Inventory Management MILP Modeling for Tank Farm Systems

Transcription

1 2 h European Sympoum on Compuer Aded Proce Engneerng ESCAPE2 S. Perucc and G. Buzz Ferrar (Edor) 2 Elever B.V. All rgh reerved. Invenory Managemen MILP Modelng for Tank Farm Syem Suana Relva a Ana Paula F.D. Barboa-Póvoa, a Henrque A. Mao b a CEG-IST, UTL, Av. Rovco Pa 49-, Lbon, Porugal, uanacr@.ul.p apovoa@.ul.p b CPQ, IST, UTL, Av. Rovco Pa 49-, Lbon, Porugal,henrmao@.ul.p Abrac Proce ndure face complex problem when dealng wh he opmzaon of producon, conrol and operaonal ak. Whle producon and conrol are wdely covered, he de operaon relaed wh logc upply and demand are uually underemaed, nce hey are no core acve. However, her conrbuon o bune effcency and margn maxmzaon crucal, becaue hey guaranee proce npu and oupu a he dered quane mng and qualy. One of hee acve rele on nvenory managemen. Th paper preen MILP model ha can be negraed wh oher proce model whch repreen a flexble orage ank farm. Under h general ank vew, dfferen logc rucure can be modeled: proce feedng ank nermedae ank or a fnal produc ank. The propoed MILP model eed for wo example problem. Keyword: Tank, Invenory Managemen MILP, flexble model. Inroducon Supply chan nvenory managemen a crcal ue o addre n order o enhance ervce level, compeve advanage and co reducon, beng a common ource of mmanagemen (Lee and Bllngon, 992 and You and Gromann, 28). Gven he benef relaed wh nvenory managemen proce ndure hould gve more focu o logc ue when degnng and plannng her upply chan. Invenory managemen polce are rongly developed for dcree produc (e.g. componen par) eher accounng for he orderng or for nvenory managemen. In he fr cae here are polce from radonal approache a he Economc Order Quany o alor-made mehodologe. Invenory managemen baed on warehoue opmzaon approache ha ake no accoun flow and co mnmzaon. On he oher hand, for connuou quane ored n ank farm he problem raher complex o repreen model and opmze. Th due o he hgh dependency ha ex beween nvenory, proce produc pecfce and requremen whch may lead o complex model o be coupled o he complee proce opmzaon model. The publhed leraure on nvenory managemen for proce ndure appear on wo drecon: ) orage polce appled o operaon chedulng model uch a zero wa orage, unlmed nermedae orage, non-nermedaed orage, fne nermedae orage (a reved n Mendez e al., 26) or ung mple capacy lmaon (akng a example upply chan plannng model) and ) operaon pecfc model uch a he one propoed for he peroleum ndury (Relva e al. 26). The preen work develop a ank farm chedulng model, where nvenory managed under common conran relaed wh proce ndure.

2 S. Relva e al. 2. Problem Saemen The man yem deal n h work a common nvenory ank farm ha can be locaed eher n a chemcal plan or oher upply chan node, uch a drbuon cener or por. For he purpoe of he paper, we wll conder ha he ank farm conneced o a upply yem ha provde npu and o a demand yem where oupu are uppled, a preened n Fgure. A ank farm requre ome operaon managemen relaed o ank ervce, orage capacy, elng perod qualy ak and fulfllng demand. The npu requred are produc quane and mng of arrval whle oupu are he produc demand and mng. Supply Syem Demand Syem Fgure Mulproduc ank farm yem The ank farm conneced hrough nernal lne o he upply and demand yem. I wll be condered ha only one produc receved a a gven nan. A any pon h aumpon can be levered. On he oher hand, he demand yem ha an ndependen delvery chedule per produc. I condered ha each ank a a fxed ervce,.e., he allocaon of produc o ank a problem daa, whch a common procedure for chemcal produc. The ank can ore eher lqud produc or gae. For h end, he operang volume of each ank aumed a operang capacy. For h yem, requred o deermne he chedulng of orage acve a he ank farm ha mnmze produc mxng wh orgn n dfferen recevng bache. Oher objecve can be mplemened for pecfc problem yem. 3. Invenory Tank Farm MILP Modelng A he ank level, ome uual procedure mply ha each ank, a any nan can only have a maxmum of one acve connecon,.e., npu from he upply yem and oupu for he demand yem. For h reaon, defned a roaon cheme he procedure ha perm knowng, durng he curren me horzon and a any me pon he chedule of ank ae for each ank of each produc. The ae are defned from he ank operaonal cycle, whch repreened n Fgure 2. Each ank mu accomplh h cycle n normal operaon a he ank farm. I ar o be flled up unl he oal orage capacy reached. A h pon he elng perod carred ou o mee qualy andard. Whenever he elng perod compleed, he produc ored now avalable for clen afacon, unl he ank compleely empy. Fgure 2 - Indvdual ank operaonal cycle

