Developing A Model-Based Software To Optimize Wheat Storage and Transportation System: A Real-World Application

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1 Developng A odel-baed Sofware To Opmze Whea Sorage and Tranporaon Sem: A Real-World Applcaon Reza Zanran Farahan a,b,c*, Narn Agar c, Hoen Hoabr a and Amr Ardean Jaafar a a Logc & Suppl Chan Reearche & Sude Group, Inue for Trade Sude & Reearch, Tehran, Iran b Deparmen of Indural Engneerng, Amrkabr Unver of Technolog, Tehran, Iran c Cenre for arme Sude, Naonal Unver of Sngapore, Sngapore Abrac The cae o be uded a va counr wh a vare of clmae Due o h dver n clmae and, conequenl, dfferen farmng condon n dfferen area of he counr, whea produced a dfferen me of ear all over he counr Therefore, whea producon rae no conan durng h perod all over he counr Lack of balance beween whea producon and conumpon n dfferen provnce durng dfferen perod neceae orage and ranporaon of whea In h paper, we nend o fnd he anwer o he followng queon: How much whea n each monh of ear mu be ranpored from each exporng provnce o each mporng provnce? Fr, he cae problem ncludng aumpon, obecve and conran comprehenvel decrbed Then, a xed Ineger rogrammng (I) model developed for he problem and run on a commercal opmzaon ofware Snce, he model mu be run each monh n order o ue updaed daa and runnng me of he I model no reaonable, a Genec Algorhm (GA) developed o olve he real-ze problem n an accepable me To prove he effcenc of h echnque n erm of runme and qual of he compuaon, reul are compared wh hoe of LINGO 1000 for mallzed and medum-zed e nance Keword: Agrculure; Tranporaon; Invenor; xed Ineger rogrammng; Genec Algorhm Inroducon * Correpondng auhor Fax: ; Tel: ; Emal: zanranreza@gmalcom; cmzfr@nuedug 1

2 The nvegaed cae n a va counr wh a vare of clmae Due o h dver of clmae and herefore dfferen farmng condon n dfferen regon of he counr, whea produced a dfferen me of he ear all around he counr (from earl prng ll he mddle of fall) For example, n he ouh of he counr, whea reaped a he begnnng of prng, and n he norhwe, harveed a he mddle of fall Therefore, he whea producon rae durng a ear no he ame all over he counr A he begnnng of he prng, he whea producon rae low, bu n he ummer, ncreae enormoul, and fall agan n he fall However, whea demand of each provnce conan all over he ear, and depend on he populaon of he provnce The lack of balance beween producon and conumpon of whea n dfferen provnce n dfferen monh of ear make orage and ranporaon of whea necear In ome provnce, whea producon more han he demand for ; h urplu whea carred o oher provnce or ored o be ued laer In h paper, we focu on whea ranporaon and nvenor em Th em con of fxed ene uch a warehoue, flour facore and roue Warehoue n h em are demand pon a well a uppl pon; moble ene of h em are a flee of mlar vehcle There are man reearch ude ha can ndrecl help u o realze, model and olve h problem For nance, ranporaon capac ha alo been uded for mul-age nvenor em wh deermnc and dnamc demand wh fne horzon (Bregman e al, 1990) A comprehenve leraure ummar of mlar problem ncludng he ochac cae can be found n Kleweg e al (2002) Z-Farahan and Elahpanah (2008) developed and olved a b-obecve model for u-n-me (JIT) drbuon n he conex of uppl-chan managemen The preened a comprehenve leraure n all level of drbuon n uppl chan wh her clafcaon Smlarl here are real-world cae ude n dfferen area of applcaon ha can help u ee her experence For example, De Boon (1978) ha examned flower drbuon and ranporaon em n he world fr flower exporer (he Neherland) I noable ha n h em, 200 dfferen knd of flower mu be ranpored and drbued from 3500 ource o more han

3 denaon The dal npu con of 4-8 mllon flower, whch are old n 4 hour hrough approxmael ranacon each nvolvng bunche or boxe of flower Carlon and Rönnqv (2007) ud Södra, one of he larger Swedh fore compane, whch nvolved n all age of he wood-flow The focu n parcular on Södra Cell AB, a compan whn Södra, whch reponble for pulp producon The decrbe he operaon a Södra Cell and he decon uppor ool ued for uppl chan plannng The decrbe fve maor proec or cae (ncludng a new drbuon rucure) whch focu on mprovng her uppl chan managemen and opmzaon Soua e al (2008) addre a cae ud, npred b a real agrochemcal uppl chan (n UK), wh wo man obecve, rucured n wo age In he fr age he redegn he global uppl chan nework (ncludng he producon and drbuon plan conderng a me horzon of one ear) In he econd age, a hor erm operaonal model ued o e he accurac of he derved degn and plan If we wan o fnd a relevan leraure ha cloe o our cae ud a lea from he applcaon pon of vew, we hould menon Blgen and Ozkarahan (2007) The addre a blendng and hppng problem faced b a compan ha manage a whea uppl chan (n Turke) The problem formulaed a a mxed-neger lnear programmng model The obecve funcon eek o mnmze he oal co ncludng he blendng, loadng, ranporaon and nvenor co Conran on he em nclude blendng and demand requremen, avalabl of orgnal and blended produc; a well a blendng, loadng, draf and veel capac rercon However, one of he be and much relaed reearche Ahumada and Vllalobo (2009) The revew he man conrbuon n he feld of producon and drbuon plannng for agr-food baed on agrculural crop The parcularl focu on hoe model ha have been uccefull mplemened The model are clafed accordng o relevan feaure, uch a he opmzaon approache ued, he pe of crop modeled and he cope of he plan, among man oher Through her anal of he curren ae of he reearch, he dagnoe ome of he fuure requremen for modelng he uppl chan of agr-food 3

