Integrated Campaign Planning and Resource Allocation in Batch Plants

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1 20 h European Sympoum on Compuer Aded Proe Engneerng ESCAPE20 S. Peru and G. Buzz Ferrar (Edor) 2010 Elever B.V. All rgh reerved. Inegraed Campagn Plannng and Reoure Alloaon n Bah Plan Nareh Suarla, I. A. Karm Deparmen of Chemal & Bomoleular Engneerng, Naonal Unvery of Sngapore, 4 Engneerng Drve 4, Sngapore Abra In h work, we develop a mple MILP model for mulaneou ampagn plannng and reoure alloaon n mul-age bah plan. We apure everal real lfe enaro nludng manenane plannng, produ ouourng, and NPI and udy he effe of varou proe deon on he oluon of he negraed and reoure onraned plannng problem. Gven he produ, her projeed demand, and avalable reoure for a gven me horzon, our model deermne ampagn lengh, produ hedule on dfferen produon lne, and reoure alloaon profle. Alo, we onder equene-dependen hangeover me beween wo ampagn. To demonrae he performane of our mahemaal formulaon, we onder a ae udy from a ypal mulage pealy hemal bah plan. We valdae our approah onderng a ere of dynam bune enaro. Keyword: Campagn hedulng, mulprodu bah plan, reoure alloaon, MILP 1. Inroduon Bah-we manufaurng very popular for pealy produ (pharmaeual, ome, polymer, bohemal, food produ, e.) whh are of hgh added value, low volume or requre loe onrol of proe ondon. Operaonal plannng eek npu and revewed by everal deparmen uh a proe, manenane, laboraory, uppler, ale, and hgher managemen. Th manly beaue operaonal plannng ofen onraned by he avalably of reoure (manpower, ule, laboraory, par, e.). Thu, plannng a ollaborave avy of everal deparmen. For h reaon, a mple plannng ool or raegy requred ha an qukly aer o he need of all he akeholder. In general, he problem of operaonal plannng n mulprodu bah plan ha been addreed by everal reearher. Reenly, Corano e al. (2009) developed a MINLP model for he degn and plannng of mulprodu bah plan. Sefanon e al. (2006) preened a 3-level herarhal framework for he plannng and hedulng n pharmaeual plan. Sundaramoorhy and Karm (2004) uded he effe of new produ nroduon n he medum-erm plannng n he onex of a pharmaeual produon faly. Sundaramoorhy e al. (2006) developed a mple LP model a a deon uppor ool for medum erm negraed plannng deon o he manager n pealy hemal ndury. Suryad and Papageorgou (2004) ondered a produon plannng problem and norporaed manenane plannng and rew alloaon onran. Clearly, ampagn plannng problem ha been well uded n bah plan, few work udy he effe of negrang reoure alloaon In h work, we ue a ba model of Sundaramoorhy and Karm (2004) and modfy o develop a mulperod MILP plannng model. Our model le omplaed, n erm

2 N. Suarla and J.A. Karm of oluon raegy and model ruure, and an addre he need of hgher managemen readly. Our model apure everal real lfe enaro uh a he effe of reoure (manpower, ule, laboraory, and wae-reamen apay) avalably n proe plannng, roune manenane, new produ nroduon (NPI), ouourng of nermedae produ, and equene-dependen leanng me. Furhermore, o apure he dynam hange n he plan, we propoe a reave hedulng raegy for our model. Fnally, o demonrae he performane of our approah, we onder a ae udy from a ypal mulage pealy hemal bah plan. Alo, we evaluae our model onderng varou bune enaro. 