Hierarchical Production Planning in Make to Order System Based on Work Load Control Method

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1 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, 205 DOI: 0.389/ujbm hp:// Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod Ehsan Faah,*, Maha Khodadad 2 Mazandaan Unvesy of Scence and Technology, Ian 2 Islamc Azad Unvesy, Fouzkoh Banch, Ian *Coespondng Auho: ehsan_f60@yahoo.com Copygh 205 Hozon Reseach Publshng All ghs eseved. Absac Subjec o compeon makes, connues change n expecaons, cusome equson and decease of accessble poducon esouce, he poducon sysem of make o ode s he appopae selecon fo esponse o oday s makes specfcaons and n ode o povde he lage specum of cusome s odes. In hs eseach expend he conol and plannng poducon sysem (wok load conol) n make o ode poducon sysem o manage he delvey me. Fo hs, we ecommend he heachcal poducon plannng sucue. The majo age s managng he acvy n make o ode sysem n ode o acheve he sho eleased me and enance odes compeon fee. To acheve hs age we pesen he appopae decson models wh aenon o escon of poducon sysem. Fnally due o consequen below: Pesen he expended elease model o plan he poducon lne and decease he delvey me; Pesen he odes mng mehod n vaous saons. Ths mehod do subjec o exsences of pevous level. Synchonsc pefomed he wo mehods sae bee pefomance n compae o ohes eseaches. Keywods Make o Ode Sysem (MTO), Make o Sock Sysem (MTS), Wok Load Conol (WLC), Heachcal Poducon Plannng (HPP). Inoducon Poducon Managemen Sysems (PMS) nvolves he need fo a sysemac look a he poducon. In absence of such a holsc look, poducon wll be doomed o falue. Managemen of poducon, whch s n a hghe level han he poducon plannng, s a way o mplemen a poducon schedule by managng all s componens. In he above expesson, he wod Managemen s based on he fac ha poducon plannng s no nsumenal alone, unless each componen of he poducon schedule s managed and aves a a esul. Fnally, he wod Poducon s based on he expeence ha aenon o poducon as an effecve compeve weapon can ancpae fms elave o compeos []. Wh hs backdop, we can say ha PMS seeks wh a holsc pespecve and a pope plannng o denfy all effecve elemens and complexes of he poducon pocess o delve a poduc on he make ha nceases cusome sasfacon. Today, manufacung facoes, consdeng he ole of poducon n he compeve make sysem, fnd hemselves n an envonmen oally changed. An example of hs change can be obseved n dffeen nduses of consume goods and capal goods such as auomove, eleconcs, and applances. A manage who s facng hese apd changes wll have o adop new appoaches o addess hs compeve envonmen. Old saegy of negaed poducon plannng has los cedbly and gven self up o he flexbly of new appoaches. New appoaches n poducon managemen have educed he me equed o desgnng and makeng poducs and he me beween odes and he delvey o cusomes. Key feaues of new poducon envonmens nclude [2]: a. Incease of poduc vaey b. Sevee educon of he poduc lfe cycle c. Change of socal expecaons d. Change of paens of coss Consdeng hese chaacescs and o negae hemselves wh new condons, manufacung fms mus plan and manage dffeen levels of he schedules so ha hey ge he flexbly o confon unpedcable make changes. In hs pape, we used he em Cusom Ode Decouplng Pon (CODP) o expess he dffeence beween vaous poducon envonmens. CODP s a pon whee all he followng poducon pocesses ae assgned o mee cusome demands. In ohe wods, all poducon pocesses po o hs pon ae he basc waehouse, and he subsequen pocesses ae he basc ode. Ths s also called Invenoy/ode neface pon (I/O). The moe hs pon s close o he end of poducon lne, he delvey me wll be educed and he ably o mee cusome demands and he sock of aw maeals and sem-fnshed poducs n woksaons befoe hs pon wll be nceased. Howeve,

2 2 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod he moe s close o he begnnng of poducon lne, he sock of aw maeals and sem-fnshed poducs s educed and he poduc delvey me wll be nceased. So fa, seveal models of heachcal poducon plannng (HPP) n dffeen manufacung envonmens o mpove he pefomance of manufacung managemen wee poposed. Kngsman e al. [3,4] have poposed a sucue o manage odes whch mus be eceved by he make-o-ode (MTO) sysem. In hs case, some of he ncomng odes ae accepance, and some of hem ae ejeced. Ths sage n he MTO leaue s called he ode eny sage o cusome nquy sage. In hs model, eny pocess s dvded n wo phases: he clen applcaon and he ode eny sysem. Cakavasa e al. [5] was assumng ha he ode has been acceped by he cusome, pce and delvey me should be deemned hough alkng beween he cusome and supples. Caloso e al. [6,7] povded he decson makng sucue fo negoaon beween cusomes and supples n he supply chan. In hese acles, hee coec numbe lnea models have been poposed o selec he supples and odes whch have hghes pofs fo he company. Behoup e al. [8] deemned he sensvy of he HPP sucue o paamees such as wokload hgh lms and me hozon and denfed ccal paamees. Then, a new mehod fo calculang hese paamees wee pesened o mpove he oupu of he HPP sucue. Rabban e al. [9,20] poposed he HPP sucue fo combned MTS/MTO envonmens. As a novely of hs eseach n compason o he leaue evew, he HPP sucue was poposed n fou levels. poducon and aw maeals s no a sngle acvy ha can be managed by he negaed appoach. By cons, depends on a sees of decsons abou vaous opcs n he poducon sysem. These decsons ae aken geneally n dffeen levels of managemen accodng o he heachy of poducon acves, so ha any complance wh hs heachcal sucue of decson-makng wll ghen he hozon of decsons bu wll ncease he deals of he daa needed o make decson. To bee manage vaous acves of poducon, a close elaonshp beween he decsons aken a successve levels s necessay. Heachcal Poducon Plannng (HPP) s an effecve mehod o pefom hs mullevel pocess of heachcal decson-makng. In hs heachcal appoach, he man poblem of decson-makng s decoupled no sub-poblems a dffeen levels of decson-makng; hen hese sub-poblems ae solved n a gven sequence accodng o he dffeen levels of heachcal sucue. Also, o manan he negy of he man poblem and he neconnecon of hese sub-poblems, he esponse a each level of he heachcal sucue wll be consdeed as a lmaon n he decson-makng model a a lowe level [4]. In geneal, a boom-op feedback mechansm s used n a HPP sucue o mpove decsons made a hghe levels [5]. 2. Make o Ode (MTO) Sysem In hese envonmens, CODP pecedes he poducon pocess of sem-fnshed poducs. Composes ae desgned and manufacued accodng o cusome demand. Poduc selecon n MTO poducon envonmens s made by cusomes. The mplemenaon of an envonmen whch engages n poducon only afe he cusome odes ae eceved whee all woksaons poduce only he aw maeals equed fo he compleon of cusome odes, and whee he sock of aw maeals n all woksaons ae vey low even zeo, a coodnaon s val beween dffeen levels of he facoy, educed me of supply, hgh flexbly of he poducon lne, and use of complcaed and expensve equpmen. The plannng of such poducon sysems s a dffcul and complcaed ask [3]. 3. Heachcal Appoach of Poducon Plannng n Poducon Managemen Sysem Gven he majo defecs of he negaed appoach, hs pespecve wll no be a good soluon o manage poducon n oday's oganzaons. In geneal, plannng and conol of Fgue. Heachcal Sucue of Decson-Makng n Poducon Managemen 4. Sucue of he Poposed Sysem of Plannng and Poducon Conol (WLC) n MTO Poducon Envonmens Wok load conol (WLC) s an mpoved appoach used o have a successful sysem of plannng and poducon conol n MTO poducon envonmens wh espec o he heachcal appoach. In ohe wods, we popose n hs pape a heachcal sucue of WLC n ode o bee conol he acves ha affec he delvey me of cusome odes. The poposed sucue fo heachcal poducon plannng (WLC) n MTO poducon envonmens povdes