4 In econ 2, we decrbe he cae characerc n erm of oupu, aumpon, obecve, conran and npu In econ 3, we develop a mahemacal model baed on he menoned characerc n erm of e and ndce, varable, parameer and mahemacal formulaon ncludng obecve funcon and conran In econ 4, he oluon o he model preened In econ 5 we develop a genec algorhm o olve he model and relaed compuaonal reul n econ 6 how he effcenc of he developed algorhm Implemenaon ue and concluon of he arcle preened n econ 7 and 8, repecvel roblem Defnon To have a beer underandng of he problem we llurae he au of he em n Fgure 1 Hereb we explan ome of he noaon ued and he defnon of he em Farm (F): Whea produced n farm; e farm are where he whea ener no he em Governmen Trade Corporaon (GTC): GTC, whch wan o opmze he em, he owner of he orage and ranporaon em All em co ncludng coordnaon charge, orage co and ranporaon co are pad b h organzaon GTC Warehoue (GTCW): GTCW ore he purchaed whea n fve dfferen pe of warehoue Flour Facore: Thee are he fnal conumer n he em; e here nohng lef called whea afer enerng he flour facore Flour Facore Warehoue (FW): Flour facore have ome agned warehoue where whea kep wang o change no flour Wh repec o he capac of warehoue belongng o flour facore, hee facore are dvded no hree group; mall, medum and large Snce hee warehoue are full mechanzed and capable of orng whea n good condon, and hee are he fnal denaon of whea n he em, GTC can ue he large-zed warehoue epecall durng 4

5 ummer (peak perod) and pa ren o he relaed flour facor Vllage Cooperaon Organzaon (VCO): An organzaon, whch founded o faclae purchang whea from producer Currenl, due o poor plannng mehod of he GTC and becaue of he VCO falure n managng he drbuon and orage ue (epecall n ummer when we face peak of farm producon), 70% of he oal purchang whea done b h organzaon and 40% of h whea, whch equal o 28% of oal purchaed whea, ranpored o he warehoue of VCO In Fgure 2 doed arc how hare VCO' charge pad b GTC VCO Warehoue (VCOW): Thee are ome mple warehoue whch belong o VCO Thee warehoue are no able o manan whea well enough However, becaue of he hgh volume of he produced whea, epecall durng ummer, GTCW do no have enough capac o hold all he produced whea; herefore hee mple warehoue are ued o ore he produced whea emporarl Laer, when GTCW or FW are avalable, he ored whea n VCOW ranferred o GTCW or FW; n h cae, GTC hould pa he ren o VCO Currenl, 40% of he whole whea bough b VCO fr pored o VCO warehoue and hen carred o GTCW (Fgure 2) UnUable Whea (UUW): The whea, whch ha no paed he leep perod e Newl harveed whea no ueable and mu be ored for a perod of me, named leep perod Afer pang h perod, gan he qual o be conumed; h mean ha he whea whch ha no paed he leep perod lead o low-qual bread and caue a lo of bread wae Uable Whea (UW): The whea whch ha paed he leep perod I mean ha he whea whch ha paed he leep perod ha good qual o be ued We now decrbe he curren uaon and he nece of menonng uch problem; here are dfferen pe of clmae and, herefore, dfferen condon for farmng n dfferen area of he counr Thu, for whea alo, whch uded n h paper, we have o deal wh a vare of condon, uch a dfferen harve me, qual, and leep perod (he perod n whch whea hould be ored afer beng harveed and before can change no hgh-qual flour) n dfferen par of he 5

