The Corrupting Influence of Variability

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1 Th Corrupting Influnc of Vribility Whn luck is on your sid, you cn do without brins. Giordno Bruno,burnd t th stk in 1600 Th mor you know th luckir you gt. J.R. Ewing of Dlls 1 Prformnc of Sril Lin Msurs: Throughput Invntory (RMI, WIP, FGI) Cycl Tim Ld Tim Customr Srvic Qulity Evlution: Comprison to prfct vlus Rltiv wights consistnt with businss strtgy? Links to Businss Strtgy: Would invntory rduction rsult in significnt cost svings? Would CT (or LT) rduction rsult in significnt comptitiv dvntg? Would TH incrs hlp gnrt significntly mor rvnu? Would improvd customr srvic gnrt businss ovr th long run? 1

2 Influnc of Vribility Vribility Lw: Incrsing vribility lwys dgrds th prformnc of production systm. Exmpls: procss tim vribility pushs bst cs towrd worst cs highr dmnd vribility rquirs mor sfty stock for sm lvl of customr srvic highr cycl tim vribility rquirs longr ld tim quots to ttin sm lvl of on-tim dlivry 3 Vribility Buffring Buffring Lw: Systms with vribility must b buffrd by som combintion of: 1. invntory. cpcity 3. tim. Intrprttion: If you cnnot py to rduc vribility, you will py in trms of high WIP, undr-utilizd cpcity, or rducd customr srvic (i.., lost sls, long ld tims, nd/or lt dlivris). 4

3 Vribility Buffring Exmpls Bllpoint Pns: cn t buffr with tim (who will bckordr chp pn?) cn t buffr with cpcity (too xpnsiv, nd slow) must buffr with invntory Ambulnc Srvic: cn t buffr with invntory (stock of mrgncy srvics?) cn t buffr with tim (violts strtgic objctivs) must buffr with cpcity Orgn Trnsplnts: cn t buffr with WIP (prishbl) cn t buffr with cpcity (thiclly nywy) must buffr with tim 5 Simultion Studis TH Constrind Systm (push) r, c B(1) t (1), c (1) B() t (), c () B(3) t (3), c (3) B(4) t (4), c (4) Infinit rw mtrils WIP Constrind Systm (pull) t (1), c (1) B() t (), c () B(3) t (3), c (3) B(4) t (4), c (4) r = rrivl rt c t ( i) = ffctiv procss tim t sttion i c ( i) = ffctiv CV t sttion i = CV of intrrrivl tims B( i) = buffr siz in front of sttion i 6 3

4 Vribility Rduction in Push Systms Cs t(i), i = 1,, 4 (min) t(3) (min) c(i), i = 1-4 (unitlss) TH (j/min) CT (min) bst cs WIP buffr cpcity buffr rducd vribility Nots: r = 0.8, c = c (i) in ll css. B(i) =, i = 1-4 in ll css. Obsrvtions: TH is st by rls rt in push systm. Incrsing cpcity (r b ) rducs nd for WIP buffring. Rducing procss vribility rducs WIP for sm TH, rducs CT for sm TH, nd rducs CT vribility. WIP (jobs) σ CT (min) Commnts 7 Cs t(i), i = 1,,4 (min) Vribility Rduction in Pull Systms t(3) (min) c(i), i = 1-4 (unitlss) B(3) (jobs) TH (j/min) CT (min) WIP (jobs) σ CT (min) Nots: Sttion 1 pulls in job whnvr it bcoms mpty. B(i) = 0, i = 1,, 4 in ll css, xcpt cs 6, which hs B() = 1. Commnts bst cs plin JIT inv buffr vr rduction inv buffr + vr rduction non-bottlnck buffr 8 4

5 Vribility Rduction in Pull Systms (cont.) Obsrvtions: Cpping WIP without rducing vribility rducs TH. WIP cp limits ffct of procss vribility on WIP/CT. Rducing procss vribility incrss TH, givn sm buffrs. Adding buffr spc t bottlnck incrss TH. Mgnitud of impct of dding buffrs dpnds on vribility. Buffring lss hlpful t non-bottlncks. Rducing procss vribility rducs CT vribility. Conclusion: if you cn t py to rduc vribility now, you will py ltr with lost throughput, wstd cpcity, infltd cycl tims, xcss invntory, long ld tims,or poor customr srvic! 9 Vribility from Btching VUT Eqution: CT dpnds on procss vribility nd flow vribility Btching: ffcts flow vribility ffcts witing invntory Conclusion: btching is n importnt dtrminnt of prformnc 10 5

