SCHEDULING AND THE ESOUCE-TASK NETWOK Pedo M. Caso (pedo.caso@ne.p) Inved Asssan eseache Depamen of Pocess Modelng and Smulaon Lsbon/Pougal
OUTLINE Inoducon Chaacezaon of schedulng poblems and soluon saegy esouce-task Newok pocess epesenaon Fundamenal conceps Insucons fo geneang he pocess newok Sngle me gd fomulaons Dscee-me Connuous-me Un-specfc appoaches Indusal case sudes Opmzng he cookng pocess of a bach pulp mll Bypoducs ecyclng on a ssue pape mll Equpmen allocaon on a fne chemcals plan Conclusons Sepembe 8 2008 EWO Semnas: Schedulng & he TN 2
INTODUCTION 3
Equpmen uns BASIC CONCEPTS Schedulng s concened wh allocaon of esouces ove me so as o execue he pocessng asks equed o manufacue a gven se of poducs. (Pnedo 200) A vaey of mehods can be used o solve a poblem Soluon s epesened n he fom of a Gan cha M U U3 U4 U6 U7 FP U U2 U3 U4 U5 3 2 4 5 8 6 7 4 2 3 6 5 7 8 Sage Sage 2 U2 U5 U8 U6 U7 U8 Sage 3 3 2 6 8 7 5 4 me Sepembe 8 2008 EWO Semnas: Schedulng & he TN 4
SCHEDULING POBLEMS VEY COMPLEX Wde mx of feaues peodc bach bach mxng/splng fne soage sho-em mulsage vaable bach szes due daes flowshop jobshop ules unlmed soage jus n me changeoves manpowe mnmze makespan maxmze pof mulpupose sho-em connuous Sepembe 8 2008 EWO Semnas: Schedulng & he TN 5
VISION Develop a geneal model ha can cope wh such a vaey of feaues Mosly done Exploe ways of mpovng effcency fo specal ypes of poblems Ongong eseach on decomposon echnques ha can allow o solve lage-scale poblems fas Fuue wok Sepembe 8 2008 EWO Semnas: Schedulng & he TN 6
STATEGY TO FOLLOW Sepaae poblem descpon fom mahemacal fomulaon Use he esouce-task Newok (TN) o epesen he pocess Collec nfomaon fom flowshee and pocess ecpe Conve eal enes no vual enes (esouces and asks) Use/develop TN-based mahemacal fomulaons Handlng of me s a ccal ssue Dscee-me Connuous-me Sepembe 8 2008 EWO Semnas: Schedulng & he TN 7 Pocess TN Pocess Infomaon + TN Model T v N v N ou T n I I T end FP UT UT CT CT ) ( ) ( 0???
ESOUCE-TASK NETWOK POCESS EPESENTATION 8
TN (PANTELIDES 994) Vews all pocesses as bpae gaphs wh wo enes esouces () epesened as a ccle Geneal concep ha ncludes equpmens maeals ules cleanng saes maeal locaon ec. Tasks (I) epesened as a ecangle Tansfoms one se of esouces no anohe Hea eac Clean Tansfe ec. Fs sep Idenfy esouces and asks Second sep elae esouces wh asks Tasks consume and poduce esouces Sepembe 8 2008 EWO Semnas: Schedulng & he TN 9
STATE-TASK NETWOK (STN) VS. TN STN: Uns mplc n model consans A C Make B Make D TN: Equpmen uns eaed explcly Dsaggegae asks f mulple uns ae suable B D U 0.4 0.6 Make E E A Make B B 0.4 Make E_U E C Make D D 0.6 Make E_U2 U2 Sepembe 8 2008 EWO Semnas: Schedulng & he TN 0
CITICAL POINTS Dsngush beween esouce ypes Consumed empoaly (e.g. ) Consumed/poduced pemanenly (e.g. ) Have an avalably pofle ( ) Types of asks M Connuous neacon Dscee neacon M Make_P_M ae P M EL Useful fo changeoves and soage Insananeous Useful fo maeal ansfe beween uns o o mee demands FP Dspach_P Insananeous HoldnSoage_P Duaon= me n. PM Some magnaon may be equed o fnd a pope se of asks/esouces Make_P_M2 Duaon= PM2 + PM2 Sze PM2 M2 Sepembe 8 2008 EWO Semnas: Schedulng & he TN