6 counr Becaue of dfferen weaher condon n dfferen monh of he ear, here unevenne n he producon volume of crop n dfferen monh of he ear n varou par of he counr whle he conumpon rae of he crop uch a whea almo conan durng a ear Accordng o la ear ac, a conan conumpon rae could be condered a he average conumpon rae of whea per peron There are 28 provnce n he counr Each provnce ha a dfferen capac for orng whea n avalable warehoue In ome provnce, h capac le han he provnce need, and n ome oher, oo much orage capac avalable Therefore, he provnce of he counr can be dvded no hree group To mee he conan monhl demand of dfferen par of he counr and conderng avalabl of lmed and varou amoun of whea n dfferen monh and clmae we have o degn and execue a prece and comprehenve plan for whea ranporaon and orage for all provnce Snce he problem condon change ever ear, h plan hould alo be compable and flexble enough In h par, a complee defnon of he em characerc and he problem, whch wll be olved n h paper, preened n erm of an opmzaon model Oupu The oupu of he model wll be a follow: The amoun of whea ha ranpored durng each monh of he ear Orgn and denaon provnce for ranporaon of whea durng each monh of he ear Whea ranporaon and orage co for a ear Aumpon The aumpon, whch are condered n he model, are a follow: To mee he counr demand for whea, onl he whea grown n he counr (domec whea) 6

7 ued (no whea mpored); The hore me un condered n he problem monh; The producon rae of whea n farm of provnce dnamc, and change ever monh; The number, place and capac of each pe of warehoue known; The harveed whea wll change no hgh qual flour onl afer pang he leep perod; Demand of each provnce me b flour facore agned o ; The exra demand of each provnce uppled b oher provnce (he urplu whea of each provnce carred o oher provnce); All he whea ranpored beween provnce acuall ranpored beween warehoue; The capac of all vehcle ued for whea ranporaon he ame and conan (10-on ruck); The on-klomeer ranporaon co for each provnce and among he dfferen provnce aumed o follow a lnear funcon; GTC charged for he co of whea orage (n GTCW, FW and VCOW) and alo for he ranporaon co; All of he exng whea n GTCW, FW and VCOW of each provnce (n on) a he begnnng of he fr monh of a ear are of he pe UW; All farm, warehoue and flour facore (conumer) of each provnce are vewed a a pon ha locaed a he capal of each provnce; The amoun of whea produced n he farm of each provnce and conumed n each provnce durng each monh of ear, he capac of warehoue and he qual of he produced whea n each provnce are all aumed o be known and deermnc; A menoned before, onl he whea, whch ha paed he leep perod, of he qual o be ued Th leep perod dfferen from provnce o provnce (from 20 da up o wo monh) 7

8 baed on he relaed geographcal condon In h reearch, we aume h leep perod equal o one monh for all of he provnce of he counr Therefore, n monh he whea produced n h monh ha no e paed leep perod, and, herefore, no read o be ued, bu can be ued n monh 1 Obecve Funcon The obecve of h em o mnmze whea drbuon co (ncludng ranporaon co, orage co and VCO charge) Conran The conran, whch hould be condered n he model, are a follow: The conumer' demand n each provnce mu be me n ever ngle monh of ear; Whea mu be ored for an average me of one monh n order o change no hgh-qual flour (leep perod); The raegc ock level of each provnce warehoue a he begnnng of each monh hould no be le han a predeermned ock level Th ock level a coeffcen of he repecve provnce conumpon; The average qual of he new harveed whea ored n each warehoue hould no be le han a predeermned pecfc qual level; Becaue of more avalable ule n ome warehoue (o manan whea n good condon and qual), here are ome preference n orng; GTCW are he fr, FW are he econd and VCOW are he hrd pror for orng whea On he oher hand, he equence of co of mananng whea n hee warehoue do no correpond o h warehoue' preference order (FW co>gtc co>vco co) 8

9 Inpu The npu of he em whch form a ba for defnng model parameer are a follow: Whea ranporaon co beween provnce for each roue and n each monh of he ear; The capac of each provnce warehoue ncludng GTCW, FW and VCOW; The predced amoun of produced whea n each monh of he ear n each provnce; Each provnce whea ock level a he begnnng of he ear; Each provnce raegc ock level; Each provnce monhl conumpon of whea (for he ear); The dance beween he capal of provnce where he warehoue are locaed Fgure 3 depc oupu, obecve, conran and npu of he problem decrbed ahemacal odel In h par, he mahemacal model developed for he whole counr decrbed A he end of each ear, h model run for all provnce, he requred npu are calculaed ung he ame ear daa and are ued b he model Fr, all e, varable and npu of he model are defned and hen he mahemacal model n cloe form wll be preened and hen full decrbed Se and Indce The e and ndce of he mahemacal model are a follow: ={112}: e of monh of he ear (); ={128}: e of provnce (, ) Varable Fr, we defne ome erm whch are ued n he defnon of varable (Fgure 4) Baed on he defned oupu of he em, he varable of he model are a follow: 9