3 Invenory Managemen MILP Modelng for Tank Farm Syem The modelng challenge con on he repreenaon of he dynamc ae (beng flled up or beng dcharged), he boundary ae deecon (compleely full or compleely empy) and he model flexbly. The propoed model formulaon decrbed a follow. Se: e of arrvng bache of produc T e of ank p P e of produc and S e of ank ae ( upplyng ae, r recevng ae, f full ae and e empy ae). Noe: me pon are referred o he arrval of bach o he ank farm, hu e I can eher repreen bache or me pon. Boh decrpon wll be ued hroughou he model deal. Parameer: hmax maxmum me horzon exen δ mall value, C me cale referred o he arrval of bach, D, volume of arrvng bach of produc p MD p, marke demand of produc p a me pon, Te nal elng me for produc p n orage ank TCap, ank capacy of ank of produc ID nal nvenory a ank of p produc nal ae of ank of produc Trep p, mnmum elng perod of produc p a ank. Pove varable: In volume of produc p agned o ank a me nerval, Ou volume ha uppled o fulfll marke demand of produc p from ank a me nerval, ID p,, nvenory level of produc p a ank a me nerval, Te elng me of produc p ored a ank a me nerval. Bnary varable: f ank of produc p a ae a me nerval, p,,, ba f bach of produc p agned o ank mdf f ank upple he p,, marke of produc p a me. Model Conran: p,, p, +,,, r () p, +,,, e f (2) p + p +,,,,,, ', ', >, r ' f (3) p, +, + ',, r ' f (4) p + p +,,,,,, ', ', >, r ' e (5) p, +, + ',, r ' e (6) Equaon () and (2) eablh he occurrence of mulaneou ank ae wherea equaon (3) o (6) enure how ank can ran beween ae.

4 S. Relva e al. D In In, p (7) p, ba Tcap, (8) p, Ou p MD, (9), Ou mdf Tcap, () p, Equaon (7) and (8) deermne bach agnmen o ank regardng he produc. Equaon (9) enure oupu o fulfll marke demand wherea equaon () capure wheher ank upple he marke wh produc p a me. In p, Tcap,, r () Ou p, Tcap,, (2) Equaon () and (2) enure he relaon beween ank ae and npu recepon and oupu upply. IDp, ID + In Ou, > (3) ID p, ID + In Ou, (4) ID Tcap, (5) p, Equaon (3) and (4) calculae he curren nvenory level a each ank wherea equaon (5) lm nvenory o maxmum ank capacy. ( Tcap ), f ( ), f ( ), e IDp, δ, (6) IDp, Tcap δ, (7) IDp, δ + Tcap, (8) IDp, δ Tcap,, e (9) Equaon (6) o (9) denfy nvenory level value ha allow changng o full and empy ank ae. For hee equaon a mall dfference from he nvenory boundare ued. Te p, hmax,, f (2) ( ) hmax, > f Tep, Te + C C, (2) ( ) hmax, f Te p, Te + C, (22) Te, p, Te + C C > (23) Te p Te p + C, (24),,, ( +, ), >, f ( + ),, f Te p, Trep ' (25) Te p, Trep, (26)