BINGING TN DIAGAM INTO THE MODEL Sucual paamees geneaon Tasks wll be chaacezed by wo ses of vaables N (N )- sa of a even pon (endng a ) ( )- amoun handled by ask Fve ses of sucual paamees Gve oal esouce consumpon/poducon o popoon elavely o amoun handled by ask ( )- dscee neacon a sa (end) lnked o N ( )- dscee neacon a sa (end) lnked o - connuous neacon dung ask lnked o Lage majoy=0 ohes mosly o - Easly geneaed afe some pacce Sepembe 8 2008 EWO Semnas: Schedulng & he TN 2
EXAMPLE Bach eacon 0 on A poduces 8 on B and 2 on C 5 on/h coolng wae needed Opon ecpe n absolue ems Bnay vaables N suffce Opon 2 Moe geneal ecpe n elave ems Need also =0 on leads opon Thee may be moe han one possble se of values A A A =-0 =/0 A =- =- eacon () Fxed duaon CW =-5 =- CW = Opon eacon () Vaable duaon CW =-0.5 CW = Opon 2 B =8 C =2 =/0 B =0.8 C =0.2 B C B C Sepembe 8 2008 EWO Semnas: Schedulng & he TN 3
MODELING TIME IN TN SCHEDULING FOMULATIONS 4
MODELS TYPICALLY DISTINGUISHED BASED ON TIME EPESENTATION FOLLOWED Use of explc me gd(s) Sngle me gd (a.k.a. global me nevals) Dscee-me (Kondl e al. 993; Paneldes 994) Connuous-me (Caso e al. 200; Maavelas & Gossmann 2003; Sundaamoohy & Kam 2005) Mulple me gds (a.k.a. un specfc) One me gd pe un (Floudas & co-wokes 998-2008; Gannelos & Geogads 2002 Caso & co-wokes 2005-2008) Use of sequencng vaables Immedae pecedence (Gupa & Kam 2003) Geneal pecedence (Méndez e al. 200; Hajunkosk & Gossmann 2002) Sepembe 8 2008 EWO Semnas: Schedulng & he TN 5
COMMON TO ALL TN MODELS Excess esouce vaables Keep ack of esouce avalably ove me Excess amoun mmedaely befoe end of neval end May be equed when n pesence of connuous asks Equpmen uns eaed ndvdually ( max =) Inal esouce avalably 0 Ofen know fo all esouces (model vaable ohewse) Dscee npus n and/o oupus ou can be handled Heusc: Fx =0 fo as many esouces as possble Sepembe 8 2008 EWO Semnas: Schedulng & he TN 6
VITAL TO UNDESTAND ESOUCE BALANCES Sucual paamees come no acon Mulpeod maeal balance expessons Depend on he ype of esouce/ask nvolved Illusaon fo equpmen esouces Sepembe 8 2008 EWO Semnas: Schedulng & he TN 7 T v N v N ou T n I I T end FP UT UT CT CT ) ( ) ( 0 ) ( * T T v CT I I end s c Task _M Task 2_M = 2 3 4 5 6 7 M + 0 - + - +
DISCETE-TIME MODEL Mos poweful appoach oveall Can handle poblems of ndusal elevance Smple elegan and vey gh MILP fomulaon mn N V N Few ses of consans Besdes excess balances Ccal modelng ssue max T Unfom neval lengh δ may be dffcul o selec Tade-off: daa accuacy vs. poblem acably EQ EQ mn V max T I T N I ounded-up daa No ue opmum Accuae daa δ Bnay vaables Toal vaables Consans Cos [k$] CPUs 0 4005 242 7277 9 5.36 5 8077 2254 4477 90 50 2 2037 5674 36077 89 40 4034 2378 72077 89 429 Sepembe 8 2008 EWO Semnas: Schedulng & he TN 8