10 w : Amoun of UUW ranpored from provnce o provnce n monh (,,, ); w (2) : Amoun of UW ranpored from provnce o provnce n monh (,,, ); : Amoun of UUW exng n provnce n monh (, ); (2) : Amoun of UW exng n provnce n monh (, ); (3) : Amoun of UUW ored n GTCW of provnce n monh (, ); : Amoun of UW ored n GTCW of provnce n monh (, ); (5) : Amoun of UUW ored n FW of provnce n monh (, ); : Amoun of UW ored n FW of provnce n monh (, ); (7) : Amoun of UUW ored n VCOW of provnce n monh (, ); : Amoun of UW ored n VCOW of provnce n monh (, ); = = = 1 If all GTCW of provnce are full n monh 0 Oherwe; 1 If all FW of provnce are full n monh 0 Oherwe; 1 If all VCOW of provnce are full n monh 0 Oherwe; arameer Baed on he defned npu of he em, he parameer of he mahemacal model are a follow: f : Fxed co of ranporaon (for loadng and unloadng) for each vehcle; p : Varable co of ranporaon for each klomeer for each vehcle; h 4 : Sorage co of each on of whea n a GTCW for one monh; h 6 : Sorage co of each on of whea n a FW for one monh; h 8 : Sorage co of each on of whea n a VCOW for one monh; 10

11 c : Toal capac of GTCW n provnce ; c : Toal capac of FW n provnce ; c : Toal capac of VCOW n provnce ; v : Average monhl demand for whea n provnce ; q : Qual of whea grown n provnce ( a number beween 1 and 3 baed on he roen conen of he whea produced n a regon; he larger h conen, he hgher he qual); u : Amoun of whea produced n he farm of provnce n monh ; a : Charge pad o VCO for coordnang orage and ranporaon of each produced on of whea n farm; e : Capac of whea ranporer vehcle (ruck); Q : Average qual level of whea ored n he warehoue (a number beween 1 and 3); d : Dance beween provnce and provnce ; α : Coeffcen of raegc ock level; SS : Sraegc ock level for each provnce n each monh whch a coeffcen (α) of monhl whea conumpon n each provnce; β : Coeffcen of VCOW; GTC ha decded ha more han a mnmum percen of whea ored n he counr mu be n charge of VCOW Th help VCO have enough ncome o keep operang n he em; γ : Coeffcen of VCO charge; nce here are houand of farm n each provnce, GTC ha decded ha more han a mnmum percenage of whea produced n each provnce mu be coordnaed b VCO o ore or ranpor; he co of h are pad o VCO b GTC (0 β γ 1) ahemacal Formulaon Hereb, he mahemacal model of he em decrbed: 11

12 12 ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ], (2) (7) 8 (5) 6 (3) 4 / u a e d p f w w h h h z n γ = S: w w u =,,, (2) ( ) v w w = 2, - -, (2), (2) 1, (2) 1, (2) (3) ( ) ( ) ( ) Q w w u w q w q q u,,,,, =, (7) (5) (3) (5) =, (2) v SS =, (2) α (7), c c, (3) (9) c c, (7) (10), (11) c c, (5) (12) c c, (7) (13) c, (7) (14) 1,0, ) ( ) ( (2) (7) < β β (15) = = = =, 0 1 (7) 1 (5) 1 (3) 1 (16) = 0 1 (17)

13 ,, { 0,1}, (18) w, w (2), q, q (2),, (2), (3),, (5),, (7) Hereb, he mahemacal enence are decrbed:, 0, ( ), (19) Obecve funcon : Th obecve mnmze he oal co ncludng he whea orng co n GTCW, VCOW and FW a well a he whea ranporaon co beween provnce n a ear and VCO charge whch are pad for coordnaon acve of orage and ranporaon em Noe ha all avalable ac relaed o ranporaon co are n erm of ruck B addng conran (2-19), he em condon are mpoed on he mahemacal model Conran (2): The amoun of he UUW found n provnce n monh equal o he whea produced n provnce n monh added b UUW mpored o ha provnce n monh ubraced b oal UUW expored b ha provnce n monh Conran (3): The amoun of he UW found n provnce n monh equal o he amoun of UW produced n provnce n monh -1 added b UW mpored o ha provnce n monh ubraced b he um of oal UW expored b ha n monh and he average monhl demand for whea n provnce Conran : The governmen ha decded ha he average qual of UUW n each provnce and a each monh mu be more han a predeermned qual level (here, 18) Conran (5): The oal amoun of UUW n each provnce n each monh equal o he amoun of he UUW avalable n GTCW, FW and CVOW Conran : The oal amoun of UW n each provnce n each monh equal o he amoun of UW avalable n GTCW, FW and CVOW Conran (7): For raegc reaon, he whea ored n each provnce n each monh mu be greaer han or equal o a predeermned ock level; h ock a proporon of he monhl demand of ha provnce 13

14 Conran (8-10): Thee conran how he preference of GTCW rao o VCOW Conran (11-13): Thee conran how he preference of FW rao o VCOW Conran (14): To how capac conran of warehoue, we need o have ome conran a follow: (3) (5) (7) c, c, c, (20) (21) (22) Relaon (20) and (21) are afed b (9) and (12), repecvel Therefore, relaon (22) added o he model Conran (15): Th conran repreen GTC decon; GTC ha decded ha more han a mnmum percenage of ored whea n he counr mu be n he charge of VCOW Conran (16): Th conran how ha here no an UUW n GTCW and FW a he begnnng of he ear o of he produced whea (more han 80%) n he counr reaped durng he fr egh monh of he ear; herefore, all of he whea avalable from la ear ha paed he leep perod a he fr monh of curren ear and of pe UW (no UUW) Conran (17): Th conran enure ha here no whea n VCOW a he begnnng of he ear Durng he la 4 monh of he ear, no whea reaped and all he whea ored n VCOW ranferred o GTCW or FW and a he begnnng of he ear here no whea n VCOW Conran (18-19): Thee conran decrbe he pe of varable Soluon of he odel In h econ, fr we brefl explan how o calculae he model parameer Afer ha we focu on olvng he model ung he genec algorhm 14