6 Procss Btch Vrsus Mov Btch Ddictd Assmbly Lin: Wht should th btch siz b? Procss Btch: Rltd to lngth of stup. Th longr th stup th lrgr th lot siz rquird for th sm cpcity. Mov (trnsfr) Btch: Why should it qul procss btch? Th smllr th mov btch, th shortr th cycl tim. Th smllr th mov btch, th mor mtril hndling. Lot Splitting: Mov btch cn b diffrnt from procss btch. 1. Estblish smllst conomicl mov btch.. Group mov btchs of lik fmilis togthr t bottlnck to void stups. 3. Implmnt using bcklog. 11 Procss Btching Effcts Typs of Procss Btching: 1. Sril Btching: procsss with squnc-dpndnt stups btch siz is numbr of jobs btwn stups btching usd to rduc loss of cpcity from stups. Prlll Btching: tru btch oprtions (.g., ht trt) btch siz is numbr of jobs run togthr btching usd to incrs ffctiv rt of procss 1 6

7 Procss Btching Procss Btching Lw: In sttions with btch oprtions or significnt chngovr tims: Th minimum procss btch siz tht yilds stbl systm my b grtr thn on. As procss btch siz bcoms lrg, cycl tim grows proportionlly with btch siz. Cycl tim t th sttion will b minimizd for som procss btch siz, which my b grtr thn on. Bsic Btching Trdoff: WIP vrsus cpcity 13 Sril Btching Prmtrs: k = sril btch siz (10) t = tim to procss singl prt (1) s = tim to prform stup (5) c c = CV for btch (prts + stup) (0.5) r = rrivl rt for prts (0.4) = CV of btch rrivls (1.0) r,c k t s stup t 0 Tim for btch: t = kt + s (t = 15) forming btch quu of btchs 14 7

8 q Procss Btching Effcts (cont.) Arrivl of btchs: r /k (0.4/10 = 0.04) Utiliztion: u = (r /k)(kt + s) = r (t + s/k ) (0.4(5/10 + 1) = 0.6) For stbility: u < 1 implis sr (5.0)(0.4) k > or ( k > = 3.33) 1 tr 1 (1.0 _(0.4) minimum btch siz rquird for stbility of systm Procss Btching Effcts (cont.) CT Avrg quu tim t sttion: c + c u = t = 1 u ( ) ( ) ( )( ) Avrg cycl tim dpnds on mov btch siz: Mov btch = procss btch Mov btch = 1 CT CT split non split = CT + t q = CT = = q 15 = s + kt k + 1 = CTq + s + t = (1.0) = Not: w ssum rrivl CV of btchs is c rgrdlss of btch siz n pproximtion... Not: splitting mov btchs rducs wit for btch tim. 16 8

9 Cycl Tim vs. Btch Siz 5 hr stup Cycl Tim (hrs) Optimum Btch Sizs Btch Siz (jobs/btch) No Lot Splitting Lot Splitting 17 Cycl Tim vs Btch Siz.5 hr stup Optimum Btch Sizs Btch Siz (jobs/btch) 18 9

10 Stup Tim Rduction Whr? Sttions whr cpcity is xpnsiv Excss cpcity my somtims b chpr Stps: 1. Extrnliz portions of stup. Rduc djustmnt tim (guids, clmps, tc.) 3. Tchnologicl dvncmnts (hoists, quick-rls, tc.) Cvt: Don t count on cpcity incrs; mor flxibility will rquir mor stups. 19 Prlll Btching Prmtrs: k = prlll btch siz (10) c c t = tim to procss btch (90) = CV for btch (1.0) r = rrivl rt for prts (0.05) = CV of btch rrivls(1.0) B = mximum btch siz (100) k 1 1 Tim to form btch: W = r r,c k t ((10 1)/)(1/0.005) = 90) Tim to procss btch: t = t (t = 90) forming btch quu of btchs 0 10

