A NEW METHOD OF FMS SCHEDULING USING OPTIMIZATION AND SIMULATION

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1 A NEW METHD F FMS SCHEDULING USING PTIMIZATIN AND SIMULATIN Ezedeen Kodeekha Deparmen of Producon, Informacs, Managemen and Conrol Faculy of Mechancal Engneerng udapes Unversy of Technology and Econcs E-mal: ezo@yahoo.c KEYWRDS: FMS schedulng, CIM, Convenonal schedulng mehods, reak and uld mehod. ASTRACT Nowadays, n modern manufacurng he rend s he developmen of Cpuer Inegraed Manufacurng, CIM echnologes whch s a cpuerzed negraon of manufacurng acves (Desgn, Plannng, Schedulng and Conrol) ha o produce rgh producs rgh a rgh me o reac quckly o he global cpeve marke demands. The producvy of CIM s hghly dependng upon he schedulng of Flexble Manufacurng Sysem (FMS). Shorng he makespan leads o decreasng machnes dle me whch resuls mprovemen CIM producvy. Convenonal mehods of solvng schedulng problems such as heursc mehods based on prory rules sll resul schedules, semes, wh sgnfcan dle mes. To reduce hese, he presen paper proposes a new hgh qualy schedulng mehod. Ths mehod uses mul-objecve opmzaon and smulaon. The mehod s called reak and uld Mehod, M. The M procedure has hree sages, n he frs uldng sage; he seps are o buld up se schedules usng any schedulng mehods for example: heursc ones whch are esed by smulaon. In he second reakng sage, opmum szes of baches are deermned. In he fnal Rebuldng sage, he mos proper schedule s seleced usng smulaon. The goal of use of smulaon whn manufacurng schedulng s o acheve he wo followng objecves: frs s he vsual represenaon of manufacurng process behavor of a chosen schedule. The second s esng and valdaon of schedules o selec he mos proper schedule wha can be successfully mplemened. There are wo-objecves acheved by M o he gven smple example, one s mproved producvy by 3.9% and he oher s meeng delvery daes. The mehod produces a new drecon of manufacurng schedulng usng dfferenal calculus, gves a new resuls and new nformaon for solvng smple manufacurng schedulng problem. INTRDUCTIN Flexble Manufacurng Sysem (FMS) s an auaed manufacurng sysem whch consss of group of auaed machne ools, nerconneced wh an auaed maeral handlng and sorage sysem and conrolled by cpuer o produce producs accordng o he rgh schedule. Manufacurng schedulng heory s concerned wh he rgh allocaon of machnes o operaons over me. FMS schedulng s an acvy o selec he rgh fuure operaonal program and/or dagram of an acual me plan for allocang cpeve dfferen demands of dfferen producs, delvery daes, and/or sequencng hrough dfferen machnes, operaons, and roungs ha for cbnaon he hgh flexbly of job shop ype wh hgh producvy of flow-shop ype and meeng delvery daes. FMS Schedulng sysem s one of he mos mporan nformaon-processng subsysems of CIM sysem. The producvy of CIM s hghly dependng upon he qualy of FMS schedulng. The basc work of scheduler s o desgn an opmal FMS schedule accordng o a ceran measure of performance, or schedulng creron. Ths paper focuses on producvy orened-makespan crera. Makespan s he me lengh fr he sarng of he frs operaon of he frs demand o he fnshng of he las operaon of he las demand. Convenonal mehods of solvng schedulng problems such as heursc mehods based on prory rules (FIF, SPT, SLACK ) deermned he correspondng schedule bu usually, sll havng dle mes. To reduce hese and mprovng CIM producvy, hs paper presens a new mehod so called reak and uld Mehod, M. The paper can be classfed no forh pars as follow:-frs Par: Schedulng usng M. Second Par: Applcaon of M o he smple schedulng problems. Thrd Par: Concluson, and References. SCHEDULING USING M M s a mul-crera opmzaon and smulaon approach n whch he opmum schedule of asks of Hgh Number of Pars (HNP) are dvded no opmum subseres (baches), hen rebuld he schedule agan and overlappng producon can be realzed a ceran