3 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, fou dffeen levels of plannng. 4.. Fs Level - (Cusome Enquy Sage) In hs sage, gven he demands of he cusome, we check f MTO fm s able o mee he demands of a cusome gven he lmaons of he sysem, new odes, and degee of sgnfcaon of he cusome. The oupu of hs level of WLC s o accep o ejec odes Second Level - (Ode Eny Sage) In hs sage, f he cusome s odes ae no ejeced a he fs level, hee fnal decsons wll be made: a. Deemne he pce and delvey me of new odes (delvey s deemned only f s negoable). b. Plan he ably o accep new odes. c. Choose a goup of conacos who ae able o povde necessay aw maeals fo new odes n a mely manne and a easonable pce Thd Level (Release of Odes no he Shop Floo) Ths sage ncludes only acceped odes fo whch aw maeals ae avalable (oupu of he second level). In hs sage, gven he delvey me of odes and also he densy of he wok n dffeen woksaons, delvey of new odes n he sysem wll be pemed Fouh Level (Pozng Odes n Woksaons) In hs sage, odes awang delvey n woksaons ae gven poy so ha he delvey me s mnmzed. Fo a bee communcaon and mpoved effcency of he poducon sysem, feedbacks ae aken no accoun fom lowe o hghe levels. 5. Dsngushng Feaues of he Reseach The dsncve feaues of hs eseach compaed o ohe eseaches caed ou n hs aea ae as follows: a. Consde he sgnfcance level of cusomes o decde whehe o accep o ejec new odes by appopae analycal ools. b. Inoduce a new sucue of decson-makng o accep o ejec odes a he fs level and deemne he delvey me and he pce of ncomng odes a he second level, by an nege mahemacal model. c. Consde all componens of he supply chan n he delvey and pce conol ncludng cusome MTO fm and conacos o ejec o accep odes eceved a he MTO sysem. d. Offe alenaves o deemne he delvey me of eny odes and heeafe, dffeen pces fo hese odes, and faclae he negoaon pocess beween cusome and MTO sysem ae he mos dffcul sages of decson-makng o ejec o accep odes. e. Selec conacos o pefom woks elaed o new odes eceved n he sysem a a gven pce and delvey me by an nege mahemacal model of plannng. f. Exend he pocess of ode elease no he shop floo o access he shoe delvey me and mpove he effcency of poducon lne by educng he densy of woks accodng o WLC pespecve. 6. Delvey Tme Componens n MTO Sysems Delvey me componens n MTO poducon envonmens nclude he followng: a. Negoaon Tme (NT): The me beween he aval of an ode (cusome eques) and he decson on s accepance o ejecon. b. Raw Maeal Lead Tme (MLT): The me beween pung n an ode fo aw maeals needed and he me of s accepance. c. Poduc Delvey Dae (PDT): The me of eny of aw maeals no he sysem, namely, when odes ae eady o be eleased. These knds of odes ae placed a he waehouse specfed fo odes o be eleased. The wang peod beween he eny of aw maeals and he me of he delvey no he poducon sysem s efeed o as wang peod n he waehouse of odes o be eleased. d. Ode compleon dae n he shop floo (SFTT): The me beween he elease of odes no he poducon sysem and delvey of cusome odes. Toal Tme Manufacung (TMT) ncludes SFTT and PDT. Fnally, he Due Dae (DD) whch ncludes he oal TMT, MLT and NT. Equaon (-3) shows how o calculae he TMT and DD. TMT = SFTT + PDT DD = NT + MLT + PDT + SFTT... = NT + MLT + TMT 7. Vaables Examned n hs Sudy 7.. Dependen Vaables a. Coss of a poducon sysem nclude he coss of poducon vaables n nomal me, oveme, sub-conacng, and he coss of posponed odes whee delvey delay s pemssble. b. Dffeen coss of manufacung an ode n addon o puchase coss of aw maeals and wokload of conacos, and also he penaly payable fo delvey eale o lae han desable by conacos.

