Product Layout Optimization and Simulation Model in a Multi-level Distribution Center
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1 Avbe onne t Systems Engneerng Proced (0) Product yout Optmzton nd Smuton Mode n Mut-eve Dstrbuton Center Ynru Chen,Qnn Xo, Xopng Tng Southwest otong unversty,chengdu,6003,p.r.chn Abstrct We consder the product octon probem n ogstcs engneerng, whch ows ncorportng vrous spects n horzont nd vertc drecton. These spects ncude crryng tme, the turnover rtes of products, reevnce of product demnd, eevtor wtng tme, vertc trnsportton tme, etc. we deveop 0- progrmmng mode wth two obectves-mnmzton of tot trnsportton tme nd mmzton of reevnce of product demnd. n order to obtn verge wtng tme of every eve, we estbsh n eevtor smuton mode consderng the mtton of eevtor cpcty. The proposed optmzton mode cn be soved usng Genetc gorthm heurstcy. A numerc empe shows ts effectveness. 0 Pubshed by Esever B.V. Open ccess under CC BY-NC-ND cense. ey words: Mut-eve Dstrbuton Center; Product yout Optmzton; Eevtor Smuton; ogstcs engneerng.ntroducton Dstrbuton center operton nd mngement s one of the essent prts of mnufcturng nd servce opertons. The product yout s ey to dstrbuton center opertons. The product yout probem s concerned wth the queston of postonng products to storge octons. At present tertures on snge-eve product yout re hghy etensve. Though mut-eve dstrbuton center s more nd more popur n the mnufcturng nd servce sectons, reserch on product yout n mut-eve dstrbuton center hs receved ess ttenton. The erest wor on the mutpe-eve yout probem ws done by ohnson (98). He nvestgted the probem of retve octon of fctes n mutpe-foor budng.,xue, nd Zhng(00) nvestgted mut-eve wrehouse yout probem consderng mutpe storge res n dfferent eves of wrehouse.,xue, nd Zhng(006) consdered mut-eve wrehouse yout probem gn nd proposed css of new heurstcs by combnng genetc gorthm nd pth nng strtegy to sove the probem. tertures bove shre the sme ssumpton - The eevtor cpcty s enough. Tht s, the vertc trnsportton operton s wys vbe. However n re fe t s common for product to wtng for the eevtor becuse of the mtton of eevtor cpcty. To be more prctc, ths pper estbshes eevtor smuton mode wth the hep of AUTOMOD softwre to obtn verge eevtor wtng tme. Besdes, consderng other fctors, such s chrcterstcs of products, turnover rte, reevnce of demnd nd mtton of spce, the product yout optmzton nd smuton mode s deveoped Pubshed by Esever B.V. do:0.06/.sepro Open ccess under CC BY-NC-ND cense.
2 Ynru Chen et / Systems Engneerng Proced (0) * Xopng Tng. Te.: E-m ddress: tph@6.com.. The Formuton of Mut-eve Product yout Mode. Assumptons nd Nottons n the mut-eve product yout probem, t s ssumed tht there s ony one nd of pette. Dfferent products re octed n dfferent storge spces. The dstrbuton center hs foors. There re rows nd coumns sheves t foor to foor. Foor s not for storng product. ogstcs opertons cn be done for h hours dy, d dys yer. The foowng nottons re ntroduced for the prmeters of the mode. :Tme of crryng product octed n row, coumn to the eevtor t foor ; : Averge wtng tme t eve,whch cn be obtned by the smuton mode; ; : Arrv nterv of product t eve, whch cn be obtned by nnu turnover rte of products; : nnu turnover rte of product ; M: tot number of orders n one yer; when product s ssgned to row coumn t foor 0 ese t y :Reevnce of demnd between product nd product y, 0 y f m 0 when ese product s n the order ; ym 0 when ese product or y s n the order m : when product s dcent to product y b y 0 ese : Where: =,3 ; =, ; =, ; =, ; =, -; y,+, m =, M,. Mode Formuton Sever obectves cn be formuted for the product yout probem. We w focus on two of them wth the ttempts of mprovng shpment nd meetng the needs of customs s soon s possbe... Obectve : Mnmzton of tot crryng tme Dfferent from snge-eve dstrbuton center, horzont nd vertc crryng tme shoud be consdered t the sme tme. n order to shorten crryng tme, products wth hgh turnover rte shoud be cosed to eevtor t hgh foor. Frst obectve functon s shown s foows, F mn t t f ().. Obectve : Mmzton of reevnce of product demnd
3 30 Ynru Chen et / Systems Engneerng Proced (0) Reevnce shows the orderng probbty of products t the sme tme. f products wth hgh reevnce re put n dfferent foor, order pcng tme w be ong. Besdes, wth the Strct Order Pcng pocy, reted products octed cosey cn reduce pcng nd crryng tme. Second obectve functon s shown s foows, () m y y y b F M m ym M m ym m y (3) Where: ese nd when ym m ym y y y b ) ( ) (.3 Mode Formuton We ttempt to mnmze tot crryng tme nd mmze reevnce of demnd t the sme tme wth two restrctons. The one s tht one storge spce cn contn t most one nd of product. The other s tht one product cn be ssgned to ony one storge spce. The mode s s foows: y b b f t t y y y y y y, ;, ;,, ;, ;, 3 mn ) ( ) (
4 Ynru Chen et / Systems Engneerng Proced (0) Where ω nd ω denote weghts of two obectve functons respectvey. 3. Eevtor smuton mode Eevtor s one of typc stochstc servce system. Eevtor wtng tme of every foor s rndom vrbe. t s hrd to obtn eevtor wtng tme thetrcy when cpcty of eevtor s mted. To be prctc, we estbsh eevtor smuton mode(see Fg.). Wth the pocy of hgh-eve-hgh-prorty, we smuted down pe stuton of eevtor servce bsed on Pth Mover nd Process System n the Automod softwre. Te dstrbuton center wth 4 foors for empe, 3 od s re deveoped stndng for products t the foor,3 nd 4. 4 queue s re estbsh to show wtng res t every foor. 4 recourse s re used to denote bors. Vehce mens eevtor. A Two-wy ne shows the trc of eevtor. 4 pont s men /O pont of eevtor. Product rrv nterv s n mportnt nput prmeter for eevtor smuton. We cn obtn verge rrv nterv t foor by the foowng formuton: 3600 Z d f h (4) Where s 0- vrbe nd cn be obtned by foowng formuton. 0 when ese 0 Fg. Eevtor servce system smuton mode We cn obtn verge wtng tme t dfferent foor wth smuton mode. Fg. shows the mpct of eevtor cpcty on the verge wtng tme. When eevtor cpcty s sm, there s onger queue n foor then tht n foor 3 nd foor 4 becuse of hgh-eve-hgh-prorty pocy. Wth the ncrese of eevtor cpcty, the dfference of verge wtng tme between foors s smer nd smer.