2. Problem aemen A mulprodu pealy hemal manufaurng faly (F) produe everal produ ung J proeng un/lne (j = 1, 2,, J). Operaon n F nvolve I ( = 1, 2,, I) ak, whh nlude boh proeng (I p ) and manenane (I m ) ak. A repe dagram of he manufaurng proe gve he nformaon on proeng ak, maeral ae ( = 1, 2,, S), and ma rao (σ j ) (Suarla e al., 2009). The plannng problem n F an be derbed a follow. Gven he (1) produon repe, (2) fxed bah ze and proeng and yle me, (3) plannng horzon, (4) demand and her due-dae, (5) o and revenue deal, (6) equene-dependen leanng me and o, (7) reoure avalably, o, & effe on proe performane, (8) prevenve-manenane mng, (9) poenal new produ and her demand, we deermne (1) alloaon of ak o produon un/lne, (2) reoure alloaon, (3) ampagn, hedule, and number of bahe, (4) maeral nvenory profle, (5) ouourng raegy, aumng (1) deermn enaro, (2) able nermedae maeral, (3) nananeou prouremen of raw maeral (zero nvenory o), (4) all demand due a due dae, (5) one ampagn per nerval. We onder he maxmzaon of gro prof (revenue hrough ale o of good old) a he opmzaon objeve. 3. MILP formulaon We model he plannng horzon H, on eah un j (1,, J), n NT (1,, NT) dree nerval of lengh h (h 1, h 2,, h NT ) eah. An nerval hen referred o he me beween wo produ delvery dae [DD -1 - DD ] and of lengh h. Furhermore, o model he nerval h we ue a eparae loal me ax on every un j and defne KT j (k = 1, 2,, KT j ) lo, ung a mul-grd onnuou me approah (Suarla e al., e 2009). Le Tjk and T [k = 1, 2,, KT j ; T 0; e jk j1 T h e jkt ; ; e T jk T jk T j( k+ 1) Tjk ] denoe he ar and end me of he lo k on un j for he nerval. Thu, he lo e lengh [ T -T ]. We ue [ T ] o denoe he ar of a ampagn of jk jk T jk T jk = jk I j ak n lo k of un j for nerval Campagn alloaon Eah ampagn nvolve everal bahe, every lo mu have a ampagn, and eah ampagn an be alloaed o only one lo. To alloae eah ampagn n nerval o a lo, model ranon of ampagn and exenon of a ampagn o he nex nerval we defne he one bnary (y jk ) and wo 0-1 varable y jk 1 f a ampagn of ak alloaed o lo k on un j n nerval 0 Oherwe

3 Inegraed ampagn plannng and reoure alloaon n bah plan x ' jk I j, 1 j J, 1 k KT j, 1 NT 1 f ampagn of ak n lo k preede ampagn of ' 0 Oherwe, I j, 1 j J, 1 k < KT j, 1 NT 1 f a ampagn of ak n un j rehe from nerval o + 1 yj 0 Oherwe I j, 1 j J, 1 NT Now, a lo k on un j anno perform more han 1 ampagn. Alo, we do no allow mulple ampagn of a ak n he ame proeng un, whn a me nerval. I j y jk y jk 1 1 j J, 1 k KT j, 1 NT (1a) 1 I j, 1 j J, 1 NT (1b) I ' j ' I ' j ' x ' jk x ' jk y jk I j, 1 j J, 1 k < KT j, 1 NT (2a) y j(k+1) I j, 1 j J, 1 k < KT j, 1 NT (2b) y jk + y j(k+1) - 1 x jk, I j, 1 j J, 1 k < KT j, 1 NT (2) A ampagn an reh over o he nex nerval only f he la ampagn for he urren nerval n un j. Alo, f he ampagn rehed over o he nex nerval from he urren one, wll be he fr ampagn n he nex nerval. y j y jk I j, 1 j J, k = KT j, 1 NT (3a) y j y j1(+1) I j, 1 j J, 1 < NT (3b) 3.2. Campagn and Slo lengh A ampagn of a proeng ak n un j for nerval on of nb jk number of bahe of onan proeng me (p j ) and yle me ( j ) (or manenane me, m j ), he equene-dependen hangeover/e-up me (τ ' ), and onan bah ze (b j ). We norporae followng onran for he mng of ampagn and for enurng mnmum ampagn lengh (MCL j ). e Tjk Tjk pj yjk + njkj + τ ' x ' jk ', I j, 1 j J, 1 k < KT j, 1 NT e T T MCL y H( y + y ( 1) ) jk jk j jk j j I j, k KT j e e Tjk Tjk + Tj1( 1) Tj0( 1) MCLj yjk h (1 yj ) + + I j, k = KT j (4) 3.3. Operaon me We demand ha he ar me for a ampagn of ak o be zero whenever lo k no alloaed o ak. So, (4a) (4b)