11 Prlll Btching (cont.) Arrivl of btchs: r /k (0.05/10 = 0.005) Utiliztion: u = (r /k)(t) ((0.005)(90) = 0.45) For stbility: u < 1 implis k > r t or ( k > (0.05)(90) = 4.5) minimum btch siz rquird for stbility of systm... 1 Prlll Btching (cont.) Avrg wit-for-btch tim: k WT = = = r btch siz ffcts both wit-for-btch tim nd quu tim Avrg quu plus procss tim t sttion: + + CT = ( )( ) + = ( )( ) c / k c u t t = u Totl cycl tim: CT + WT = =

12 Cycl Tim vs. Btch Siz in Prlll Oprtion Totl Cycl Tim quu tim du to utiliztion wit for btch tim N b Optimum Btch Siz B 3 Mov Btching Mov Btching Lw: Cycl tims ovr sgmnt of routing r roughly proportionl to th trnsfr btch sizs usd ovr tht sgmnt, providd thr is no witing for th convync dvic. Insights: Bsic Btching Trdoff: WIP vs. mov frquncy Quuing for convync dvic cn offst CT rduction from rducd mov btch siz Mov btching intimtly rltd to mtril hndling nd lyout dcisions 4 1

13 Mov Btching Problm: Two mchins in sris First mchin rcivs individul prts t rt r with CV of c (1) nd puts out btchs of siz k. First mchin hs mn procss tim of t (1) for on prt with CV of c (1). Scond mchin rcivs btchs of k nd put out individul prts. How dos cycl tim dpnd on th btch siz k? k r,c (1) t (1),c (1) t (),c () singl job btch Sttion 1 Sttion 5 Mov Btching Clcultions Tim t First Sttion: Avrg tim bfor btching is: c (1) + c (1) u(1) t (1) + t(1) 1 u(1) Avrg tim forming th btch is: k 1 1 k 1 = t (1) r u(1) rgulr VUT qution... first prt wits (k-1)(1/r ), lst prt dosn t wit, so vrg is (k-1)(1/r )/ Avrg tim spnt t th first sttion is: c (1) + c (1) u(1) k 1 CT(1) = t (1) + t(1) + t (1) 1 u(1) u(1) k 1 = CT(1, no btching) + t (1) u(1) 6 13

14 Mov Btching Clcultions (cont.) Output of First Sttion: Tim btwn output of individul prts into th btch is t. Tim btwn output of btchs of siz k is kt. Vrinc of introutput tims of prts is c d (1)t, whr c (1) = (1 u(1) ) c (1) + u(1) c (1) d Vrinc of btchs of siz k is kc d (1)t. SCV of btch rrivls to sttion is: kcd (1) t c () = k t cd (1) = k bcus c d (1)=σ d /t by df of CV bcus dprturs r indpndnt, so vrincs dd vrinc dividd by mn squrd... 7 Mov Btching Clcultions (cont.) Tim t Scond Sttion: Tim to procss btch of siz k is kt (). Vrinc of tim to procss btch of siz k is kc ()t (). SCV for btch of siz k is: kc () t () c () = k t () k Mn tim spnt in prtil btch of siz k is: k 1 t () So, vrg tim spnt t th scond sttion is: cd (1) / k + c () / k u() k 1 CT() = kt () + t () + t () 1 u() VUT qution to comput quu tim of btchs... k 1 = CT(, no btching) + t () indpndnt procss tims... first prt dosn t wit, lst prt wits (k-1)t (), so vrg is (k-1)t ()/ 8 14

15 Mov Btching Clcultions (cont.) Totl Cycl Tim: k CT( btching) = CT(no btching) + 1 k () + 1 t 1 t ( ) u() 1 () = CT(no btching ) + k 1 t 1 + ( ) t u() 1 Insight: Cycl tim incrss with k. Infltion trm dos not involv CV s infltion fctor du to mov btching Congstion from btching is mor bd control thn rndomnss. 9 Assmbly Oprtions Assmbly Oprtions Lw: Th prformnc of n ssmbly sttion is dgrdd by incrsing ny of th following: Numbr of componnts bing ssmbld. Vribility of componnt rrivls. Lck of coordintion btwn componnt rrivls. Obsrvtions: This lw cn b viwd s spcil instnc of vribility lw. Numbr of componnts ffctd by product/procss dsign. Arrivl vribility ffctd by procss vribility nd production control. Coordintion ffctd by schduling nd shop floor control

