Optimization of the Replenishment Strategy for the Supplier Based on Genetic Algorithm

Transcription

1 Internatonal Journal of Busness and Manageent Vol. 6, No. ; January 0 Optzaton of the Replenshent Strategy for the Suppler Based on Genetc Algorth Ke Zhu School of Busness, nversty of Shangha for Scence and Technology 334 Jun Gong Road, Shangha 00090, hna E-al: zkchwd@6.co Hengshan Wang School of Busness, nversty of Shangha for Scence and Technology 334 Jun Gong Road, Shangha 00090, hna Yuanyuan Kong School of Busness, nversty of Shangha for Scence and Technology 334 Jun Gong Road, Shangha 00090, hna Sheng L School of Busness, nversty of Shangha for Scence and Technology 334 Jun Gong Road, Shangha 00090, hna The research s fnanced by Shangha Key Dscplne of Manageent Scence and Engneerng. No. S30504 (ponsorng nforaton) Abstract In the supply chan anageent, the suppler can reduce ts total cost by provdng prce dscounts to restrct the retalers replenshent ntervals to ultples of a coon replenshent nterval. In order to accoplsh ths purpose, suppler often deterned a prce dscount that all the retalers can accept. After the cost of the suppler was further consdered, a better prce dscount was desgned, whch can eet all the retalers requreents to axze ther benefts. And a new suppler s nzaton proble odel based on stackelberg gae was desgned also. Then a genetc algorth s used to solve the suppler s replenshent odel. Experent results of the genetc algorth deonstrated the feasblty and the effectveness of the strategy. Keywords: oon replenshent nterval, Prce dscount, Genetc Algorth. Introducton In the supply chan anageent, ore and ore enterprses are aware of the portance of cooperaton. However, dfferent enterprses belong to dfferent econoc entty, so they tend to focus on ther own nterests rather than the nterests of the whole supply chan, whch lead to the cooperaton ore dffculty. onsderng that, t's necessary for us to desgn a echans to enhance cooperaton between dfferent enterprses. Prce dscount as a odel for enhancng cooperaton has been rased by rowther as early as 964. He argued that, f supplers afford prce dscount to retalers, the retaler s quantty of purchase wll be larger than ther econoc order quantty. And ths ode ncrease revenue of supplers, at the sae te nflate costs of retalers. However, rowther had not establshed odel for ths theory. Based on the study of rowther, Dolan (987) establshed a odel and gve the order strateges n the case of the lowest whole syste cost for supplers and retalers fro perspectve of retalers. MonahaIl (984) studed the proble of optal dscount fro perspectve of supplers for the frst te. Lu and Vswanathan deal wth optzaton of the ntegrated nventory proble based on the wllngness of cooperaton for supplers and retalers. 8 ISSN E-ISSN

2 Internatonal Journal of Busness and Manageent Vol. 6, No. ; January 0 The paper as at analyzng process of orderng goods based on two-echelon supply chan syste whch conssts of one-suppler and ult-retaler. Ths syste adopts the echans wth coon replenshent nterval, suggests the suppler offer prce dscounts for retalers selectvely. These tactcs reduce the cost of replenshent to retalers, so we can get further proveent on the replenshent decson-akng. In ths paper, we establsh the optal replenshent odel fro the perspectve of suppler. Prce dscounts strategy of suppler could be solved by ths odel. Satsfyng results can be getted by the Genetc Algorth whch has adaptve search characterstc. By analyzed the calculaton result, the odel s proved to be effectve n reducng the cost of suppler and the whole supply chan to soe extent.. Proble descrpton onsder a ntegrated supply chan wth one-suppler and ult-retaler. The retaler deand nforaton about next T ntervals s transferred to suppler through the Internet. As the leader of the stackelberg gae, the suppler deternes the retalers replenshent strategy on the bass of the nventory and deand nforaton provded by retalers. Ths replenshent strategy solved any probles of suppler and retalers, for exaple, how long of the coon replenshent nterval, the te to replensh goods, whether the suppler should provde a prce dscount before the te of replenshent etc. The purpose of the study s to set up a new odel to nze suppler s replenshent cost and reduce retalers orderng and holdng cost as uch as possble, whch could optze the whole syste. 3. Proble odelng 3. Assupton and notaton We consder a two-echelon supply chan whch conssts of one suppler and ult-retaler wth a sngle product. To develop the proposed odel, the followng assuptons and notatons are used: Assuptons. The deand rate of the retalers s known and constant.. The suppler can eet all the retalers deand and the lead te s zero. 3. As the the leader of the stackelberg gae, the suppler fx the coon replenshent nterval (such as every week, every onth etc). 4. Before the coon replenshent nterval strategy s pleented, the optal replenshent nterval follows the econoc order quantty odel. 5. After the coon replenshent nterval strategy s pleented, the suppler offer the prce dscounts to certan selected retalers. Notaton the nuber of the retalers d the prce dscountng rate provded by suppler P per unt prce to the retaler h per unt holdng cost per te unt for retaler D deand rate for retaler K orderng cost per order for retaler T 0 coon replenshent nterval X the set of coon replenshent nterval A s the setup cost ncurred by suppler for processng the entre order A the setup cost ncurred by suppler for processng a specfc order fro retaler A s the delvery cost ncurred by suppler for processng a specfc order fro retaler Z the lowest prce dscountng rate acceptable to retaler t the optal replenshent nterval correspondng to the EOQ for retaler t after the coon replenshent nterval strategy s pleented, the replenshent nterval for retaler 3. Before the coon replenshent nterval strategy s pleented For retaler, followng the econoc order quantty (EOQ) odel (Banerjee, 988), the replenshent nterval s gven by t K/ hd, the su of orderng and holdng cost can be expressed as K g hdt KhD t Publshed by anadan enter of Scence and Educaton 9