CONTINUOUS-TIME MODEL Moe geneal appoach Can handle a wde vaey of feaues goously Sgnfcanly moe complex oveall Addonal se mng consans & vaables Ccal modelng ssues Bach asks chaacezed by ndces (sa) and (end) Global opmal soluons only fo T No opmum T Bnay vaables Toal vaables Consans Cos [k$] CPUs 8 462 957 495 Infeasble 0.57 9 528 089 562 27.222 7.8 0 594 22 629 27.008 369 660 353 696 26.9 43 ode magnude Sepembe 8 2008 EWO Semnas: Schedulng & he TN 9
UNIT-SPECIFIC MODELS Mulple me gds bee n specal ypes of poblems Sequenal pocesses (mulsage) Compeve wh sequence-based models Mulpupose plans whou shaed esouces Ccal modelng ssue All asks las one me neval (one ndex) Fewe even pons o fnd global opmal soluons Model Tme gd T Bnay vaables Toal vaables Consans Cos [k$] CPUs Dscee-me Sngle 50 27383 60406 33054 793 65 Connuous-me Sngle 7 453 65 348 793 624 Mulple 4 65 98 295 793 0.82 Sepembe 8 2008 EWO Semnas: Schedulng & he TN 20
CASE STUDY. OPTIMIZING THE COOKING POCESS OF A SULPHITE PULP MILL 2
POBLEM CHAACTEISTICS Sysem of 4 paallel bach dgeses fo pulp poducon Heang sage was boleneck 2 dgeses shang seam smulaneously The dgese sequence affecs he cycle me Dffeen dgese capaces 90ºC @TTx5 Tcook D Dj H h h2 h3 Seam fo he cookng secon H0 Tnal T(H0) Sepembe 8 2008 EWO Semnas: Schedulng & he TN 22
MODELING OF THE HEATING STAGE Duaon of heang asks fom dynamc smulaon TN supesucue Tasks H0- hea ll 90 o C H- fnal heang esouces S3- nal empeaue S4-90 o C S8- cookng empeaue S5-S7- Tempeaue afe H0 Sepembe 8 2008 EWO Semnas: Schedulng & he TN 23
OPTIMAL PEIODIC SCHEDULE Poducon ae % hghe cycle me H= 564 mn Opmal sequence: D3-D6-D5-D4 Fom dscee-me fomulaon n 393 CPUs (δ= mn) Connuous-me appoach only fnds H=584 mn n 4 h of CPU D6 K K2 K3 K4 K K2 Seam Shang H0 H D5 H0 H K K2 K3 K4 K K2 D4 K K2 H0 H K K2 K3 K4 D3 K K2 K3 K4 K K2 Seam Shang H0 H K 0 50 00 50 200 250 300 350 400 450 500 550 Tme (mn) Sepembe 8 2008 EWO Semnas: Schedulng & he TN 24
CASE STUDY 2. OPTIMIZING BYPODUCTS ECYCLING ON A TISSUE PAPE MILL 25
POBLEM CHAACTEISTICS Scandnavan ssue pape mll (connuous plan) 5 poducs (P50 dakes qualy o P85 bghes qualy) Pa of he fbe los as boke n conveng lnes Cuen boke ecyclng polcy Mx boke wh old newspape (ONP) fo low qualy poducs (P50 P60) aw maeal ONP aw maeal MOW De-nkng lne aw maeal VF Sludge & ejec Tssue Machne Ash P50 P60 P75 P80 P85 De-nkng lne 2 Tssue Machne 2 P50 P60 P75 P80 P85 Boke Soage Inemedae Soage Inemedae Soage 2 Sepembe 8 2008 EWO Semnas: Schedulng & he TN 26
MODELING FO A NEW ECYCLING POLICY Do no mx boke fom dffeen quales B B80 and B85 ecycled wh ONP MOW and VF VF SP2_VF85 VF 85 TM_P85 TM2_P85 0.9 0.9 P85 0. 0. B 85 MOW SP_MOW80 SP SP2_ONP67 L80 DW MOW 80 ONP 67 GFS_80 GTS_80 aemax=48 /day GTS_67 aemax=48 /day S80 0.896 0.224 0.896 0.224 TM_P80 TM2_P80 TM_P75 TM2_P75 0.9 0.9 0.9 0.9 TM 0. P80 0. 0. P75 0. B 80 ONP SP2 SP2_ONP60 ONP 60 L67 GFS_67 S67 TM2_P60 TM_P60 0.9 0.9 TM2 P60 0. 0. B SP2_ONP50 ONP 50 TM_P50 TM2_P50 0.9 0.9 P50 0. 0. Sepembe 8 2008 EWO Semnas: Schedulng & he TN 27
