte allocates the e-tailes to specific DCs. We apply heuistically both the genetic algoithm (GA) and K- means cluste method to solve the poblem. A. Physical Retaile Allocation Phase The physical etaile allocation phase is the constuctive stage which andomly geneates open DCs and initially allocates physical etailes to specific opening DCs. Te obective is to allocate etailes to specific DCs selected. Each potential DC is associated with a binay vaiable epesenting Y fo each candidate DC that will cay a value of 1 if a potential DC is open at that candidate site, and 0 othewise. We andomly geneate an initial binay population containing L stings whee L is the numbe of DCs, which might poduces both legal and illegal individuals. This esult is then applied fo both physical etaile and online e-etaile channels. In the online e-etaile channel, this population can be used as input infomation to pefom the clusteing and outing pocesses. In the physical etaile channel, this chomosome can be the basic condition to conduct the assignment pocedue. The assignment esult is used to pefom the calculation of fitting function to detemine all costs involved in the system. B. Online E-taile Cluste Phase The online e-taile cluste phase mainly pefoms cluste analysis. The definition of goup chaacteistic in ou model is those e-tailes which ae geogaphically dispesed in a connected aea. We use K-means the well-

4 known clusteing method to classify a given data set though a cetain numbe of goups fixed a pioi. In this study, we allow online e-tailes to be classified into k goups accoding to the numbe of open DCs given pioi. The poposed cluste pocedue fo online e-tailes is pesented as follows (in Fig. 2). The main idea is to define k centoids, one fo each goup. These centoids should be placed in a cunning way because of diffeent location causes diffeent esults. So, the bette choice is to place them as much as possible fa away fom each othe. The next step is to assign each online e-taile to the goup that has the closest centoid. When no online e-taile is pending, we need to e-calculate k new centoids in each goup. Afte we have these k new centoids, a new binding has to be done among the same online e-tailes and the neaest new centoid. A loop has been geneated. As a esult of this loop we may notice that the k centoids change thei locations step by step until no moe changes ae done. 1: Specify a cetain numbe of k goups a pioi 2: Place one point inside each goup as the initiated centoid 3: Repeat 4: Assign each online e-taile to the goup with the closest centoid 5: Re-compute the new centoid in each goup 6: Until all centoids don t swift Fig. 2. The online e-taile s cluste pocedue Afte clusteing all e-tailes into k goups (o called segments), the next pocess called the Goup-DC allocation pocedue is pefomed to allocate each open DC to one of the segments based on the shotest distance between DCs and the segment centoids. It is allowed fo each segment including a set of e-tailes to select the seconday closest DC, if its closest DC has been assigned without sufficient capacity, until segments ae all assigned. C. Online E-taile Routing Phase The online e-taile outing phase is to detemine the minimal outing distance in each cluste. Since many B2C businesses implement on-time delivey sevice unde EC envionment, they ely heavily on effective vehicle outing once the mechandise is out the supplie s doo and on its way to the custome. Theefoe, they allow the customes to choices thei acceptable ode delivey time peiods athe than the exact time. Without lost of geneality, we set thee diffeent deliveing time peiods fo satisfying custome s equiements. In this phase, we use GA to solve this poblem. Each solution in the GA chomosome is encoded in an intege sting in which the value of each gene denotes a specific e-taile, and the gene sequence of the chomosome epesents the vehicle outing ode of these e-tailes. Fistly, we andomly geneate each goup of online e-tailes into thee sub-goups accoding to thei time peiod equiements. Secondly, we andomly geneate an initial population epesenting the sequence of online e- tailes in each sub-goup. The algoithm evaluates the outing cost of each chomosome. Then, the tounament selection is used to choose paents fom the cossove pool. Next, the step, flip, swap, and slide cossove pocesses ae applied on the selected paents to geneate thee diffeent offsping. When the geneation numbe t eaches the maximum numbe of T, the algoithm stops. The E-taile Routing pocedue is depicted as follows in Fig. 3. 1: Randomly geneate 3 sub-goups of online e-tailes accoding to time peiod equiements in each goup 2: Randomly geneate an initial 4n population of e-tailes outing sequence within each sub-goup 3: Fitness evaluation of the population accoding to the outing cost 4: Select 4 outing sequence fom the population each time 5:Evaluate the best solution fom 4 outing sequence as the paent 6: Geneate 3 offspings fom paent by the outing cost by applying slide, swap and flip pocesses 7: While t T do 8: New population = paent (t) offsping (t) 9: End Fig. 3. The online e-taile outing pocedue VI. EXPERIMENTAL RESULTS The fomulated poblem is consisting of LIP and LRP issues. Thee ae diffeent benchmak instances povided to evaluate eithe LIP o LRP models, howeve, these pioi benchmak questions ae not suitable to be fitted in the poposed integated model. To evaluate the pefomance of ou oveall solution pocedue, we povide extensive computational expeiments by geneating seveal poblem instances in which diffeent size of physical etailes and online e-tailes ae in the distibution netwok. The test poblem instances ae constucted as follows. We geneate poblem