15 The Daa Here he mehod b whch, he model parameer are calculaed decrbed Demand: Regardng annual populaon growh rae (g) and formula p 1 =p 0 (1g), he demand of he curren ear equal o he la ear demand ncreaed b 1%; Whea producon rae b he farm of he provnce: I equal o he la ear producon ncreaed b 7%; Whea qual: I calculaed regardng dfferen qual level of whea n each provnce and agnng a value o he whea produced n each provnce Th value calculaed b agrculural laboraor baed on he proen n he whea of each provnce; Sraegc ock level n each provnce: I a afe ock ha equal o a coeffcen (α) of whea conumpon n each provnce; Sock level a he begnnng of he ear: I equal o he ock a he end of he la monh of he prevou ear; Capac of he warehoue: I equal o he oal nomnal capac of all warehoue n he counr a he preen me; Dance beween warehoue: In h model, dance beween warehoue of dfferen provnce uppoed o be equal o he dance beween he capal of he provnce; Tranporaon co: I reuled b fng a lne for ranporaon co n he prevou ear and conderng nflaon rae o fnd he prce for he curren ear (Fgure 5) Tranporaon co for carrng each un of wegh for each un of dance emaed The correlaon rao of he menoned fne 087, whch wa accepable for u In Fgure 5, x dance parameer (d ), f=12874 and p=88402 whch defned before Solvng he odel 15

16 The model conan varable, 1008 of hem are bnar varable, and 5070 conran In largeze problem of he preen lnear neger programmng model, ncreang he ze of he problem n polnomal order wll reul n an exponenal ncreae n he compuaon me Th model generae a mderm plan and could be run once a ear Bu we have decded o run he model monhl; n oher word, a he end of each monh we run he model ung updaed daa of he lae monh Conequenl, n order o olve large-zed problem, a genec algorhm degned a hown n Fgure 6 Runnng h model wh he GA for he real-zed problem ake econd e 7:29:53 Th runme mee me requremen of plannng horzon In he model, he co breakdown a follow: 1127% ranporaon co, 6529% GTCW co, 1617% FW co, 714% VCOW co and 013% VCO coordnaon co Genec Algorhm The followng noaon are ued o repreen he parameer of he degned genec algorhm: pop_ze: populaon ze co: coeffcen of fr populaon; n order o ncreae he number of feable nal chromoome n fr populaon, co* pop_ze chromoome are generaed a he fr populaon cro_rae: cro-over rae muaon_rae: muaon rae for chromoome gen_mu_rae1: fr muaon rae for gene gen_mu_rae2: econd muaon rae for gene max_generaon: maxmum number of generaon o be produced Generang fr populaon A chromoome repreened a a bnar rng wh he lengh of 3*I*T, equvalen o he bnar varable of he model, a hown n fgure below 16

17 11 12 IT IT IT Wh repec o he model conran, he probabl of a randoml produced chromoome o be feable ver low Thu, ome fac, epecall he conran, hould be condered n generang he fr populaon chromoome o acheve he hghe poble chance of feabl Baed on he model, ome fac hould be drawn ou and ome aumpon hould be regarded n order o e he amoun of ome gene n each chromoome produced n he fr populaon o ncreae he number of feable chromoome b a man a poble Fr, a he capac of he VCO warehoue n each provnce almo equal o he whea produced n a ear hroughou he counr, all are equal o 0 Second, he gene relaed o had beer o be e equal o 1 wh he probabl of 08:, for whch he followng nequal afed, u c Bede, for {, } whoe are 1, he gene correpondng o are e equal o 1, wh he probabl of 09 Thee reul were acheved hrough olvng a grea number of e nance oreover, conderng he pror of warehoue, afer eng for each chromoome, he amoun of hould be equal o or le han Fnall, n generang fr populaon, n order o ncreae he number of feable chromoome, and alo o mprove he fne of fr populaon chromoome, co*pop_ze chromoome are generaed (co>1, co N) Thu, he followng procedure propoed o generae co*pop_ze chromoome of he nal populaon: 1 The e of gene whch are relaed o GTCW are denoed b GTCpace 2 chr=1 (chr he chromoome' ndex), numberone=1 (numberone he number of gene equal o 1 n each cheomoome) 3 To generae he chromoome chr, randoml chooe numberone gene from he e 17