4 4 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod 7.2. Independen Vaables a. Toal capacy of woksaon ncludng nomal me, oveme and sub-conacng assgned o ode n peod. b. A cean capacy of woksaon assgned o ode dung oveme. c. Degee of delay n delvey of ode n due dae. d. Ode compleon Dae. e. A cean capacy of woksaon dung oveme s assgned o ode. 8. Fs Level of he Poposed WLC Appoach: Cusome Inquy Sage A hs level of he poposed sucue, we wll dscuss he queson of accepng o ejecng new odes. Ths decson s based on hee man cea ncludng oal capacy avalable dung plannng, cusome sgnfcance level fo he oganzaon, and ode chaacescs such as he wokload equed on he poducon lne. Ths model s dvded no wo levels dependng on ode delvey me. The fs level consss of wo seps: In he fs sep, ncomng odes ae gouped accodng o he numbe of cusomes who made an ode. In he second sep, he ably of poducon sysem and all odes ae geneally compaed o see whehe new odes can be compleed whn he plannng hozon. If he cuen capacy can mee new odes, he odes ene no he second level; ohewse, ohe decsons ae made. The seps menoned n he fs level ae he same fo boh ypes of odes wh negoable and fxed delvey me. 8.. Fs Sep - Goupng Incomng Odes Accodng o Cusome Sgnfcance fo he Oganzaon Goup - The oganzaon complees cusome odes n he bes condon. - Fxed and long elaonshp wh he oganzaon. Goup 2 - The compeon beween dffeen manufacung oganzaons o boos cusome sasfacon. - Impovng he funconng of he oganzaon leads o nceased sales. Goup 3 - Casual odes - Weak elaonshp and lowe ably o delve odes a due dae. Goup 4 - Iegula and small amouns of puchases 8.2. Second Sep - Capacy Esmaed Calculaon In hs sep, each me a new ode comes n, he suffcency of cuen capacy s consdeed whn he plannng hozon a he fs level. To hs end, esmaed calculaon s pefomed as follows:. If an ode s hghly sgnfcan, he followng elaon s used o esmae he capacy heeof: : Ode ndex O ( TWK, = p ) C (,..., T ) now : Woksaon ndex O : All odes needed n woksaon : Plannng peod ndex now: Tme now T: Lengh of plannng hozon a he fs level C :Maxmum capacy of woksaon n peod ncludng nomal me, oveme, and sub-conacng. TWK j : Wokload equed by he ode n woksaon j. P : Possbly o accep ode pu n by a cusome. Dung he eny of a new ode, hee knds of ode exs n he oupu sysem: odes appoved by he cusome and all of whch ae eleased n he poducon sysem (RO); odes appoved by he cusome whch ae no ye eleased n he poducon sysem and ae planned o be backlogged (PO). The hd knd of ode s conngen ode (CO) n whch delvey me and pce ae deemned by he poducon sysem, whose appoval o cancellaon s no ye decded by he cusome. The new ode s of he hd knd. Conngen odes may be fnally canceled by he cusome. P-value fo odes appoved by he cusome (RO and PO) s. Fo ohe odes (CO) whch ae no ye canceled o acceped by he cusome, hs value wll be 0 o usng pevous daa and expeences of makeng and sales un. If fo he new ode, whch s hghly sgnfcan, hee s no suffcen capacy n some woksaons, he followng alenaves ae suggesed fo decson makng abou he ode: a. Incease he capacy of poducon sysem o pepae a new ode: due o he sgnfcance of he new ode n wokplaces whee hee s no suffcen capacy whn he plannng hozon T, basc decsons ae aken by managemen o ncease he capacy. b. Delay cean odes n he sysem ha ae of medum sgnfcance: n hs alenave, we examne whehe he delay n pepaaon of some odes of medum sgnfcance gves us he possbly o complee hem a he plannng peod. c. Cancel odes ha ae unmpoan (o of low sgnfcance) and ae no ye appoved by he cusome (conngen odes). Ths way we wll have he capacy o complee he new ode. d. Rejec he new ode: he new ode can be ejeced f s compleon eques consdeable addonal capacy whch s unavalable. 2. If an ode s of small o medum sgnfcance, he followng equaon s used o calculae he esmaed capacy: ;

5 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, O ( TWK, = (,..., T ) now p ) C ( α ); α s a pecenage of oal C capacy ha s consdeed fo hghly sgnfcan odes n fuue. Ths value s deemned by he managemen of oganzaon accodng o fuue odes foecased by sales and makeng un. If he above equaon s no esablshed, decson makng on hs ode wll nclude he followng cases: a. Delay new odes of medum sgnfcance: Ths alenave can be used only when he delay of an ode allows s fabcaon whn he plannng peod T. b. Rejecng a new ode of low o medum sgnfcance: In case he compleon of a new ode eques consdeable addonal capacy whch s unavalable, hs ode may be ejeced. c. Delay some PO and RO wh medum sgnfcance: A manage s dsceon, some PO and RO wh medum sgnfcance can be posponed o ceae suffcen capacy fo new odes. 9. Second Level of he Poposed WLC Appoach Ode Eny Sage The second level of he poposed sucue ncludes deemnng he delvey (f unspecfed) and pce of odes aved n he poducon sysem accodng o vaous lmaons and nsde and ousde of oganzaon. Two man cea fo decdng he accepance o ejecon of new odes s he pce and delvey me. These wo cea ae hghly nedependen. If he delvey me s sho and compac, n addon o nomal poducon me, poducon sysem shall adop ohe polces, ncludng oveme, delayng ohe odes n he sysem, employmen of new saff and sub-conacng o complee he ode. All hese polces mpose coss on he fm and affec he cos pce of new odes. The second level consss of fou seps. If he ode s no ejeced a he fs level and f he delvey of he new ode s fxed, we use backwad mehod n he fs sep of he second level o calculae he laes o eales elease me nsde he poducon sysem. These mes wll be compaed o he aveage delvey me and he wokload equed by conacos o make appopae decsons. In case delvey me s negoable, hee wll be suable alenaves o ceae dffeen delvey mes. If an ode s acceped n he fs sage, we use a mahemacal plannng model n he second sage ha we call IP o calculae he pce and delvey me. As fo odes wh sable delvey me, cos pce wll be announced o he cusome, and fo odes wh negoable delvey me, he delvey me wll be made known o he cusome n addon o he pce. In he hd sage, he cusome compaes hese daa wh hose fom ohe MTO fms and akes no accoun s own cea o deemne he ejecon o accepance of he ode. In he fouh sage, a good goup of conacos wll be seleced by a mahemacal model of plannng (IP2) o pefom he wokload equed fo he delvey of acceped odes. Snce he mplemenaon of he second and fouh sages s me consumng because of he use of nege mahemacal models, hese sages ae compleed accodng o he followng condons: a. A sgnfcan ode enes he sysem. b. When he numbe of new odes aved n he sysem exceeds a cean lm. c. When he dffeence beween he me he fs ode comes n exceeds a cean lm afe compleon of he second sage. 9.. Decdng on Rejecon o Accepance of Odes wh a Sable Delvey Tme If a new ode has a sable delvey me, he saus of he new ode wll be deemned n fou sages: a. Ceae dffeen alenaves o calculae he pce of he new ode b. Resolve he nege lnea model (IP) o deemne he pce of he new ode c. Decde o accep o ejec he ode by he cusome d. Selec conacos o povde aw maeals and equed wokload o complee he new ode Ceang Dffeen Alenaves o Calculae he Pce of he New Ode Afe consdeng he esmaed capacy o deemne f an ode can be compleed whn he plannng hozon of he fs level, we engage n fs sage of he second level. To un he nege plannng model (IP) and deemne he pce of he new ode, s necessay o specfy he npu paamees of he poblem ncludng Ode Compleon Dae () a each woksaon, Eales Release Dae (ERD) and Laes Release Dae (LRD). If he ode s sen no he sysem afe LRD, wll no be possble o complee he delvey a due dae. Snce delvey me s no known, he backwad mehod s used o calculae he and ERD. In pevous eseach, he followng fomula was used by Kngsman e al [5]. o calculae and ERD:, µ ( n, ), µ ( n, ), µ ( n, ), µ ( n, ), µ (, ), µ (, + ), µ (, + ) p, µ (,), µ (,) p = dd = TWK W = TWK W LRD = TWK W ERD = LRD pool delay p