2 condon and esed usng one of smulaon mehods (e.g.: Taylor ED). M has wo-objecves for hs suaon, one s a hgher producvy and he second s meeng delvery daes. M Procedure The M procedure s consss of he followng hree sages:-. uldng Sage In he buldng sage, he seps are o bul up an opmum schedule usng any schedulng mehods such as heursc mehod and esed by smulaon Schedulng Problem The shop consdered n hs paper conss of -dfferen ndependen machnes M, M of load, L, L respecvely wll process demands, d, d of uns,,.each demand processed by operaons, each operaon consss of run me and se up me δ wh precedence relaonshp precedes and he processng mes are P, P respecvely, The due dae of d and d s D. Daa s summarzed a demand able n fg.. The bjecve s o deermne he bes schedule usng producvy crera. Table () Demand Table. d P d d P P L L L S Heursc Schedulng Mehods A heursc s a rule of humb procedure ha deermnes a good-enough, sasfacory and feasble soluon whn ceran consrans, bu no necessarly guaranees he bes or opmal, soluon o a problem. A good heursc s generally whn 0% of opmaly, he amoun of error s no known and degree of opmaly s no known. Heursc mehods based on prory rules for job-shop schedulng problem are no a convenence bu a necessy for selecng whch job s sared frs on ceran machne. Se of he rules used o schedulng problems are FIF (Frs In Frs u), SPT (Shores Processng Tme) and SLACK. rules. n hs paper he number of schedules o be evaluaed s Π = n!= schedule, where, n: number of s demands =. The prory rules used n he presen paper are FIF and SPT as followng:- a) SPT rule Table () SPT Table M M s f s f 0 f L L T b) FIF rule Table (3) FIF Table M M s f s f 0 f Noaons L L T : (peraon me), o (operaon number), Mahemacal Model m (machne number), (demand number), The mahemacal model for he formulaed problem s : run me, bjecve Funcon: Mnmze r: ready me, s: sar me, f: flow me, S : Schedule T = δ.() me, Π s :Number of schedules, T: Makespan Subjec o L max :boleneck machne load, η :Schedule Producvy, Index, η R :Schedule Producvy Rae, L T D S Assumpons T = L max +. No Cancellaon. No reakdown. No Preempon., where L max = max (L, L) = L. perang cos s consan. T = L max + 3. δ s consan, r =0 Snce, L max = consan Demand char as n fg. (), shows how much me T T requred o processng each demand P, P,. Load char as n fg. () Shows how much me o be loadng each T = T = L max +, L max = + = + machne L, L requred o produce he wo demands. δ Soluon As n fg. (3), Gan char clearly dsplay ha he schedule s sasfed accordng o he precedence relaonshp bu s nfeasble schedule due o he conflc of overload. T = δ () The makespan of FIF (T ) T s beer han of SPT (T ) bu s no he opmal.

3 d d P Fg. ()Demand char P TIME M D S M Fg.()Load char L L TIME M D S M Fg.(3) Gan char TIME M M δ δ L D S T Fg.(4)SPT Gan char f TIME M M TIME δ δ L D S T Fg.(5) FIF Gan char f M δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ D S M Fg. (6) M Gan char /q TIME T 3

4 The soluon of equaon () can be esed by one of smulaon mehods (e.g.: Taylor ED) as shown n fg.(7 ). Then, buld up he proper desgn of schedule model, bu, sll here s dle me n machne and alsot D. To mnmze (opmze) T and o mee he delvery dae, he followng breakng sage of producvy crera orened-makespan s used.. reakng Sage y dvdng he boleneck machne mes (L ) no subdvson of baches of me q wh oal se up mes of oleneck machne, (qδ), he las sub-dvson of bach of me of las operaon me a dle machne s he Schedule lack ox ( /q), as shown n he Gan char fg.(6).the purpose of breakng sage s o deermne he schedule breakeven pon usng breakeven analyss. The schedule breakeven pon s defned as he opmal subdvson quany of me a whch he oal se mes (qδ) of oleneck machne s equal o he Schedule lack ox ( /q),a he schedule breakeven pon he makespan s a mnmum and he schedule producvy rae s a maxmum. Deermnaon of Schedule reakeven Pon T 3 = + Snce, /q (3) are consan, +qδ + and Deermnaon of pmum Uns Per ach To fnd ou (un/bach) and L whch s he number of uns of las bach (un/bach of me). mus be deermned frs, he Number of baches of me per operaon of demand hrough machne m, q (bach of me), Lengh of bach me (h/bach of me) τ, and : τ L : Las bach lengh (h/bach) also can be specfy he me requred o process one un of bach of demand hrough ceran machne, α (mn/un). Approxmaon can be done f requred. The followng formula are used. q = τ = / q /( + ), q, τ = / q, q = τ L = L q /( + / q = / q, = / q, = α = τ /, α = τ /, L α = τ / ) L 3. Rebuldng Sage In hs sage he mos proper schedule s seleced usng smulaon. The smulaon model rebuld up a gan accordng o he new condon due o he effec of M ha o desgn he fnal Smulaon Model. Correcve acons could be aken f necessary, hen, esng and valdaon of schedules guaraneeng o selec he mos proper schedule and can be successfully mplemened. =T 3 - ( + ) and called Schedule reak me Applcaon of M =T 3 - ( + )= qδ + /q, (4) Takng he dervave of w.r. q and equalng zero uldng Sage = δ - = 0 q = As shown n demand able fg,(4) =000 h, =800 h,.. (5) q q δ =900 h, =700 h, δ =.75 h, =00 un, = 540 un, D=000 h = δ (6) Table (4) Demand Table s called Schedule reakeven Pon T 3 = + + δ If T 3 T and T 3 D, hen, T 3 = T = + + (7) η =( T / T ) η R =( η -)00 (8) I concluded ha as he number of sub-dvson of baches q ncreases, E.(3), he oal me(qδ) ncrease, he Schedule black box( /q) decrease.(4), makespan decrease and schedule producvy rae ncrease.(8) unl ceran pon whch s schedule breakeven pon,e.(6) a whch he makespan T s mnmum and schedule producvy rae η R s maxmum. T d P d d L Soluon L max =L =903.5h SPT: T = h FIF: T =603.5 h T T T = T u, T D. so, he followng breakng sage mus be done.