18 GTCpace and e hem equal o 1 oreover, e he gene relaed o, for whch he followng nequal afed, equal o 1 wh he probabl of 08: Then, for {, } whoe are 1, e he mlar gene for u c Check he pror of warehoue Se he re of he gene equal o 0 4 If chr<co*pop_ze, hen go o ep 5; oherwe op he procedure equal o 1, wh he probabl of 09 5 If co* pop_ze<i*t hen e numberone= numberoneround(i*t/co*pop_ze), chr=chr1; oherwe, f co *pop_ze>i*t, e numberone=round(chr*i*t/co*pop_ze) Then go o ep 3 Chromoome Evaluaon To deermne he fne of chromoome n each generaon, a one-o-one relaonhp mu be eablhed beween he chromoome rng repreenaon, and he e of model varable or he obecve funcon value For each chromoome, deermnaon of he equvalen value of, and n he mahemacal model wll ranform he lnear neger programmng model o a lnear programmng model wh connuou varable The mnmum of z for each chromoome can hen be mpl calculaed ung ATLAB opmzaon oolbox for lnear programmng However, f he reuled problem doe no have an feable oluon, he relaed chromoome nfeable and hould be omed from he populaon Afer applng h procedure o all he nal chromoome, pop_ze chromoome wll be eleced among curren feable chromoome a paren o generae nex generaon chldren Sorng Afer evaluaon, feable chromoome are ored accordng o he value of z The more prorzed chromoome ha le value of z 18

19 Selecon of aren The paren are eleced ung he followng mehod, and are coped no he mang pool a well The proce of elecon done (pop_ze/2) me among feable chromoome for each populaon o ha he number of chromoome for each generaon reman pop_ze A each age, wo chromoome are randoml eleced n a wa ha one wh he greaer fne value have more chance o be coped no he mang pool a paren The appled mehod a follow: Devoe he neger number n ( 1) pop _ ze,( ) pop _ ze = [ ] chromoome number, repecvel (for =1pop_ze) pop _ ze( pop _ ze 1) 2 Generae 2 random neger number: rand1, rand2 1, 2 3 Selec chromoome and a paren for whch rand1[a, b ], rand2[a, b ] 2 2 a, o b Cro-over A each age, wo chromoome are randoml eleced from he mang pool A random number rand [0, 1] generaed If rand cro_rae, chldren are produced and added o he populaon n he mang pool; hence, he do no replace her paren If rand>cro_rae, no croover performed and paren reman n he pool A mulple-pon cro-over appled here If he lengh of a chromoome' rng dvded no 3*I equal par, each par wll repreen 19 or or value of a provnce n T monh wh varng from1 o T In each par of a par of eleced paren, wo cro-pon are randoml eleced and he econ beween hem exchanged Afer he cro-over done for each chromoome, a number of gene mu change o af he pror of warehoue n order o manan he feabl of he chromoome If he wo eleced cro-pon n each par are he ame, nohng wll be exchanged beween he paren Here an example o clarf he croover procedure

20 Cro-pon Chr1: Chr2: Chr1 : Chr2 : uaon Afer cro-over, each paren n he mang pool muaed wh he probabl of muaon_rae A random number rand[0,1] generaed for each chromoome If rand muaon_rae, he followng procedure wll be appled For each gene, anoher random number rand1[0,1] generaed If rand1 gen_mu_rae1, he correpondng gene muaed and f value equal o 0, wll be replaced b 1; oherwe, f value equal o 1, anoher random number rand2[0,1] generaed If rand2 gen_mu_rae2, he correpondng gene value replaced b 0 A number of gene afer dong muaon for each chromoome hould be changed o af he pror of warehoue and o manan he feabl of each chromoome For feable chromoome, he value of z recorded Fnall, all he chromoome n he mang pool are evaluaed, and wll be omed f he are proved o be nfeable Selecng he New Generaon Feable chromoome, hen, have o compee, o ha pop_ze chromoome can be eleced o ener he nex generaon If he oal number of feable chromoome n he mang pool greaer han pop_ze, he are ored ung he orng procedure menoned n econ 53and pop_ze chromoome wh hghe fne are eleced If he oal number of he feable chromoome n he mang pool equal o 20

21 pop_ze, all he chromoome wll ener he nex generaon Fnall, he followng procedure wll be appled f he oal number of he feable chromoome le han pop_ze Fr, he feable chromoome are ored, and her fne value are calculaed Then, he neare neger equal o or le han he number of feable chromoome, b whch pop_ze dvble, deermned a fch fch chromoome of he fe one are hen eleced, and pop_ze/fch cope of each ener he nex generaon Th, n oal, wll add up o pop_ze chromoome no he pool For each generaon, he fe chromoome are recorded a he end Reporng Fnall f he ermnaon condon afed, whch o repea he algorhm for max_genearon me, he fe chromoome among he one of fnal populaon deermned, and repored a he oluon of he problem Compuaonal Reul Te roblem For he mall-zed problem, he reul obaned from he genec algorhm are compared wh he reul obaned b LINGO 1000 opmzaon ofware The large-zed real-world problem, whch canno be olved b LINGO or oher commercal ofware, olved b he propoed genec algorhm The comparon beween he reul of he genec algorhm and LINGO, for mall-zed problem, how ha we can alo ru he genec algorhm for he large-zed problem Degnng Te roblem Varou e problem, wh dfferen ze, are olved o evaluae he performance of he preened algorhm The ze of he degned e problem are led n Table 1 For each problem ze, a ere of problem, whch have feable oluon, are degned wh dfferen 21