6 6 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod n : Numbe of woksaons on he opeaonal oue of ode µ(,) :Woksaon on he opeaonal oue of ode W p dd : Delvey me of ode C : Ode compleon dae n esouce Pool delay: Toal wokload of all PO odes : ng d n each woksaon fo one wok of poy p. p ncludes boh nomal and hgh poes. Fo odes of medum and low sgnfcance, nomal poy s aken no accoun, bu fo odes of hgh sgnfcance, n addon o he nomal poy, f delvey of he ode s no possble a dd, we can complee he ode by educng he (hgh poy) wang peod. Due o he capacy lmaon of he empoal waehouse of woksaons, a pecenage of odes of hgh sgnfcance can be gven hgh poy. Wp can be calculaed by he followng equaon : R T ( Wp = = O R TWK In he above equaon, R' s he aveage numbe of woksaons o complee an ode. Ode compleon dae n a woksaon s deemned by educng he wang peod (Wp) and wokload equed by he ode (TWK) fom ode compleon dae n he nex woksaon. Ths fomula can deemne elavely accuae daes fo ERD and only when hee s suffcen capacy n each woksaon. In addon o he above equaon, he followng s pesened fo he fs me gven he capacy of ndvdual woksaons:, µ (, n ), µ (, n ), µ (, n ), µ (, ), µ (, ), µ (,), µ (,) LRD = ST = ST = ST ST = ST ST = ST ST ERD = LRD, µ (,), µ (, n ), µ (, ), µ (,), µ (, 2), µ (, n ), µ (, n ), µ (, + ) + TWK + TWK + TWK pool delay, µ (, n ) + TWK, µ (, ), µ (,) P + B ; P + B ; ) P + B, µ (, n ) = dd P + B n ( n ) ST : Is he eales me when woksaon has he ; suffcen capacy o complee he ode. Ths me, n he example of he pevous page, s he hd day of he nnh week. Ode compleon dae n he pevous woksaon s less han o equal o ha dae, whch s wen as an unequal n fon of each equaon. B : Is he wang peod a woksaon befoe he necessay opeaon s accomplshed n hs saon on he new ode. Queung a each woksaon s sepaaed no wo pas: a. Queue of ode wh nomal poy: In hs saus, he new ode s placed a he end of he queue n each woksaon. b. Queue of ode wh hgh poy: Ths queue consss of wo pas: One s fo odes of medum and low sgnfcance, and he ohe fo odes of hgh sgnfcance. The fs pa pecedes he second. The sage whee a hgh poy s gven o new odes s descbed below. Because of capacy poblems, calculaed values of and ERD wll be moe accuae and he possbly of a elable delvey me wll be nceased. In addon o capacy, he calculaon me necessay fo he odes accodng o he possbly of he accepaon (P) s a fuhe advanage of he poposed fomula. Po o he mplemenaon of IP model (second sage), s necessay o compae he Raw Maeal Aval Dae (MAD) by conacos and LRD and ERD values o ensue ha s possble, consdeng he MAD, o complee he new ode a due dae. A fs and second level of he poposed WLC appoach n MTO sysems, medum em plannng sysem s made and we do no need moe accuae daa. We only calculae an aveage value of MAD accodng o he pefomance of conacos n he pas. Whee aw maeals ave on me no MTO sysem, hee s no need o poze o make ohe addonal woks ncludng oveme and sub-conacng, and he ode wll be placed a he end of he queue of odes o be eleased. Ohewse, f aw maeals do no ave o he fm a due dae, he followng soluons ae poposed fo bee decson-makng and managemen of new odes. To hs end, now, LRD, ERD and MAD values wll be compaed. The followng saus wll occu when compang hese values: A- LRD < now : In hs case, s no possble o complee he ode a due dae, and s bee o ejec he ode. B- ERD < now <LRD : Unde such condons, s no possble o complee he ode n a nomal saus. The ode (MAD-ERD) wll be compleed wh delay (assumng ha hs ode s a he end of he queue of odes o be eleased). Hee ae he alenaves poposed o delve he ode a due dae: ) Inceasng he poy n he queue of odes o be eleased: As ndcaed n he above equaons, new odes ae queued n ode of aval a he end of he queue; n ohe wods, hese odes wll be gven a nomal poy. Reducng he wang peod fo backlogged odes s one of he mehods o access a

7 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, shoe delvey me. Ths educon wll allow hs elaon ERD = MAD o be esablshed. Ths educon also nceases he poy of odes wang o be eleased. In ohe wods, n hs alenave, he ode s gven a hghe poy a leas o he pon of MAD - ERD. The new value s equal o Pool Delay: Pooldelay = LRD MAD 2) Change n values: Change of n dffeen woksaons s anohe way o educe delvey me. Ths change can be pefomed by hee ways: a. Changes n he values of fo a new ode by nceasng he capacy of woksaons: In hs saus, all woksaons ha ae necessay o accommodae he new ode ae consdeed and, n case of nceased capacy, new values wll be calculaed. The change n values should be calculaed as he new ERD s equal o MAD. Ths alenave does no change he fo ohe odes n he sysem. b. Changes n he values of fo a new ode hough changng he fo ohe odes: Odes whee ERD s geae han MAD, s lkely o change he values of, whou he delvey me s aleed. By changng he values fo ohe odes, capacy fo he new ode wll be nceased; wh hs new capacy, values of he new ode wll be educed and, subsequenly, ERD wll also be educed. Raw maeals equed fo odes whee ERD s geae han MAD wll be eneed no he sysem befoe due dae and, heefoe, we need o keep he aw maeals n he elevan waehouse. Ths alenave wll educe he wang peod fo aw maeals needed by such odes and, heefoe, he cos of aw maeals waehoused wll be educed, whch s one of he goals of MTO sysems. c. Changes n values usng he capacy assgned o ohe odes: by assgnng he capacy fo odes n he poducon sysem, s possble o acheve a new ode whee ERD value s less han ha of MAD, heeafe, educe he values of n ndvdual woksaons and acceleae he delvey. Ths alenave changes he values whee addonal capacy fo he new ode s ceaed. Usng he capacy assgned fo hese odes wll delay he delvey. Ths addonal capacy wll be calculaed so ha he new ERD s a leas equal o MAD. Ths alenave s used fo new odes of hgh sgnfcance. 3) Hgh poy n he queue beween dffeen souces of poducon: Gvng hgh poy o a new ode, wll be possble o educe he wang peod and hus delvey me. Hgh poy fo odes of low sgnfcance nclude placng he new ode a he end of he queue of he fs pa, and fo odes of hgh sgnfcance nclude placng he new ode a he end of he queue of he second pa. Reducng wang peod n dffeen woksaons shall be such ha he elaon ERD = MAD s esablshed. 4) Laeness: If possble, odes can be compleed behnd schedule. Ths alenave s only possble fo odes of less sgnfcance. 5) If s no possble o use such alenave and f hee s no ohe suable soluon fo he delvey of he new ode a due dae, he ode wll be ejeced a he dsceon of managemen. I s also possble o use a combnaon of hese alenaves o complee he ode a due dae. C- now <MAD <ERD : Raw maeals ae delveed on me and he ode s placed a he end of he queue fo odes wang o be eleased. D- ERD <MAD <LRD : Ths saus esembles he saus (B). E- MAD > LRD : In hs saus, MAD s lae han LRD. Hee, s dffcul o pepae he ode on schedule and s hghly possble ha he ode s posponed. All such alenaves of he second pa ae also avalable n hs saus, wh he dffeence ha he level of educon of delvey me wll be so ha MAD and LRD values ae equal Resolvng he Inege Lnea Model (IP) o Deemne he Pce of he New Ode A he fs level of heachcal poducon plannng model, nege lnea model s used o calculae he pce of ncomng odes whee he delvey me s specfed. If he ode s no ejeced by he MTO sysem n he second sage, n hs sage, an nege lnea model s used o calculae vaous coss mposed on he sysem because of he new ode. Fnal pce of he ode s calculaed by oalng coss. As n he pevous sage vaous and ERD values wee calculaed by dffeen alenaves, heefoe, IP model was appled n exchange fo each se of values ( and ERD). In addon, he lowes pce of he ode wll be announced o he cusome. The opmal value ( and ERD) s chosen fo each opmal esponse a IP model. Indexes, paamees and vaables of he decson aken by he IP model ae lsed: Indexes: : Ode ndex ( =,..., n ) : Woksaon ndex ( =,..., R) : Tme ndex ( =,..., T ) Inpu paamees: c : Manufacung cos of ode n woksaon n nomal me and peod co : Manufacung cos of ode n woksaon dung oveme n peod