3 Internatonal Journal of Busness and Manageent Vol. 6, No. ; January 0 and the total cost can be expressed as PD g. orrespondngly the suppler s orderng and delvery cost for retaler can be wrtten as ( )/ g s 0 AA t. 3.3 After the coon replenshent nterval strategy s pleented When the strategy s pleented, the suppler wll provde prce dscounts to restrct the retalers replenshent ntervals to a coon replenshent nterval wth the purpose of reducng ts total replenshent costs. If the suppler provdes prce dscount for the retaler, the optal replenshent nterval of the retaler s t nt 0, where n, and nteger, T 0 X () Otherwse, ts value s the sae as the replenshent nterval of EOQ. orrespondngly, the su of order and holdng cost g, and total cost for retaler (who accept the prce dscount) are gven by g K nt hdnt 0 () 0 ( d) PD g (3) where g s convex wth respect to n, because of g n g n hdn K 0 nt 0 3 K n T 0 * Fro g / n 0, we obtan a unque root n that nze g and. And n * satsfes * * K * * n ( n ) n ( n ) (4) hdt 0 In the case of the coon replenshent nterval strategy, f the retaler accept the prce dscount, the total cost for retaler ust be saller than those wthout prce dscount. In the paper, the retaler wll accept the prce dscount f t can save S% of ther total cost. So the prce dscountng rate should satsfy K( S) K dp h( S) Dt hnt 0 (5) Dt DnT 0 After rearrangng the ters n (5), we thus get K ( S) d ( ) hnt 0 ( S) t (6) PD nt 0 t P Fro (6), we can get the lowest prce dscountng rate acceptable to retaler Z K ( S) Z ( ) hnt 0 ( S) t (7) PD nt 0 t P As the leader, the suppler wll offer prce dscounts to certan selected retalers to nze ts total replenshent cost. For the retaler, f t s offered prce dscount, ts replenshent nterval wll be a ultple of T 0, ts su of orderng and holdng cost and total cost should be calculated followng Eq.() and Eq.(3). Otherwse these ones should be calculated followng the EOQ odel. Accordng to above, the suppler s nzaton proble can be rewrtten as s.t. T 0 As A As A A As g ( ) ( ) 0 dpd y T 0 t nt 0 t (8) X, d Z, n and nteger, =,,, offer prce dscount y 0, otherwse 4. Genetc algorth pleentaton The process of bologcal evoluton s anly accoplshed through the crossover operator and the utaton 0 ISSN E-ISSN