5 Fg.(7) Smulaon Model Value Schedule Producvy Dagram 70 3, No. of cases No. Sub-Dvson Sch. lack ox Sch. Producvy Rae Toal Seup Tme Sch. reak Tme Fg.(8) Schedule Producvy Dagram

6 reakng sage Deermnaon of Schedule Producvy Rae q = 0 (bach of me), T 3 =973.5 h R T 3 T, T 3 D T 3 = T =973.5 h, = 70 h η = 3.9 % The schedule breakeven pon (70h)a whch he Mnmum makespan T(973.5h) and he maxmum schedule producvy rae η R are(3.9%) as shown n fgure (8). Deermnaon of pmum Uns Per ach of Tme q =0 (bach of me), q = 9 (bach of me) τ =00h/bach, τ =00h/bach, τ L =35 h/bach = 0 (un / bach of me), =60 (un/ bach of me), L = 0(un/bach of me) α =50 mn/un, α = 70 mn/un, mn/un α L =7.5 Rebuldng Sage Accordng o he prevous fgures of he breakng sage, could be desgn he opmum schedule of such problem and esed by smulaon CNCLUSIN The sub-dvson of baches s a powerful ool for mprovng he qualy of FMS schedulng. In he presen paper, for he smples case (wo machne group, wo par ypes), a new mehod s proposed o use he above approach. The proposed M (reak and uld Mehod) provde soluon for he problem. The resuls clearly show he effecveness of he gven approach. Fuure research should be dreced o generalze he mehod o mulpar, mul machne group cases. REFERENCES CARRIE A Smulaon of Manufacurng Sysems, PP. 48. Wley CHASE, AQUILAN Producon and peraon Managemen : A lfe cycle approach, PP 853.Irwn FRENCH S. 98. Sequencng and schedulng: An nroducon o he mahemacs of he Job-Shop, Wley, PP. 45. GRVER P., 987, Auaon, Producon Sysems, and Cpuer Inegraed Manufacurng, PP.808.Prence- Hall HARLD T.,.JHN A., LIVER S., 975. Manufacurng rganzaon and Managemen, PP. 588.Prenc-Hall JACK R, 99, The Managemen f peraons: Concepual Emphass, PP 77.Wley PAUL LMA N., 978, Managemen-A Quanave Perspecve, PP 594.Coller Machllan SML J., 00, Hybrd Dynamcal Approach makes FMS schedulng more Effecve, PERIDICA PLYTECHNIC SER. MECH. ENG. VL.45, N..PP udapes TAKESHI YAMADA, RYHEI NAKAN, Job- Shop Schedulng, IEE Conrol Engneerng Seres 55,Genec Algorhms n Engneerng Sysems, Eded by A.M.S. Zalza and p.j. Flemng, Chaper 7, PP THMAS M., RERT A., 98, Inroducon o Managemen Scence, PP 764.Prenc-Hall U. REMLD,..NNAJI,A. STRR, 993, Cpuer Inegraed Manufacurng and Engneerng, PP.640.Addson-Wesley.