4 N. Suarla and J.A. Karm T h y 1 j J, 1 k KT j, 1 NT (5) jk jk A ampagn of ak anno ar unle all of he ak, whh preede n he produ repe, have produed uffen amoun of maeral ae ha are requred by. Now, f boh and our n he ame nerval, we demand he followng. ( T + p y ) T + h (1 y ) jk j jk ' j ' k ' j ' k ( T + p y + nb ) jk j jk jk j I j, I j, 1 j, j J, σ > 0, σ < 0 ( T + p y + nb ) + h (1 y ' j' k ' j' ' j' k ' j' k ' j' ' j' k I j, I j, 1 j, j J, σ > 0, σ < Invenore max Le I (I ) denoe he nvenory of he maeral ae, I ) (6a) (6b) o I he amoun of maeral ae ououred, I up he amoun of maeral ae uppled o he uomer, and I v he afey ok volaon a he end of a nerval. We wre a balane on he nvenory of maeral ae n he orage/uppled o uomer/arry over o he nex nerval, mlar o hoe of Sundaramoorhy and Karm (2004, p.8293) Reoure All hemal plan n general and pealy hemal plan n parular requre everal oher ule and reoure for her general operaon. Thee reoure broadly nlude human, ule, wae-reamen apay, aaly, and laboraory. For h reaon, a ypal enaro n he plan ha he nal plan revewed by varou oher deparmen (manenane, proe, and laboraory). We apure h varably of produvy dependng on he avalably of reoure nb j a( mp ); nb b( u ) (7) j where, mp avalable number of human reoure for he perod, u avalable quany of eah of he ule u, and a, b are he onveron onan whh are pef o eah plan and an be alulaed baed on he experene or plan log. Le, u u monor onumpon of uly u. Gven he pef onumpon rae (μ u ) and he oal avalable amoun (U u ) of uly u for he nerval, we wre ) u = μ ( p y + nb u u j jk jk j j k u u U u 3.6. New Produ Inroduon (NPI) Followng Sundaramoorhy and Karm (2004), we defne he followng 0-1 onnuou varable 1 f un j begn ampagn of ak n he lo k of nerval for he fr me yvjk 0 Oherwe Now, ne he valdaon one-me, and happen n he begnnng of he fr ampagn of a ak of he new produ n un j. (8a) (8b)

5 Inegraed ampagn plannng and reoure alloaon n bah plan yvjk 1 I j, 1 j J (9a) k yv y yv I j, 1 j J, 1 k < KT j, 1 NT (9b) jk jk jk ' ' ' < k' To nlude he valdaon me (v j ) no our mng onran, we modfy 4a, 4b, and 6a aordngly Sraege o nlude manenane and reave hedulng The me nerval and he duraon for roune manenane are known a pror. So, we fx bnary varable n our model o perform he manenane. Our model an ealy handle unerane and revon of plan. For h, we redefne he nerval from he urren me and updae model au by fxng he urren value of varable a he nal ondon for he reved model Plannng Objeve: o and prof The mo preferred objeve n plannng proe he maxmzaon of gro prof (revenue hrough ale o of produon). Co of produon nlude proeng o (p j ), equene-dependen hangeover/leanng o ( ), manenane o (m j ), nvenory holdng o (h ), maeral prouremen o (m ), wae reamen/dpoal o (w ), uly uage o (u u ), lo for delayng order delvery (d ), and a penaly (p ) for he volaon of afey ok lm. Le υ denoe he revenue per un ale of maeral ae. Thu, up max NGP = υ I o (10) Th omplee our model (SK plannng, eq and few oher onran) for operaonal plannng. 