8 8 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod cs : Manufacung cos of ode n woksaon by conaco n peod c : Cos of delayng he ode pe un of me wp : Toal wokload fo odes behnd he schedule w : Toal wokload of ode n woksaon wh a ST me n peod (comng no he sysem) ow : Toal wokload of ode n woksaon wh an n peod (comng ou of he sysem) CR : Maxmum capacy avalable n woksaon n nomal me and peod α : A pecenage of CR oal capacy s aken no accoun fo odes of hgh sgnfcance. CO : Maxmum capacy avalable n woksaon n peod dung oveme CS : Maxmum capacy avalable n woksaon n peod by conacos of he fm OS(): All odes ha ae compleed on me. M: A vey lage numbe. Decson vaables: Y : Toal capacy n wokplace ncludng he nomal me, oveme and sub-conacng assgned o ode n peod. O : A cean capacy of woksaon assgned o ode dung oveme. S : A cean capacy of woksaon assgned o ode by conacos. LT : Delay of delvey of ode FT : Ode compleon dae Ohewse = 0 x Y, µ (, n ), > 0 ST.. [ ( ) ] O = = OS() () ( Y O S ) CR ( α );, O (2) O CO ;, O (3) S CS ;, O R T MIN Z = c Y O S + co O + cs S + c LT (4) (5) (6) (7) (8) (9) wp k = (3) LT, FT OS( ), k = O Y, µ (, n ), LT w O = O = ( FT ow p w k = FT + M ( X 0 & X p Y OS( ), k = O ;, OS( ), O ;, OS( ), dd ); OS( ) ; ;, );, OS( ) (0) LT T dd; OS( ) + ( T dd ) () owk p = Yk ;, OS( ), O k = k = (2) Y, O, S > 0;,, O + k T k M X = k p T Y Y k { 0, };, OS( ), (,..., dd ), (,..., dd )

9 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, The objecve funcon of he model consss of mnmzng he poducon sysem s coss ncludng he coss of poducon vaables n nomal me, oveme and sub-conacng, and also hose fo posponed delvey of odes ha may be compleed behnd schedule. By esolvng he IP model, man componens of he new ode s cos pce wll be deemned ncludng all coss of poducon vaables and posponed delvey of odes ha may be compleed behnd schedule due o he addon of new odes. Gven he necessay wokload ha mus be acqued fom conacos and he benef ha s deemned by managemen, we can calculae he cos pce of he new ode. Lmaon (): Lmed capacy n nomal me; lmaon (2 and 3): Lmaon of maxmum me fo oveme and sub-conacng; lmaon (4): Ths lmaon guaanees ha all npu woks ae compleed whn he plannng hozon T. Only he lmaon (4) does no guaanee f odes can be compleed a due dae, because akes place a dffeen peods whn he plannng hozon of he fs level. Lmaons (5 and 6): These lmaons ae abou odes o be compleed a due dae. Applcaon of lmaon (5) helps he compleon of odes n dffeen woksaons a he elevan. Ths lmaon ncease he possbly of ode compleon a due dae. Plannng a fs level s pefomed weekly. An may be on hd day of he week. Applcaon of hs lmaon (5) smply guaanees ha he ode wll be compleed a he end of a week. To make sue ha he ode wll be compleed exacly on he hd day of he week, lmaon (6) s appled. Ths lmaon s consdeed only fo odes of hgh sgnfcance ha mus be compleed a due dae. In ohe wods, he lmaon (6) guaanees ha he emanng wok elaed o he ode shall be compleed n peod on due dae. In lmaon (7), s calculaed a he fnal woksaon. Ths me s saved by X = akng he bnay value of ( ) X. By applcaon of hs lmaon (8), s calculaed. In lmaon (9), hs me s compaed wh he pomsed delvey me o calculae he delvey delay. Lmaon (0) ensues ha he maxmum delay of any ode s o he exen ha he ode wll be poduced whn he plannng hozon. Lmaon () s smla o lmaon (5) wh hs dffeence ha, hee, may be delayed (LT). In ohe wods, lmaon () ensues ha he amoun of wok emanng unl peod fo odes ha ae delayed should be compleed n he me neval beween and dd+lt. Ths lmaon causes ha suffcen capacy fo mely delvey of odes s eleased. Lmaons (2 3) ae nonnegave lmaons o make sue ha decson vaables ae coec Decdng o Accep o Rejec An Ode by he Cusome A new ode s pce s deemned by mplemenng IPmodel. Ths pce s announced o he cusome. If he cusome appoves he ode o be compleed a MTO fm, he fm wll pefom necessay acons n he nex sage by povdng necessay wokload and aw maeals hough conacos Selecng s o Povde Raw Maeals and Requed Wokload o Complee New Odes The queson of selecng a se of conacos o povde necessay wokload fo acceped new odes s he las sage of he suggesed sucue. Cea fo conaco selecon ae pce and delvey me. As menoned befoe, n exchange fo vaous alenaves, each of whch conans he own ERD and, IP model s mplemened and, fnally, he lowes pce offeed s chosen. IP mplemenaon has an ERD and value n dffeen woksaons n exchange of whch he lowes pce s obaned. Gven he oupu of he IP, f MTO fm s oblged o use conacos o povde new odes wokload and ensue he delvey me, s necessay ha some of he exsng conacos ae chosen. ST mes a he second sage of he poposed sucue ae calculaed. ST s he laes me ha necessay opeaon s commenced n woksaon egadng ode. If necessay wokload fo ode whch s povded by conacos enes poducon sysem afe hs me, wll no be possble o ge a pe-calculaed. Snce s possble ha some specfed o unspecfed odes ae ejeced fom he me hese values ae calculaed o he mplemenaon of IP2 model, ST values should be ecalculaed and updaed. In hs sage, he objecve s o deemne a se of conacos who offe he leas delvey me dffeence wh espec o ST values, and sugges a lowe pce o povde necessay wokload. IP2 model s suggesed o fnd hs se of conacos. Accodng o equemens of odes whose fabcaon has been newly acceped n he sysem, he necessay amoun of aw maeals and wokload ae povded by conacos. Theefoe, he amoun of aw maeals and wokload ae aleady known. In ohe wods, IP2 s an allocaon model n whch gven he cea of pce and delvey me some of he conacos avalable n he pesen se ae seleced. Unlke IP model, IP2 model s applcable only fo odes ha ae acceped by he cusome and he poducon has been ensued. Odes ha have no been ye appoved by he cusome can cause aw maeals and wokload o be odeed moe han needed. Ths also may mpose many coss on MTO sysems. Afe he new ode pce s announced o he cusome, a me shall be spen by he cusome o pefom he negoang pocess and confmaon of he ode. Dung hs me, some of he odes ha wee no sll appoved by he cusome n he IP model may be appoved befoe a new ode s confmed by he cusome n IP2 model. I s assumed n IP2 model ha wokload equed by an ode n a woksaon can be povded only by one conaco. Indexes: s: s ndex (s =,,S)