22 combnaon of he provnce Genec Algorhm arameer Fng arameer of he degned genec algorhm nclude co, max_generaon, pop_ze, cro_rae, muaon_rae, gen_mu_rae1and gen_mu_rae2 rmar e are carred ou n order o deermne he value of hee parameer In h cae, a rade-off beween oluon me, and qual of oluon deermned he approprae value for hee parameer For mall-zed problem co, pop_ze and max_generaon are e o be correpondng value n Table 2 For large-zed problem, hee hree parameer are e equal o 5, 35, and 130, repecvel In addon, he value for cro_rae, muaon_rae, gen_mu_rae1 and gen_mu_rae2 are e o be 05, 09, 01 and 02 repecvel, afer man run of he propoed GA wh dfferen e of parameer value The eleced value proved o reul n beer qual of oluon The qual of oluon faled o mprove, movng forward he eraon, n run wh lower rae e for hee four parameer Furhermore, he hgher rae for muaon_rae and gen_mu_rae1 and gen_mu_rae2 ncreaed he rk of nfeabl and ncreae n z value of he chromoome Reul The genec algorhm coded n ATLAB 750, and LINGO 1000 ofware ued o compare he reul of mall-zed problem All he e problem are olved on a enum 4 compuer wh 1024 B of RA and 226 GHz CU In order o compare he oluon of he wo mehod, he mnmum value of he obecve funcon (z) for he reulng model calculaed Therefore, he repored me for LINGO ofware wll be recorded for hee opmzaon problem The reul are ummarzed n Table 2 A qual creron, he percenage of error, defned o how he percenage of devaon of he z 22

23 value of he GA oluon from he z value of LINGO, accordng o he followng equaon: GA Z LINGO Z % error = *100 LINGO Z For each e problem, he value of h creron, calculaed The reul how ha he compuaonal me ncreae wh a re n he number of he bnar varable However, he rao of GA me o LINGO me decreae when he problem ze ncreae whch demonrae he me effcenc of he propoed algorhm compared wh LINGO Furhermore, he average of error percenage for all e problem of each problem code never exceed 54, whch how a mall value of error Implemenaon Benef of he odel Th model ha he followng benef for GTC: Toal co of h model for he curren ear 1429% le han he hand-made plan, whch had been prepared before he begnnng of h ear; a bg value whch enough for orage and ranporaon of more ha 11 mllon on of whea! The plan, whch obaned afer olvng he model, made afer abou 7 hour; h plan can be updaed a he end of each monh b ung he daa of he prevou monh a npu or parameer on he model Currenl, hee decon are made b hand-made plan baed on prevou peronal experence; a full me peron workng on generang and updang h plan In curren uaon, conran of qual, raegc ock level and pror of GTCW, FW and VCOW are no afed bu n our model, he are Havng more whea n VCOW and no afng qual conran, we wll fnall ge low-qual bread n ome of he provnce and h mean more wae In he prevou ear, he amoun of mpored whea o he counr wa equal o he value of waed bread! 23

24 Senbl Anal Hereb we repreen he reul of he enbl anal done Th anal wll be a ba for uggeon o mprove he em and propoe ome fuure work Dong he anal ook man da; e more han one da ha been pen o appl ever change n he mode and runnng GTC he owner of he em, o we can nvegae he effec of ncreang he capac of GTCW In Fgure 7, h anal depced We ee ha ncreang 10% n GTCW oal capac decreae oal co of he em n comparon wh he curren uaon Of coure, h anal no well enough o make uch decon becaue we have no calculaed warehoue conrucon co; however conducng a feabl ud on uch ncreae n capac ma be worhwhle Fgure 8 how an anal on he mnmum qual level of new harveed whea n each provnce In he bac model, he mnmum qual level wa e on 18 Fgure 8 how ha for low qual level ( 14), he qual conran redundan and we alread have he mnmum co For hgh qual level ( 2) no feable oluon wa found Qual conran ver mporan n decreang he amoun of bread waed n he counr and 19 mnmum qual level ma be a beer oluon However, ung addve o ncreae he qual of whea (nead of bearng orage and ranporaon co) worh nvegang Bede mporng hgh-qual whea o he counr and exporng low qual whea o poor counre ma be a worhwhle fuure work For ever counr, whea condered raegc and, herefore, havng ome afe ock of whea mporan In h problem, we e coeffcen of raegc ock level on α=1 Fgure 9 how changng of h coeffcen agan oal co of he em For α 3 no feable oluon wa found A we ee n he Fgure, changng oal co from α equal 1 up o α equal 3 caue oal co o ncreae from 291E10 o 333E10 un; h change n he em no gnfcan from he owner pon of vew Therefore, he oupu plan baed on α=3 24