4 Internatonal Journal of Busness and Manageent Vol. 6, No. ; January 0 operator of chroosoes. orrespondngly, Genetc Algorth s a hgh-effcency ethod by sulatng the process of the bologcal evoluton to search for the optal soluton. And It could apply soe genetc operators to act on the populaton P(t), then obtan newer populaton P(t + ) by usng soe easures of ftness. In the next subsectons, we wll descrbe the steps requred to solve the odel gven n Eq.(8) by a genetc algorth. 4. hroosoe codng Encodng s the frst step of developng a Genetc Algorth. In the process of searchng for the optal soluton, the tradtonal codng ethod s to encode the proble s varables as a bnary strng or a decal strng called chroosoe. In ths paper, because the values of decson varables( y )are 0 or, the bnary codng s appled to generate N chroosoes randoy represented by a strng of bnary dgts, as the ntal populaton. After a stoppng crteron s satsfed, a fnal populaton wll be avalable. Accordng to the value of the fnal populaton, we can get the optal replenshent decson of the vendor. For exaple, when = 0, the set {, 0, 0,, 0,, 0,, 0, 0} represent that vendor would offer prce dscount to retaler, retaler 4, retaler 6 and retaler Ftness evaluaton In the Genetc Algorth, each ndvdual n the current populaton s evaluated only by the ftness, not usng any external nforaton. The probablty of survval of any ndvdual s deterned by ts ftness. And the populaton evolves by the way of the ftter ndvduals overtakng the less ft ones. In order to calculate the probablty of survval of any ndvdual correctly, the ftness value of any ndvdual ust be non-negatve. Besdes, the value of objectve functon n Eq.(8) s always non-negatve, and our a s to fnd out the nu value of the objectve functon. For ths reason, the ftness functon can be expressed as follows F(X) = ax - f (X), where ax s a relatvely larger nuber specfed n advance. 4.3 Selecton The algorth use the roulette wheel selecton. Several rounds of choce are requred to select ndvduals to go nto the next generaton. A new rando nuber descrbed by 0 or can be created n each round, as the ponters decde the selected ndvduals. The selecton operator s used for flterng the ntal populaton. 4.4 rossover In ths paper, a ethod of one-pont crossover s used to select a cut pont K n the nterval [, -] randoly, where s the nuber of genes of populaton. The cut pont dvdes the chroosoe nto two dsjont parts. Then the crossover creates a offsprng by exchangng parts of the parent chroosoes wth the step sze. 4.5 Mutaton In order to avod the answer becong trapped n local opta, utaton wll arse wth a very sall probablty. Let s desgnate the loc of chroosoes as change pont wth the utaton probablty P = 0.0. Then each gene of the change pont s utated over the ntegers fro 0 to. 5. Nuercal exaple In ths secton, we suppose that: the nuber of the retalers s = 0, per unt prce to the retaler s p = $, the unt holdng cost of product at unt te s h = $0. for every retaler. The deand and the cost for per orderng are gven n table. In order to calculate easly, we assue that dfferent retalers have the sae setup cost and transportaton cost supported by suppler. Each paraeter of suppler: A s = $500, A s = $300, A = $00, the set of coon replenshent nterval s X = {, 7, 4, 30, 60, 90}. After the coon replenshent nterval strategy s pleented, the retaler wll accept the prce dscount f t can save S=0% of ther total cost. Insert Table here. Based on the data fro the above, we can derve that f prce dscounts provded for every retaler are the sae (Vswanathan, 00), the nu replenshent cost of suppler s $34544, the orderng and holdng cost of the whole syste s $5869. In ths paper, we use the odel establshed to solve ths proble. Then nuercal results are calculated by genetc algorth. Each ntal paraeter of genetc algorth: the populaton sze s M = 0, the teratons s MaxGeneraton = 000. After any experents, we can draw a concluson that when the probablty of crossover s 0.8, and the probablty of utaton s 0.08, genetc algorth has a better convergence. We fnd that the replenshent cost of suppler can reach nu $683 when T 0 =4, and the orderng and holdng cost of the whole syste s $ orrespondngly, suppler's percentage savngs, retalers' percentage savngs and syste percentage savngs are 6.%, 0.06%and.5%, respectvely. Fgure shows the relatonshp between teratons and best ndvdual of populaton of every generaton correspondng replenshent cost of suppler durng the process of calculaton of genetc algorth. After 300 teratons, the global approxate optal value of the replenshent cost of suppler can be obtaned. Fro the coputatonal process and the results, ths strategy can reduce both the suppler s cost and the retaler s orderng and holdng Publshed by anadan enter of Scence and Educaton

5 Internatonal Journal of Busness and Manageent Vol. 6, No. ; January 0 cost furtherly, whch can be used for gudng enterprse to ncrease profts and reduce costs. 6. oncluson By a few calculatons, we can coe to the concluson that: ths odel can be used ore effectvely ether when we solve the orderng proble wth lots of retalers, or when the condton about orderng cost (requreent, the optal cycle of orderng etc) of the retalers are very dfferent wth each other. In realty, for large suppler, the proposed ethod n ths paper s effectve n both strengthenng cooperaton between suppler and retalers, and akng replenshent decson n short te. Therefore, ths proble s worth to carry out by ore study and researches. References Banerjee, A. (986). A jont econoc lot sze odel for purchaser and vendor. Decson Scence, 7, 9-3 Gannoccaro, I., & Pontrandolfo, P. (004). Supply chan coordnaton by revenue sharng contracts. Internatonal Journal of Producton Econocs, 89, 3-39 Goyal, S. K. (988). A jont econoc lot-sze odel for purchaser and vendor: A coent. Decson Scences, 9, 36-4 Hoque, M. A. (006). An optal soluton technque for the jont replenshent proble wth storage and transport capactes and budget constrants. European Journal of Operatonal Research, 75, Jaes, Hll., Mchael, R., & Galbret, h. (008). A heurstc for sngle-warehouse ult retaler supply chans wth all-unt t ransportaton cost dscount. European Journal of Operatonal Research, 87, Moon, I. K., & ha, B.. (006). The jont replenshent proble wth resource restrcton. European Journal of Operatonal Research, 73, Munson,. L., & Rosenblatt, M. J. (00). oordnatng a three-level supply chan wth quantty dscount. IIE Transactons, 33, Qn, Y., Tang, H., & Guo,. (007). hannel coordnaton and volue dscounts wth prce-senstve deand. Internatonal Journal of Producton Econocs, 05, Vswanathan, S., & Pplan, R. (00). oordnatng supply chan nventores through coon replenshent epochs. European Journal of Operatonal Research, 9, Wu, K. S., Ouyang, L. Y., & Yang,. T. (006). An optal replenshent polcy for non-nstantaneous deteroratng tes wth stock-dependent deand and partal backloggng. Internatonal Journal of Producton Econocs, 0, Table. The Retalers deand and the cost for per orderng Retaler Orderng cost K ($) Annual deand (n llons) Retaler Orderng cost K ($) Annual deand (n llons) Fgure. The convergence path of suppler s replenshent cost ISSN E-ISSN