Pof (.m.u./y) Excess 49 Amoun () Amoun () Amoun () EVALUATION OF ECYCLING POLICIES Pof.5% hghe Double benef of lowe aw-maeal coss and no dsposal coss Wh a MINLP connuous-me fomulaon Bee soluon n sgnfcanly less me han dscee-me fomulaon 00 60 B 60 B 60 B 20 20 20 98 80 80 80 40 40 40 0 0 0 96 0 2 4 6 8 Tme (days) 0 2 4 6 8 Tme (days) 0 2 4 6 8 Tme (days) 94.87 94 93.5 92 9.95 SP MOW80 MOW80 MOW80 MOW80 MOW80 SP MOW80 MOW80 MOW80 MOW80 MOW80 SP MOW80 MOW80 MOW80 MOW80 MOW80 20% B80 90 SP2 ONP50 VF VF ONP67 ONP60 SP2 ONP50 20% B VF VF ONP67 ONP60 20% B SP2 ONP50 7.6% B VF 9.2% B85 VF 9.2% B85 ONP67 ONP60 20% B TM P50 P85 P85 P75 P60 TM P50 P85 P85 P75 P60 TM P50 P85 P85 P75 P60 88 TM2 P80 P80 P75 P75 P80 TM2 P80 P80 P75 P75 P80 TM2 P80 P80 P75 P75 P80 DW GTS80 GTS67 DW GTS80 GTS67 DW GTS80 GTS67 86 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 Tme (days) Tme (days) Tme (days) No ecyclng Cuen saegy Fuue saegy Sepembe 8 2008 EWO Semnas: Schedulng & he TN 28
CASE STUDY 3. OPTIMAL EQUIPMENT ALLOCATION IN A FINE CHEMICALS PLANT 29
POBLEM CHAACTEISTICS Pouguese fne chemcals bach plan How many uns o allocae o poducon of API? The moe uns he lowe he makespan Bu fewe uns fo ohe APIs (flexbly deceased) Vual equpmen uns n he TN Model wll make coespondence o eal plan uns Sepembe 8 2008 EWO Semnas: Schedulng & he TN 30
OPTIMAL COST AS FUNCTION OF CYCLE TIME Thee soluons deseve fuhe analyss Fom dscee-me MILP fomulaon (oal CPU=078 s) Uns no allocaed o poducon API Sepembe 8 2008 EWO Semnas: Schedulng & he TN 3
ANALYSIS OF POMISING SOLUTIONS Toal poducon me fo 20 baches of he API (E) 9 days + shf 78 days + 2 shfs 6 days + 2 shfs Sepembe 8 2008 EWO Semnas: Schedulng & he TN 32
CONCLUSIONS & EFEENCES 33
CONCLUSIONS Thee s a wde vaey of complex schedulng poblems ou hee The undelyng pocess/poducon ecpe can be descbed as a esouce-task Newok Ths pocedue s mosly ndependen on he mahemacal fomulaon used o solve he poblem Thee concepually dffeen models can be used Gudelnes gven o selec mos appopae Indusal poblems have been ackled Thee s sll a lo of eseach o be done Sepembe 8 2008 EWO Semnas: Schedulng & he TN 34
IMPOTANT TN EFEENCES Paneldes C.C. Unfed Famewoks fo he Opmal Pocess Plannng and Schedulng. In Poc. 2 nd FOCAPO; Cache Publcaons: New Yok 994; pp 253. Caso P. e al. Smple Connuous-me Fomulaon fo Sho-Tem Schedulng of Bach and Connuous Pocesses. Ind. Eng. Chem. es. 2004 43 05. Caso P. e al. Smulaneous Desgn and Schedulng of Mulpupose Plans Usng esouce Task Newok Based Connuous-Tme Fomulaons. Ind. Eng. Chem. es. 2005 44 343. Caso P.M.; Gossmann I.E. New Connuous-Tme MILP Model fo he Sho-Tem Schedulng of Mulsage Bach Plans. Ind. Eng. Chem. es. 2005 44 975. Méndez C.A. e al. Sae-of-he-a evew of Opmzaon Mehods fo Sho-Tem Schedulng of Bach Pocesses. Compu. Chem. Eng. 2006 30 93. Shak M.; Floudas C.A. Un-specfc even-based connuous-me appoach fo shoem schedulng of bach plans usng TN famewok. Compu. Chem. Eng. 2008 32 260. Sepembe 8 2008 EWO Semnas: Schedulng & he TN 35