5 Invenory Managemen MILP Modelng for Tank Farm Syem Te p, Trep + hmax, >, (27) Te p, Trep + hmax,, (28) Equaon (2) enure ha he elng me accouned when he ank full. Equaon (2) o (24) updae he elng perod for each ank a each me nerval. Equaon (25) o (28) enure ha whenever he mnmum elng perod acheved, he ank ae can change from full o upply. mn ba I + mdf P I (29) p, p p Equaon (29) repreen he objecve funcon whch nend o mnmze he dfference beween oal number of bach agnmen o ank and he cardnaly of e I, o a o avod ha one bach agned o everal ank and, herefore, ha each ank receve everal bache before elng. The econd erm mnmze he dfference beween number of upple from dfferen ank and oal number of marke demand. Th objecve funcon relevan when produc qualy raceably mporan. 4. Implemenaon and Reul Two cenaro (S and S2) are propoed o evaluae model performance and model ze. S repreen a movaon problem wh 3 produc 3 ank per produc and arrvng bache. S2 repreen a larger problem and accoun for 5 produc 25 ank drbued by all he produc and 25 arrvng bache. S addree a me horzon of day wherea S2 ha 25 day. The model wa mplemened n GAMS 22.8, CPLEX. on an Inel Penum Core 2 Duo P94, 4 GB Ram. The objecve o oban eher he opmal oluon or a oluon n 6 (plu 2 of oluon polhng). Table ummarze he model ac and performance. Table. Model Performance S S2 Tme () Objecve funcon (OF) 3 2 OF Term 2 2 OF Term 2 Relave gap (%) Ieraon Node Connuou Varable Ineger varable Conran From able can de een how model ze ncreae wh he ze of he cenaro. Addonally, n S only wo bach pl occurred wherea for a larger problem a n S2, wo bach pl were neceary o accommodae all he ncomng produc. Regardng ank upply, n S here wa only one marke demand fulfllmen ha requred wo ank wherea n S2 h uaon occurred en me. However, a can be een, here pace for mprovemen n he model performance. Depe locang oluon n an early age of he ree earch, he lower bound mprovemen low. The relaxed oluon wa. and afer a hgh number of eraon and node exploraon, he lower bound mproved o.2976.

6 S. Relva e al. Fgure 3 repreen he nvenory profle of ank of produc P for example S2. Table 2 ummarze he monorng of h ank cycle, whch ha a capacy of 2 m 3 and a mnmum elng perod of 24 h. The dynamc and boundary ae are mached agan he nvenory profle evoluon, o a o verfy he effecvene of he model. The boundary ae only occur when he nvenory a lm and he elng perod referred o he full ae. 2 6 Invenory (m 3 ) Day Fgure 3 Invenory profle for ank of produc P, S2 Table 2. Tank cycle monorng: S2, P, ank Day Boundary ES ES ES ES ES FS FS Dynamc RS RS RS RS RS RS RS RS RS RS RS SS SS SS SS SS SS SS SS SS SS SS SS SS SS Selng 24 Inpu Invenory Oupu Concluon and Fuure Work In h paper wa preened a flexble MILP model ha can be coupled o chedulng and/or plannng model for proce ndure where lqud or ga produc mu be ored and managed under he requremen of a preceden upply yem and a demand yem ahead. The model accoun for ank farm conran uch a elng perod bu can be furher exended o accoun for oher ank farm requremen ha may decrbe oher ype of yem. A fuure work, he auhor propoe o negrae he model wh real world chedulng model for furher eng. The developmen of he model hould accoun for he opon of havng dfferen me cale for he upply and demand yem. The formulaon can alo be reved o a o become gher. Reearch on alernave yem ype requrng oher conran alo an objecve of he auhor. 6. Acknowledgemen The auhor acknowledge fnancal uppor provded by Companha Logíca de Combuíve. Reference H.L. Lee; C. Bllngon, 992, MIT Sloan Managemen Revew, v.33, 3 (Sprng), 65-73; C.A. Mendez; J. Cerda; I.E. Gromann; I. Harjunkok; M. Fahl, 26, Compuer and Chemcal Engneerng, v.3, ue 6-7, ; S. Relva; H.A. Mao; A.P.F.D. Barboa-Póvoa; J. Falho; A.S. Pnhero, 26, Ind. Eng. Chem. Re., v.45 (23), F. You; I.E. Gromann, 28, Ind. Eng. Chem. Re., v.47,