An Optimization Model for Empty Container Reposition under Uncertainty

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n Omzon Mode o Emy onne Reoson nde neny eodo be n Demen o Mnemen nd enooy QM nd ene de Reee s es nsos Moné nd Mssmo D Fneso Demen o Lnd Enneen nesy o Iy o Zdds Demen o Lnd Enneen nesy o Iy Inodon. onne sn omnes ode seded mme nsoon wod-wde. snn o o e omeeness s e by o emy onnes n os o mee some odes. De o e ob de mbne some os end o me emy onnes esn n nneessy soe oss we oes e soes eose sn omnes o e sk o omeos odn onnes s eesed. s onseene sn omnes ms be ee o mee some needs nd eom e mme eosonn o emy onnes. mo dy n s oeon s e mny soes o neny edn e.. e nmbe o onnes my be eesed n e e e me wen emy onnes beome be nd e esse y o emy onnes. See deemns modes wee oosed e.. oon e. 00 b ey ke no on sne ezon o nen mees. Sos omzon modes wee esened s we e.. en nd en 998. owee ey ee ood knowede o ndom be dsbons o od ow y soons. We esen deson o ene nsoon newok oe w emy onne eosonn s eomed. We en oose n omzon mode o soe s sse o eeoeneos ee o emy onnes kn no on neny o se o eesene senos. we n be ssned o e seno o eze s ee mone. Wes my eesen obbes o oene o sbee mees ssned by mnes odn o e on. Fny e mos snn ess o e sdy e noded nd dsssed. obem deson. Emy onnes n be be n os de o s nenoy ks nd ns n om e ndsde nd esses n om e sesde. ey n be dsed o e ndsde o see eoes oded on esses o e soe os. Emy onnes n be soed n os one ssned o seded esses o ke s no-ye-ssned nenoy. In e s se sn omnes ms dede now o w esses seded os n e me-eods o ssn e n emy onnes. In e seond se sn omnes n soe n emy onnes nd dede e. See onne yes e onsdeed nd e deen szes es n deen zons o e be se. In ode o ke no on e m o en desons on e e se o e sysem we need o ey onsde e me esee. Moeoe some desons ms be mde wen ee s ony knowede o some mees. Fo nsne esses en oe so mme dsnes do no oe se nomon bo e omoson. Indeed we ey e son n en o sn omnes ms dede ow mny onnes w be oded nd noded n e ne one. Fny noe mo soe o neny s eesened by e so-ed nd Rn oy s wen beed esses e deys n

e sede somemes emn oeons e onded wo odn emy onnes. Fo nsne de o dese m ondons some os ne e y nd wen ey es e oeons emes e o n me. Fe sows s n eme o me-eended newok mde o os denoed by ees nd wee emy onnes ms be ssned o esses nd o nded by ee B wee ey n be ke nssned. Nmbes om o nde o nes oeed by o deen esses. Fo nsne esse w e n eod o B. s o n od on s esse emy onnes be om e d eod nd nod emes w beome be om e eod. I s wo non sn omnes nno dede now esses o emy onnes be n e s eod os nd bese s deson ws mde beoe e. s eds o B sn omnes ms dede now e zon o onnes e beome be beoe e s eod. 5 B B B B B S DEISIONS OR KNOWN SLY OF EMY ONINERS NERIN SLY OF EMY ONINERS Fe. Sme me-eended newok. DEISIONS O BE MDE NOW ESSEL FRE DEISIONS SER-SINK KNOWN DEMND OF EMY ONINERS NERIN DEMND OF EMY ONINERS Omzon mode. Sn omnes ms dede e nmbe o emy onnes eosoned soed oded noded nd ke on esses. s nded beoe we ke no on wo eoes o desons o emy onnes soed n os deendn on e eemen o be ssned o nssned o seded esses. We onsde m-eod newok nd ssme desons e memened n on ozon son. Redn noon we onsde se o onne yes se o onos me-eods se o esses nd se o senos ssoed w wes w. Le be e se o os n w nssned emy onnes n be soed nd e eesen e se o os n w s oon s no owed. Moeoe we nde by θ e me o w desons ms be e sme o eey seno. Femoe we denoe by e ne o me beween e o emy onnes os o se nd e ben o esses o w s onnes e o be ssned.