5 304 Ynru Chen et / Systems Engneerng Proced (0) Averge wtng tme Foor 4 Foor 3 Foor Cpcty of eevtor Fg. The retonshp between verge wtng tme nd eevtor cpcty 4. Numerc empes There s dstrbuton center wth 4 foors, 5 sheves re octed t foor,3 nd 4. ogstcs opertons re done for 8 hours dy, 300 dys yer. 5 nds of products re stored n ths dstrbuton center. One storge spce cn contn 0 unts of sme products. Cpcty of eevtor s 3 unts. od tme s 5 second nd unodng tme s 0 seconds. Mter hndng tme s rndom vrbe wth dstrbuton of U (0,).The reevnce of products s shown s Fg.3
6 Ynru Chen et / Systems Engneerng Proced (0) Fg.3 The reevnce of products The mode s heurstcy soved by GA wth poputon sze of 50, terton tmes of 500, crossover rte of 0.85, mutton rte of 0.08.The weght of frst obectve s 0.7 nd tht of second obectve s o.3. The resuts of mode re shown n Fg.4 nd Tbe.
7 306 Ynru Chen et. / Systems Engneerng Proced (0) Ftness optm Averge ftness ftness Fg.4 retonshp of ftness terton tme terton tme Tbe product yout resut octon product octon product octon product octon product octon product (,,) M (,,4) A (3,,7) O (3,,0) V (4,,3) X (,,) M (,,5) B (3,,8) O (3,,) M (4,,4) C (,,3) A (,,6) B (3,,9) O (3,,) H (4,,5) (,,4) B (,,7) G (3,,0) Q (3,,3) N (4,,) B (,,5) B (,,8) O (3,,) D (3,,4) (4,,) G (,,6) A (,,9) E (3,,) O (3,,5) E (4,,3) G (,,7) O (,,0) D (3,,3) N (4,,) E (4,,4) G (,,8) G (,,) Q (3,,4) N (4,,) M (4,,5) T (,,9) (,,) Q (3,,5) F (4,,3) M (4,,6) T (,,0) (,,3) Q (3,,) E (4,,4) M (4,,7) H (,,) R (,,4) D (3,,) Y (4,,5) M (4,,8) H (,,) V (,,5) P (3,,3) H (4,,6) P (4,,9) (,,3) V (3,,) Y (3,,4) T (4,,7) H (4,,0) (,,4) (3,,) H (3,,5) (4,,8) V (4,,) A (,,5) C (3,,3) B (3,,6) R (4,,9) V (4,,) U (,,) X (3,,4) G (3,,7) O (4,,0) V (4,,3) F (,,) X (3,,5) R (3,,8) O (4,,) U (4,,4) S (,,3) U (3,,6) R (3,,9) Q (4,,) U (4,,5) W 5. Concusons Dfferent from estng reserch, ths pper consders the mtton of eevtor cpcty,.e., t s common for product to wt for eevtor. Snce wtng tme s rndom vrbe whch t s hrd to obtn theoretcy, we estbsh eevtor smuton mode to get the verge wtng tme of every foor. Puttng order pcng tme nd verge wtng tme together, we cn get hertc trnsportton tme.wth two obectves-mnmzton of tot
8 Ynru Chen et / Systems Engneerng Proced (0) trnsportton tme n the hertc nd vertc drecton nd mmzton of reevnce of product demnd., We deveop product yout optmzton mode whch s soved by GA heurstcy. 6. Copyrght A uthors must sgn the Trnsfer of Copyrght greement before the rtce cn be pubshed. Ths trnsfer greement enbes Esever to protect the copyrghted mter for the uthors, but does not renqush the uthors' propretry rghts. The copyrght trnsfer covers the ecusve rghts to reproduce nd dstrbute the rtce, ncudng reprnts, photogrphc reproductons, mcrofm or ny other reproductons of smr nture nd trnstons. Authors re responsbe for obtnng from the copyrght hoder permsson to reproduce ny fgures for whch copyrght ests. References. G. Q. Zhng,. Xue,...A css of genetc gorthms for mutpe-eve wrehouse yout probem[].nternton ourn of Producton Reserch.00,40(3):73 ~744. G. Q. Zhng,...Combnng pth renng nd genetc gorthms for the mutpe-eve wrehouse yout probems[].europen ourn of Operton Reserch. 006,69():43 ~45
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