Cargo-Loading Decisions: A Goal Programming Approach
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1 Cr-Ldn Desns: A Gl Prrn Apprh K K L nd Yue Wu Deprtent Mneent Senes Ct Unverst Hn Kn Hn Kn Etended Astrt Kerds: r ldn l prrn nd enet lrth Intrdutn. Bkrund the stud Anst the krund llztn rket nd the rpd develpent nterntnl trde rprtns hve sustntll nresed the spe nd ntude ther ll prdutn nd dstrutn netrks hh represent ll nterted sstes r servn vrus rld rkets []. Ths stud s nspred the prle n ultntnl rent nuturn pn hh hs hedqurters n Hn Kn sles rnhes n Nrth Aer nd Eurpe nd tres n nlnd Chn s ell s ther Suth-est Asn untres. The Hn Kn hedqurters llets the rders thruh Nrth Aern nd Eurpen rnh es nd lltes the n ts tres. The rtes ts prduts re nutured n Chn. The pn s r s ntnerzed n the tres r dspth thruh Hn Kn s nterntnl tprt. The hedqurters ust rent ts ntners r the rlnes n rder t shp the r t the Nrth Aern nd Eurpen rkets. The r-ldn prle s t deterne the tpes nd nuer ntners rented r rlnes nd t pk uster res s llted nt the. Currentl the pn s ntner rentl pertn s rked ut null sed n persnl eperene. As ths desn-kn pprh lks sstetztn the pn des nt kn h eetve the urrent desns re. It s ls trde n tpes nd nuer ntners the lltn r nt these ntners nd ntner vlue utlt. The ptl r ldn desn s vusl end the pltes nul pressn. As n pnes n Hn Kn hve ther tres n Chn nd the shp t nterntnl rket ths knd ldn prle s prle tht these pnes e.. Prle desrptn Tpll rlne pnes prvde severl derent tpes r r ntners r rent r n ven lht. Eh ntner hs ts n vlue nd eht lts. The rentl hres r eh ntner re the su ed st r usn the ntner nd vrle st dependn n the eht the r n the ntner. The vrle
2 st s nn-deresn pee-se lner untn. Cntner rentl sts tke up lre perente the pn s ttl r ldn pertn sts. Fr ven r vlle t e shpped eh r hs t n vlue nd eht. The ttl vlue nd eht the r ssned t ntner d nt eeed the ntner s lts. Eh r ust e pked nt snle ntner. Brekn r nt derent ntners s nt pertted. B the pn s eperene the ttl eht the r llted nt se ntner s nt lkel t eeed the eht lt the ntner. Fr ths resn e d nt nsder eht s lt n ur del. The prle s rentn the ntners nd lltn the r n the ntners s tht the etve untn s heved nd s ptl. Three etves rdn t tret levels nd prrt struture re: ttl rentl st; the nuer ntners; nd utlztn spe. In ths stud e ll present l prrn del r the r ldn prle.. Overve the stud In ths pper e present l prrn r ldn del r ultntnl rent pn. In setn l prrn del th the lln three etves s presented: nzn ttl rentl sts; nzn the nuer ntners; nd zn the utlztn spe n the ntners. The plet the prpsed del hs requred us t desn enet lrth. Ths s presented n setn. In setn tul dt the pn nput nt the del. We nlude the stud n setn. A l prrn del In ths setn e prpse l prrn del r the r-ldn prle. The lln nttns re used n ths stud: I r ssned t ntner therse I ntner s t e rented therse n ; r ; ntners n the nuer r the nuer ntners v the vlue r n V the vlue lt ntner. The rentl st s the su ed st ( ) plus vrle st ( ed st rentn ntner hh s nstnt. ). dentes the dentes the vrle st
3 hh s ssted th the eht the r llted t ntner. s dened s lls here k (k ; ) nd re dened n Fure. ( ) 6 0 st eht Fure : The vrle st ntner. Let ) ( dente the rentl st ll ntners. Thus e hve: ( ) ( ) Where ) ( s dened s: ( ) ( ) Let ) ( dente the nuer rentl ntners. Thus e hve: ( )
4 Let h ( ) dente the utlztn vlue the ntners. Thus e hve: h ( ) As result dsussns th neent nernn ther requreents prrt struture the desn s lsted s lls: Prrt : The ttl rentl ntner sts shuld e nzed. Then e hve: d d v ( ) F n hh d s nzed here the netve devtn d r the tret F s dened s: F ( ) I F ( ) > 0 d therse nd the pstve devtn d r the tret F s dened s: d ( ) F I ( ) > F therse Prrt : We shuld ssn the nu nuer ntners pssle. Thus e hve: ( ) d d 0 n hh devtn. d s nzed here d s the netve devtn nd d s the pstve Prrt : We shuld ze the utlztn rt eh ntner s. We thus hve: h d d V n hh d s zed. ( ) In rder t sts these trets l prrn del r the r-ldn prle s prpsed s lls: Len : d d d Suet t: ( ) d d F ( ) d d 0 h ( ) d d V n 0 r n; 0 r
5 Cputtns Due t the plet the del e desn enet lrth r slvn the del. Bsed n rel stutn tht the pn s n e denstrte se nterestn hrtersts the r-ldn prle.
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