25 Fuure Work Whle udng dfferen cenaro and uaon, he followng ue eemed approprae for laer reearche concernng relave problem: Feabl ud of ncreang orage capac of GTCW and fndng he relave co In addon, ome nvegaon hould be conduced no he locaon of new warehoue n he provnce; Feabl ud of addng addve o whea o mprove average qual level and fndng relevan co; Sudng he pobl and nfluence of mporng hgh qual whea and exporng poor qual whea o mprove average qual level of whea and fndng relave co of ; Carrng ou facl locang, ranporaon plannng, nvenor plannng and conrol proec mulaneoul o opmze he em Concluon In h paper, whea orage and ranporaon em n he counr defned and formulaed b an I model Ung he propoed genec algorhm, h model ha been olved Some env anal ha been performed and he reul have been uded; ome relaed fuure reearch opc have been uggeed a well However, conderng h problem a a naonal one and beng aware of economc de-effec for he counr, uch a he remarkable co of garbage bread a a reul of poor qual, ll effcen and ueful Acknowledgmen We would lke o hank Nam Akbarzadeh and Nabeh Zanran Farahan for her nvaluable 25

26 commen on h work and We expre our graude for her mndful uggeon Reference Ahumada, O, Vllalobo, JR 2009 Applcaon of plannng model n he agr-food uppl chan: A revew European Journal of Operaonal Reearch 196: 1-20 Blgen, B, Ozkarahan I 2007 A mxed-neger lnear programmng model for bulk gran blendng and hppng Inernaonal Journal of roducon Economc 107: Bregman, RL, Rzman, L, Kraewk, LJ 1990 A heurc for he conrol of nvenor n a mul-echelon envronmen wh ranporaon co and capac lmaon Journal of he Operaonal Reearch Soce 41: Carlon, D, Rönnqv, 2007 Backhaulng n fore ranporaon model, mehod and praccal uage Canadan Journal of Fore Reearch 37: De Boon, H 1978 A flower ranporaon-drbuon em Journal of Operaonal Reearch Soce 29: Kleweg, AJ, Nor, VS, Savelbergh, W 2002 The ochac nvenor roung problem wh drec delvere Tranporaon Scence 36: Soua, R, Shah, N, apageorgou, LG 2008 Suppl chan degn and mullevel plannng-an ndural cae Compuer and Chemcal Engneerng 32(11): Z-Farahan, R, Elahpanah, 2008 A genec algorhm o opmze he oal co and ervce level for u-n-me drbuon n a uppl chan Inernaonal Journal of roducon Economc 111(2):

27 Governmen Trade Organzaon Warehoue Vercal lo Auomaed horzonal lo 30% Flour Facore Smple horzonal lo Vllage Cooperaon Organzaon Warehoue 28% Farm 42% Ground warehoue Flour facore warehoue Fgure 1 Sau of whea orage and ranporaon em 27

28 VCO u coordnae he hpmen The whea wll be fr ored n VCOW; afer a whle wll be en o he oher hgh qual warehoue 60% 40% Farmer drecl hp her whea o GTCW Farmer end her whea va VCO 30% 70% Farm Fgure 2 Curren proporon of whea orage and ranporaon em Each provnce ock level a he begnnng of he ear The amoun of whea purchaed n each monh of he ear b each provnce Warehoue prore Sraegc ock level Sleep perod Qual Each provnce monhl conumpon of whea The capac of each provnce warehoue Inpu Opmzaon model Oupu Tranporaon and Sorage lan Qual level of each provnce whea Tranporaon and orage co nmzng whea ranporaon and orng co Fgure 3 Semac approach o he orage-ranporaon model 28

29 -1 w rovnce (denaon) F UUW (3) GTCW (7) VCOW (5) FW UW (2) w (2) UW (2) (3) (7) (5) FW UUW F rovnce (orgn) -1 Fgure 4 Uable and unuable whea orage and ranporaon em Fgure 5 Tranporaon co char for a 10-on ruck 29

30 Sar Inpu Generae fr populaon Evaluae chromoome Generaon=1 No Generaon<max _generaon Ye Oupu Selec he paren Cro-over uaon Evaluae chromoome Generaon=generaon1 Sop Selec he new generaon Fgure 6 ropoed Genec Algorhm Fg7 Toal co agan he percenage of ncreae n GTCW oal capac 30

31 Fg 8 Toal co agan mnmum qual level of newl harveed whea Fg 9 Toal co agan coeffcen of raegc ock level 31

32 Table 1 Te roblem Sze Small ze Large ze roblem code No of provnce No of monh No of fr provnce No of la provnce

33 Table 2 Summar of Te Reul % error Te problem roblem code No of oluon co pop_ze max_generaon beween GA & LINGO ax n Average LINGO run me () Average GA run me ()

34 >