10 0 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod Inpu paamees: ST : The laes me ha necessay opeaon s commenced n woksaon egadng he ode ; ohewse, he ode wll be posponed. P s : Suggesed pce of conaco s o delve he equed wokload fo he ode n woksaon. MAD s : Delvey me of he equed wokload fo he ode n woksaon by conaco s. S s : Maxmum amoun of wokload fo he ode n woksaon ha conaco s can povde n peod. β : Penaly fo he aval of necessay wokload of ode n woksaon po o schedule. β' : Penaly fo he aval of necessay wokload of ode n woksaon behnd schedule. Consdeng ha he lae aval of aw maeals and, consequenly, lae delvey of odes may mpose many coss on he fm, he amoun of he delay should be so ha aw maeals ene he fm on o po o schedule (β >> β' ). NO(): Se of new odes acceped. L'(): Se of conacos who can delve he wokload equed by ode n woksaon befoe he S. S( ): Se of conacos who can delve he wokload equed by ode n woksaon. Decson vaables: X =, f wokload fo ode n woksaon s povded by conaco s. Ohewse, X = 0 I R R MIN Z = ( P X S ) + β ( ST MAD ) X s s s s s = = s S ( ) NO() = s L () R I R T + β ( MAD ST ) X + c ( Y O ( S X )) + co O s s s s NO() = L ( k) = = = s S ( ) I () ( Y O ( ( S X )) CR ( α );, s s = s S( ) I (2) O CO ;, = I T I T (3) wp + w Y ; I = = = = ( 4 ) ow = Y ;, k OS () k= = k= I (5) w Y ;, OS( ), (,..., dd ) k k k k= k= + LT (6) ow = Y ;, OS( ), (,..., dd ) k k k= k= (7) X = ;, NO( ) s S( ) s (8) Y, O 0; X ; s,,, S ( ) s

11 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, 205 The objecve funcon of IP2 model ncludes dffeen coss of manufacung an ode plus he coss fo puchasng aw maeals and wokload fom conacos and he penaly fo delvey po o behnd schedule by conacos. In IP2 model, npu paamees nclude he followng: necessay amoun of wokload and aw maeals o be povded by conacos, and also aw maeals delvey me befoe unnng he model. As pevously menoned, IP2 model only apples o odes confmed and appoved. Theefoe, he value of such odes s n IP2. Lmaons ( 6) ae smla o IP poblem lmaons, bu hey ae only fo appoved odes. Lmaon (7) guaanees ha he necessay wokload egadng an ode n a woksaon may be povded jus by one conaco. The applcaon of IP2 model only fo appoved odes wll updae daa and paamees a he fs level. In ohe wods, ffh sage ndcaes he modaly of mplemenng he ollng hozon appoach fo he fs level of heachcal poducon plannng sucue. By mplemenng IP and IP2 models, one he one hand, he ode s compleed wh he leas possble cos and s moe lkely accepable by cusome; one he ohe hand, a goup of conacos ae seleced who wll povde necessay wokload and aw maeals a he lowes possble cos and a he laes peod. MTO manufacung fms have an appopae and effecve elaon wh dffeen componens of supply chan whch plays a majo ole n he effecve pefomance of MTO sysems; also ceaes a flexble poducon schedule whch comples wh nenal and exenal lmaons n ode o ean geae pofs. Ths plannng mehod can faclae elease and schedulng of odes a low levels of plannng Decdng o Rejec o Accep Odes wh Negoable Delvey Tme In hs saus, no fxed me fo ode delvey s offeed o he fm by he cusome, bu asks he fm o offe a combnaon of delvey me and pce so ha makes s decson accodng o s own cea. In hs case, smla o fxed delvey me, fou man acves ae caed ou ha ae as follows: B () Poducon of vaous alenaves o calculae he delvey me fo new odes B (2) Deemnng delvey me and pce of new odes by mplemenng nege lnea model (IP) B (3) Decdng o ejec o accep odes hough negoaon wh MTO fm and cusome B (4) Selecng conacos fo he supply of aw maeals and wokload equed by appoved odes Poducon of Vaous Alenaves o Calculae he Delvey Tme fo New Odes If an ode s no ejeced a he fs sage, n ode o mplemen IP model and calculae delvey me and pce of new odes, we need o calculae and ERD values. Because delvey me s no offeed decly by he cusome, so n hs case, dffeen delvey mes ae poduced by usng fowad mehod and he followng elaons: LRD = ERD + pool delay = LRD + TWK P + B, µ (,), µ (,) = ST + TWK P + B ST, µ (,2), µ (,2), µ (,2), µ (,2), µ (,) = ST + TWK P + B ST, µ (, ), µ (, ), µ (, ), µ (, + ), µ (, ) = ST, µ ( n, ), µ ( n, ), µ ( n, ), µ ( n, ), µ ( n, ) = ST + TWK P + B dd, µ ( n, ), µ ( n, ), µ ( n, ) =, µ ( n, ) 2 + TWK P + B ST n ( n )