4. Model Evaluaon and Reul We preen a ae udy from a mulprodu pealy hemal plan, o demonrae he performane of our model. Our ae udy nvolve 13 ak (9 proe ak, 3 manenane ak), 13 maeral ae (m1 m13), 3 un (j1 j3), 25 operaor, and 1 poenal new produ (ak 7, 8, 9). We onder a plannng horzon of 6 monh. Table 1 onoldae he model and oluon a for all he enaro. For our evaluaon, we ued CPLEX 11/GAMS 22.8 on a LENOVO ompuer wh AMD Ahlon 64X2 Dual Core Proeor GHz CPU, 3.25 GB RAM, runnng Wndow XP Profeonal. Alo, we preen reul by olvng h ae udy for 4 dfferen enaro Senaro 1: 25 Operaor Th he bae enaro and nvolve hedulng of produ ampagn, manenane, equene-dependen hangeover me, and 25 avalable operaor. Th enaro doe no nlude he nroduon of he new produ Senaro 2: 19 Operaor We olve enaro 1 agan wh a lmng human reoure. In h enaro, number of operaor avalable are only 19. A expeed, here he gro prof le han he enaro 1 ( Kg v Kg). Smlarly, we an olve our model for oher lmng reoure uh a laboraory, wae reamen, par, and ule.

6 N. Suarla and J.A. Karm Senaro 3: Ouourng For h enaro, we allow ouourng for one of he nermedae (maeral - m6). We onder he bae enaro wh 25 operaor. The gro prof for h enaro Kg Senaro 4: Ouourng + NPI In h enaro, we allow boh ouourng of nermedae (maeral - m6) and he nroduon of he new produ (maeral - m13). Table 1 Model and Soluon Sa Sa Senaro 1 Senaro 2 Senaro 3 Senaro 4 25 Operaor 20 Operaor Ouourng Ouourng+NPI bnary varable onnuou varable onran non-zero MILP objeve (Kg) Relave gap (%) CPU % Relave gap [(be emae - be neger) / be neger] - repreen he upper bound for he dane beween he be neger and opmal oluon 5. Conluon and Fuure Work We uefully modfy he model of Sundaramoorhy and Karm (2004) o develop a mpler MILP model for ampagn plannng. We alo demonrae he uefulne of our model by evaluang 4 enaro for a mulprodu pealy hemal plan and a plannng horzon of 6 monh. Our model uefully apure proe varably wh lmed reoure, equene-dependen hangeover me, and everal real-lfe reoure, feaure, and enaro. We are urrenly workng on furher mprovng he oluon effeny of our model and nera furher wh a loal ompany o mprove he uly and aepably of our model by he ndury. Alo, we are developng a plannng ool ha an readly generae everal enaro and adap o he dynam requremen of varou akeholder of a ompany. Referene Corano, G., Agurre, P. A., Monagna, J. M., Mulperod degn and plannng of mulprodu bah plan wh mxed-produ ampagn. AIChE Journal 55, 9, Sefanon, H., Shah, N., Jenon, P., Mulale plannng and hedulng n he eondary pharmaeual ndury. AIChE Journal 52, 12, Sundaramoorhy, A., Karm, I. A., Plannng n pharmaeual upply han wh ouourng and new produ nroduon. Indural and Engneerng Chemry Reearh 43, Sundaramoorhy, A., Xanmng, S., Karm, I. A., Srnvaan, R., Preened n PSE-2006, July An negraed model for plannng n global hemal upply han. Suryad, H., Papageorgou, L. G., Opmal manenane plannng and rew alloaon for mulpurpoe bah plan. Inernaonal Journal of Produon Reearh 42, 2, Suarla, N., L, J., Karm, I. A., A novel approah o hedulng mulpurpoe bah plan ung un-lo. In pre AIChE Journal