e noon b 0 0 eesens o o e sy demnd o emy onnes o ye me n seno. E o n s eesened by wo nodes nd. e s node s eed o e sy s o emy onnes o ye be n o me n seno. e node s ssoed w e demnd o emy onnes o ye eesed n o me n seno. oe y onsns e oosed o od son nd eosonn n ndmssbe nmbe o emy onnes. Moeoe sne we e mnn eeoeneos ee o onnes o deen szes we onsde e es onne ye nd eess es n ems o nmbe o be sos be o nde -ye onnes. en e onne ye e be se o - ye onnes n be deemned sn onesons o noded by n e. 99. In e noon doed eee eesens e soe y o o e soe y o o nd e esd y o emy onnes ed by esse k en mon os nd n seno. e soes o neny noed n e sse e b s d nd. e obem s esened s n nee ommn mode wose deson bes e denoed by ee nd oss by ee wee mens oded noded eosoned nd od.. be ndes e nmbe o emy onnes o ye be n o ; d me o be oded on esse n me n seno eesens e eed ny os.. be ndes e nmbe o emy onnes o ye be n o ; me o be oded on esse n me n seno eesens e eed ny os.. be ndes e nmbe o emy onnes o ye o be noded n seno om esse n me o wee ey beome be me ; eesens e eed ny os.. be ndes e nmbe o emy onnes o ye o be noded n seno om esse n me o wee ey beome be me ; eesens e eed ny os. 5. be ndes e nmbe o emy onnes o ye o be eosoned n seno by esse beween os nd w esee ben me nd ; eesens e eed ny os. 6. be ndes e nmbe o no-ye-ssned emy onnes o ye o be soed n o beween mes nd n seno ; eesens e eed ny os. 7. be ndes e nmbe o emy onnes o ye o be soed n o beween mes nd n seno ; eesens e ee os. e esn mem mode n be eessed s oows:

w mn sbe o b s d 0 5 6 7 8 { } θ K 9 { } θ K 0 { } θ K { } θ K { } θ K { } θ K { } θ K 5 wee ± nd ms beon o. deson bes ke ony non-nee nee es. ± ± e obee non mnmzes e os o odn nodn eosonn nd son emy onnes oe mme newok. sn newok noon onsn se eesens

ow onseon o emy onnes o eey ye n e node eey me oe e seno. onsn se ees o ssn o esses emy onnes be n e node eey me oe e seno. onsn se moses o ssy e demnd o emy onnes ssoed w e node eey me oe e seno. onsn se 5 eesens ow onseon o -ye onnes o e o e esse k ben me n o. onsn ses 6 nd 7 ense nenoy ee o emy onnes soed does no eeed e eessed n nmbe o onnes o en ye. onsn se 8 nees onnes eosoned beween os does no eeed e se be o emes on esses. onsn ses om 9 o 5 eesen e non-ny ondons. Mn ess nd onsons. We onsde see eoson obems n o 5 onne yes nd 500 senos. o soe nme nsnes e we-known soe e 995 s sed. In o omon ess obems e soed n ess n 50 seonds w s me sbe o e oen needs o e sn ndsy. e esn eoson n w be dsed o os o n n me e nen y o nsne ey ms onze e so-ed osekeen. mo ese esee n s sse onsss o esmn ow mny senos sod be ken no on. Moeoe e mode ebs son eb ses newoks ommodes nd senos n be eoed o deeo sezed esoon enes. Reeenes. en RK nd en Y 998. wo-se Sos Newok Mode nd Soons Meods o e Dynm Emy onne oon obem. nsoon Sene - 6. oon S oe M nd Kno E 00. Emy onne mnemen o nemod nsoon newoks. nsoon Rese E 86-8. LEX Omzon Inooe 995. sn e LEX be Lby nd LEX Med Inee Lby Inne e Ned. n ende M nd De 99. Dynm nd Sos Modes o e oon o Emy onnes. Oeons Rese 0-6.

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