12 2 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod Fou geneal alenaves ae poposed fo calculang dffeen delvey mes so ha vaous delvey mes ae deemned by he combnaon of hese alenaves: ) Calculaon of dffeen values of ERD: n hs saus, hee dffeen mes fo ERD ae poposed whch nclude he mos opmsc, modeae, and he mos pessmsc mes fo he delvey of aw maeals by conacos. 2) Gvng dffeen poes o an ode a he waehouse of backlogged odes: By gvng dffeen poes a he waehouse of backlogged woks, dffeen delvey mes may be deemned smla o ode wh fxed delvey me. These poes nclude he followng condons: a. Nomal poy: In hs condon, he ode s placed a he end of queue fo uneleased odes. b. Hgh poy: In hs saus, upon aval of aw maeals, he ode s placed on he elease lne, and ERD and LRD values become equal (Pool_delay = 0). c. Ohe poes: In addon o he wo above poes, dependng on he ode sgnfcance, we can assgn dffeen poes a he waehouse of non-eleased odes. 3) Change n values: In hs alenave, by poducng dffeen values smla o odes of sable delvey me, dffeen delvey mes ae poduced. Ths change can be done n hee ways: a. Change n of new odes by nceasng he capacy of woksaons whee new opeaons ae caed ou on new odes. b. Change n of new odes by changng values of ohe odes. c. Change n of new odes by usng he capacy allocaed o ohe odes. 4) Change of wang peod poy n each woksaon: Lke he pevous saus, dependng on he sgnfcance of odes, wo nomal and hgh poes ae gven o elevan odes. Fo each alenave, a se of values (dd,, LRD) ae povded ha consue he mos mpoan npus of IP model. Some of hese values can be emoved: 5) dd values ha have a sho me neval wh he me now. Alhough hs delvey me s sho, bu we need exa acves such as sub-conacng and oveme o mee hs need. Also, a sho delvey me may poduce a poblem fo poducon schedule and esul n lae delvey of some appoved odes. 6) add values whose due dae ae beyond plannng hozon T Deemnng Delvey Tme and Pce of New Odes by Resolvng he Inege Lnea Model (IP) IP lnea model whch was dscussed n secon (A2) s used o deemne he pce of new odes n whch delvey me s negoable. In hs case, fo each se of values (dd,,erd), IP model s appled. Thus, fo each dd value, one pce s obaned. Fnally, dffeen values (dd,p) wll be offeed o he cusome Decdng o Rejec o Accep Odes hough Negoaon wh MTO Fm and Cusome By applyng IP model, dffeen combnaons of (dd,p) values ae geneaed fo new odes. These combnaons ae offeed o he cusome. A he end, boh paes agee on one combnaon of pce and delvey me Selecng s fo he Supply of Raw Maeals and Wokload Requed by Appoved Odes Fnally, smla o odes wh sable delvey me, and usng IP2 nege lnea model, a se of bes conacos, who offe he lowes cos o he sysem, s seleced o povde necessay wokload. 0. Thd Level of he Poposed WLC Appoach (Release of Odes no he Shop Floo) In hs model, he laeness n delveng odes occus n one of he followng condons: If he amoun of wokload avalable n a woksaon appoaches o zeo. If all odes n a woksaon ae non-ugen. If one ode becomes ugen n he waehouse of odes o be eleased. 0.. If he Amoun of Wokload Avalable n a Woksaon Appoaches o Zeo Ths does no mean ha avalable amoun of wokload s ceanly zeo. As soon as he avalable wokload appoaches zeo, he poducon sysem sends sgnals o nfom he se supevso of hs ssue. To avod unemploymen of such a woksaon, some of he odes ha ae fsly pocessed n hs woksaon ae eleased so ha he amoun of wokload whch s avalable dsances self fom zeo. To do hs, he followng seps ae pefomed n sequence: A () Deemne he se of odes n he waehouse of odes o be eleased whee fs opeaon s caed ou. A (2) Release ugen odes wh a hghe LRD. A (3) If wo o moe ugen odes have dencal LRD, he sequence of eleasng odes accodng o he me spen n he woksaon o pocess hem. Odes fo whch shoe me s spen ae eleased fs. A (4) Non-ugen odes wh a hghe LRD: A (5) Lke he second case, f wo o moe non-ugen odes have dencal LRD, he sequence of he elease wll depend on he me spen fo opeaons pefomed on hem n he elevan woksaon If All Odes n a Woksaon Ae Non-Ugen

13 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, If all exsng odes ae n he queue of woksaon fo non-ugen odes (he pe-deemned a fs level s hghe han he me of compleon n he pevous saon), ugen odes on whch he fs opeaon has been pefomed n he elevan woksaon ae eleased so ha he compleon s possble a due dae. Ode eleasng pocedues ae as follows: B () Deemnng he se of ugen odes n he waehouse of woks o be eleased he fs opeaon of whch s pefomed n he elevan woksaon. B (2) Releasng he ugen odes based on LRD poy. B (3) By eleasng each new ode, oal wokload of he woksaon s checked If One Ode Becomes Ugen n he Waehouse of Odes o Be Released As soon as an ode becomes ugen n he waehouse of odes o be eleased, we check f, by eleasng he new ode, he amoun of wokload n he woksaons, whee fs opeaon has been pefomed, s o s no beyond he pemssble lm. If none of hese woksaons ae blocked, he ode s eleased. Howeve, f some of hem ae blocked, exa capacy equed o povde necessay wokload fo he new ode s compued (he dffeence of oal avalable wokload and uppe lm); f he capacy equed by all blocked woksaons can be povded, hen he ode s eleased. As you can see n he poposed WLC model, focus s on wo essenal cases of on me elease o ensue he delvey me compued a fs level of he poposed sucue and o have a smooh and balanced poducon sysem. The only pon o be menoned n he developed WLC model s he way o calculae oal wokload of each woksaon ncludng he se of avalable wokload, wokload geneaed n woksaons agans he flow and wokload geneaed because of newly eleased woks. The followng seps ae suggesed n ode o make sue f oal wokload fo one woksaon s hghe han uppe pemssble lm: Fs sep Calculang he uppe lm fo he wokload of each woksaon Second sep Calculang oal wokload n woksaons Thd sep Compang oal wokload and uppe pemssble lm Fs Sep Calculang he Uppe Lm To do hs, we use he fomula povded by Beche(8): LL = 00 ( PP + LT ) / PP LL: Pemssble uppe lm fo woksaon PP: Lengh of plannng hozon a he second level LT: Planned lead me fo woksaon. Accodng o he above fomula, lead me s deemned by dvdng wo aveage amouns of sock n he queue of woksaon and he elevan oupu aveage. To calculae he lead me n each woksaon, fs level daa ae used. A he fs level, he amoun of odes eneng weekly o a woksaon (w) and he amoun allocaed o each ndvdual woksaon n dffeen peods ae compued. Theefoe, he lead me fo each woksaon n he weekly peod s calculaed fom he followng elaon: QUEUE w LT = = I Capacy Y = Lead me has no been calculaed n pevous eseach accodng o he oupu of fs level Second Sep Calculang Toal Wokload n Each Woksaon The followng elaon ndcaes how o calculae he wokload n woksaon : TL = TWL P TL : Toal wokload n woksaon Py: A pecenage of ode eleased fom he cuen woksaon y and eneed no woksaon whn he plannng hozon. If = y, hs pobably wll be. In ohe wods, he woksaon y s he agans-he-flow woksaon fo he ode. To calculae p a agans-he-flow woksaons, he followng fomula s poposed: P jy PQy = = TL y I = Y TL POy: Planned oupu value n woksaon y whn he plannng hozon of he second level. Ths value s equal o he planned capacy n woksaon y of he fs level of heachcal sucue poposed. If p s hghe han, hs means ha he planned capacy n he woksaon s moe han he oal wokload and, consequenly, oal wokload n woksaon y s compleed whn he plannng hozon and eneed no anohe woksaon. Thus, f ode whch s now n queue n woksaon y eques m exa woksaons befoe s eny no woksaon, a pecenage of hs ode, whch s expeced o ene he woksaon whn he plannng peod, wll be equal o: POm Py = m { y, y +,...,, } TL m m The advanage of calculang p n hs eseach n compason wh ohe pevous eseaches s ha, n many fomulas poposed fo calculang p, he cuen saus of poducon sysem has no been aken no accoun. In many pevous eseaches, he followng fomula has been used o y y y