instances on a supply chain netwok with 30 potential DCs which ae andomly dispesed within a squae of 50 distance units of width. Fo simplicity, Euclidean distance is used fo measuing distibution distances. In additions, vaious tanspotation-cost and inventoy holding-cost scenaios ae consideed in ode to evaluate how tanspotation cost and inventoy cost impact on the DC location decisions. All these instances ae andomly geneated and unifomly distibuted locations within a squae of 50 distance units of width fo the coodinates of all etailes and e-tailes. Fo instance, the poblem instance P_50_300_T1_S1 epesents that thee ae 50 etailes and 300 e-tailes which ae unifomly distibuted within the squae aea of width 50 distance units. The poposed pogam is coded in MATLAB 7 and executed on an INTEL I GHz pocesso. The input paametes ae: population size = 100, cloning = 20%, cossove ate = 80% and mutation ate vaies fom 5% to 10%. We modify the geneation size until each instance poblem solution is convegent. Table II shows the computational esults of cost pecentages fo the P_50_300_T1_S2 poblem instances indicating how the numbe of open DCs

5 impacts on the supply chain costs. Fig. 4 depicts the tadeoff tends among these costs as the numbe of open DC inceases. It is obseved that as the numbe of open DCs is inceased then the facility cost [13], odeing cost (OC), inventoy cost (IC) goes up as well. Howeve, the tanspotation cost (TC) (including the outing cost (RC) which delivey poducts to E-tailes) goes down on the contay. The esults ae consistent with [15]. It implies that the moe potential DCs ae opened the moe chances to close to the etailes/e-tailes locations so that deceases the tanspotation cost. Howeve, moe opened DCs also incu the incease of facility, odeing and inventoy costs. Thee ae multiple tade-off effects as the numbe of etailes/e-tailes inceases. TABLE II COMPUTATIONAL RESULTES FOR P_50_300_T1_S2 # of Pecentage of costs (%) DCs FC TC OC IC RC COST , , , , , , , Fig. 4. Tade-off tends among costs in P_50_300_T1_S2 V. CONCLUSION AND FUTURE RESEARCH The main eseach contibution is to simultaneously optimize location, allocation, inventoy and outing decisions without any appoximation. We have established thee-echelon supply chain netwok involving one supplie, DCs and etaile/e-tailes which incopoates facility location, inventoy and vehicle outing decisions. We have pesented an effective heuistic method. Aftewad we geneated expeiments to evaluate how the DC selection impacts on tanspotation, inventoy costs and outing costs. Expeiments have evealed that the poposed genetic algoithms can yield a nea-optimal solution in stochastic demand envionments. The poposed model can also help to make decisions egading facility locations with clusteing popety appopiately. Fo futue wok, it is inteesting to develop moe effective and elegant heuistic methods to solve the integated model poblem. The poposed genetic algoithm (GA) povides a vaiety of options and paamete settings that ae woth fully examined. Moeove, the model can be extended in seveal ealistic and pactical diections. The poposed GA can be applied to diffeent pefomance citeia. Fo example, a multi-obective fomulation by consideing minimal supply chain cost and maximal custome sevice simultaneously should be equied to povide the tadeoffs of Paeto optimal altenatives. REFERENCES [1] G. Lapote, Y. Nobet, and S. Taillefe, "Solving a Family of Multi-Depot Vehicle Routing and Location-Routing Poblems," Tanspotation Science, vol. 22, pp , August 1, [2] D. W. Wallace, J. L. Giese, and J. L. Johnson, "Custome etaile loyalty in the context of multiple channel stategies," Jounal of Retailing, vol. 80, pp , [3] A. V. Hill, D. A. Collie, C. M. Foehle, J. C. Goodale, R. D. Mettes, and R. Vema, "Reseach oppotunities in sevice pocess design," Jounal of Opeations Management, vol. 20, pp , [4] G. Nagy and S. Salhi, "Location-outing: Issues, models and methods," Euopean Jounal of Opeational Reseach, vol. 177, pp , [5] T. H. Wu, C. Low, and J. W. Bai, "Heuistic solutions to multi-depot location-outing poblems," Computes & Opeations Reseach, vol. 29, pp , [6] M. Albaeda-Sambola, J. A. Dıáz, and E. Fenández, "A compact model and tight bounds fo a combined locationouting poblem," Computes & Opeations Reseach, vol. 32, pp , [7] C. K. Lin and R. C. Kwok, "Multi-obective metaheuistics fo a location-outing poblem with multiple use of vehicles on eal data and simulated data,"euopean Jounal of Opeational Reseach, vol. 175, pp , [8] D. Ambosino and M. Gazia Scutellà, "Distibution netwok design: New poblems and elated models," Euopean Jounal of Opeational Reseach, vol. 165, pp , [9] J. H. Lee, I. K. Moon, and J. H. Pak, "Multi-level supply chain netwok design with outing," Intenational Jounal of Poduction Reseach, vol. 48, pp , 2010/07/ [10] T. C. Du, E. Y. Li, and D. Chou, "Dynamic vehicle outing fo online B2C delivey," Omega, vol. 33, pp , [11] N. Azi, M. Gendeau, and J.-Y. Potvin, "An exact algoithm fo a single-vehicle outing poblem with time windows and multiple outes," Euopean Jounal of Opeational Reseach, vol. 178, pp , [12] D. Aksen and K. Altinkeme, "A location-outing poblem fo the convesion to the click-and-mota etailing: The static case," Euopean Jounal of Opeational Reseach, vol. 186, pp , [13] S. Axsäte, "Using the Deteministic EO Fomula in Stochastic Inventoy Contol," Management Science, vol. 42, pp. pp , [14] M. Desoches and G. Lapote, "Impovements and extensions to the Mille-Tucke-Zemlin subtou elimination constaints," Opeations Reseach Lettes, vol. 10, pp , [15] Z. J. M. Shen, C. Coullad, and M. S. Daskin, "A Joint Location-Inventoy Model," Tanspotation Science, vol. 37, pp , 2003.