14 4 Heachcal Poducon Plannng n Make o Ode Sysem Based on Wok Load Conol Mehod calculae p: P jy 00 = LL Accodng o he above fomula, p-value s only dependen upon LLy-value whch s a fxed value. So, dung he calculaon of p-value, cuen saus of he woksaon s no calculaed n ems of capacy and wokload avalable n hee. Ths faco mpedes he access o a smooh poducon sysem Thd Sep Compang he Toal Wokload wh Pemssble Uppe Lm Afe fs and second seps, becomes possble o compae he oal wokload and pemssble uppe lm. Befoe pemng he elease of any new ode, we need o calculae and compae he oal wokload and pemssble uppe lm fo woksaons whch ae a pa of opeaon oue of he new ode. If afe he elease of new odes no poducon sysem, he oal wokload of any woksaons s no beyond he pemssble uppe lm ( TL LL ), new odes ae pemed o be eleased; ohewse, ( TL > LL ) odes wll eman a he waehouse of odes o be eleased.. Fouh Level of he Poposed Heachcal Poducon Plannng Sucue: Odes Poy Sage n Woksaons The focus of hs level s on educng he queung n ndvdual woksaons. The only faco affecng he wang peod n woksaons s he mehod used o poze odes nsde woksaons. Unl now, dffeen mehods have been used o poze woks n woksaons. In he poposed sucue, snce values ncludng delvey me, lengh of he queue n dffeen woksaons, and elease me ae calculaed accodng o he cuen condon of poducon sysem, so a he fouh level, we need no complcaed mehods o poze odes. In pevous eseaches whee only second and hd levels wee used y smulaneously, he use of FIFO, whch s one of he smples mehods oday, led o accepable esuls []... Mehod fo Pozng Odes n he Queue of Woksaons Snce delvey me n MTO poducon envonmens s he mos mpoan objecve of he sysem, so, he pozaon of unfulflled odes beng queued n dffeen woksaons should be done o begn opeaon n a manne ha he delvey me s ensued. s he mos val chaacesc of each ode n a woksaon and s obvous ha f occus on me, he mely delvey of odes n each woksaon wll be ensued. In hs level, o poze odes n each woksaon, we sugges ha all odes ae gven poy accodng o he. Ths mehod of pozaon s called S (shoes ode compleon dae). If wo odes have equal n one woksaon, he ode wh hghe sgnfcance wll be gven poy. In he fs level of he poposed sucue, he degee of hadness of IP and IP2 mahemacal models was nvesgaed va LINGO 6.0, and o make sue of he oupu accuacy, oupus geneaed n he sofwae wee analyzed. 2. Evaluaon of Heachcal Poducon Plannng Sysem a he Second Level: Ode Eny Sage A he second level of IP and IP2 mahemacal plannng models, we fs saw how compuaonal me n hese models nceases along wh he ncease of he dmensons. Requed daa on es poblems ae andomly geneaed. One week was assumed fo me un and 2 weeks fo he lengh of me hozon. Sx ypes of poblems wh dffeen dmensons wee consdeed and fom each poblem 0 samples wee geneaed andomly. Vaables used o deemne dmensons nclude he numbe of odes n he sysem, esouces and odes ha can be posponed. Fo each esed poblem, one LINGO model was ceaed and all geneaed poblems wee un n a PC. The followng ables show he esuls obaned fom IP and IP2 models. Table. Sucue of IP Model n Tesed Poblem Dmensons of poblems Numbe of Numbe of odes n he Numbe of Numbe of odes Numbe of sample Numbe of sysem Souces o be delayed vaables of he Numbe of poblem nege connuous lmaons vaables numbe

15 Unvesal Jounal of Indusal and Busness Managemen 3(): -20, Numbe of sample poblem Numbe of conacos Table 2. The Sucue of IP2 Model n Tesed Poblems Numbe of nege vaables Dmensons of he poblem Numbe of vaables of he connuous numbe Numbe of lmaons Table 3 shows he mean CPU me equed o acheve an opmal soluon n IP and IP2 models fo each se of esed poblems. A noable pon s ha fo sample poblems wh dmensons of 8 x 8 x n IP model, hee s no possbly o each an opmal soluon n a easonable CPU me. The compuaonal esuls also ndcae ha IP model can povde an opmal soluon fo small-szed and medum-szed poblems n a easonable CPU me. Bu fo some medum-szed poblems and all lage sze poblems, s no possble o access an opmal soluon because, n popoon o he ncease n he sze of poblems, he me fo an opmal soluon nceases exponenally. As a geneal concluson and accodng o esuls, IP model s sensve o he numbe of odes o be delayed, because he numbe of nege vaables n IPmodel s dependen on he numbe of odes o be delayed. Unlke he IP model, IP2 model s able o compue an opmal soluon fo all dmensons n a easonable CPU me, because IP2 model sucue s a smple allocaon poblem n whch fom he se of he conacos, accodng o he cea of pce and delvey me, a numbe of hem ae seleced. Numbe of sample poblem Table 3. CPU Mean Tme n Tesed Poblems Numbe of esed poblems CPU mean me o ge an opmal soluon (Mn) IP Model IP2 Model NA - Now, a MTO poducon sysem wh wo woksaons and fou odes (hee odes n he poducon sysem and one new ode wh hgh sgnfcaon) s consdeed. In hs example, sx weeks ae assumed fo he plannng hozon a he fs level. All odes have sable delvey me and wo odes can be posponed. Based on defnons of ow and w paamees and also he daa on able 4, values of hese paamees ae calculaed n able 5. Meanwhle, all wp values ae consdeed zeo. Tables 5 0 show ohe daa needed n IP model. Odes ERD (wk) dd (wk) Table 4. Daa on Odes p c Woksaon (wk) TWK (h) Woksaon 2 (wk) TWK (h) A B C D Table 5. Inpu Values (w) and Oupu Daa (ow) fo One n IP Model Woksaon (w / ow) Woksaon 2 (w / ow) A B C D A B C D /-20 /-40 /-30 / / /-0 / / /-25 / / 30 -/ 30 -/ / / 40 -/