16 Attcking Vribility Objctivs rduc cycl tim incrs throughput improv customr srvic Lvrs rduc vribility dirctly buffr using invntory buffr using cpcity buffr using tim 31 Cycl Tim Dfinition (Sttion Cycl Tim): Th vrg cycl tim t sttion is md up of th following componnts cycl tim = mov tim + quu tim + stup tim + procss tim + wit-to-btch tim + wit-in-btch tim + wit-to-mtch tim dly tims typiclly mk up 90% of CT Dfinition (Lin Cycl Tim): Th vrg cycl tim in lin is qul to th sum of th cycl tims t th individul sttions lss ny tim tht ovrlps two or mor sttions. 3 16

17 Rducing Quu Dly CT q = V U t c + c u 1 u Rduc Vribility filurs stups unvn rrivls, tc. Rduc Utiliztion rrivl rt (yild, rwork, tc.) procss rt (spd, tim, vilbility, tc) 33 Rducing Btching Dly CT btch = dly t sttions + dly btwn sttions Rduc Procss Btching Optimiz btch sizs Rduc stups Sttions whr cpcity is xpnsiv Cpcity vs. WIP/FT trdoff Rduc Mov Btching Mov mor frquntly Lyout to support mtril hndling (.g., clls) 34 17

18 Rducing Mtching Dly CT btch = dly du to lck of synchroniztion Rduc Vribility High utiliztion fbriction lins Usul vribility rduction mthods Improv Coordintion schduling pull mchnisms modulr dsigns Rduc Numbr of Componnts product rdsign kitting 35 Incrsing Throughput TH = P(bottlnck is busy) bottlnck rt Rduc Blocking/Strving buffr with invntory (nr bottlnck) rduc systm dsir to quu CT q = V U t Incrs Cpcity dd quipmnt incrs oprting tim (.g. spll brks) incrs rlibility rduc yild loss/rwork Rduc Vribility Rduc Utiliztion Not: if WIP is limitd, thn systm dgrds vi TH loss rthr thn WIP/CT infltion 36 18

19 Improving Customr Srvic LT = CT + z σ CT Rduc Avrg CT quu tim btch tim mtch tim Rduc CT Visibl to Customr dlyd diffrntition ssmbl to ordr stock componnts Rduc CT Vribility gnrlly sm s mthods for rducing vrg CT: improv rlibility improv mintinbility rduc lbor vribility improv qulity improv schduling tc 37 Cycl Tim nd Ld Tim CT = 10 σ CT = CT = 10 σ CT = Cycl Tim in Dys 38 19

20 Dignostics Using Fctory Physics Sitution: Two mchins in sris; mchin is bottlnck c = 1 Mchin 1: t0 = 19min c = MTTF = 48 hr MTTR = 8 hr Mchin : t = min c = 1 MTTF = 3.3 hr MTTR = 10 min Spc t mchin for 0 jobs of WIP Dsird throughput.4 jobs/hr, not bing mt Dignostic Exmpl (cont.) Proposl: Instll scond mchin t sttion Expnsiv Vry littl spc Anlysis Tools: c + c u CTq 1 u c = u c + (1 u d Anlysis: Ask why fiv tims... Stp 1: At.4 job/hr CT q t first sttion is 645 minuts, vrg WIP is 5.8 jobs. CT q t scond sttion is 89 minuts, vrg WIP is 35.7 jobs. Spc rquirmnts t mchin r violtd! t ) c VUT qution propogtion qution 40 0

21 Dignostic Exmpl (cont.) Stp : Why is CT q t mchin so big? Brk CT q into CT q c + c u 1 u t = Th 3.11 min trm is smll. Th 1. corrction trm is modrt (u 0.944) Th 3.16 corrction is lrg. ( 316. )( 1. )( 311. min) Stp 3: Why is th corrction trm so lrg? Look t componnts of corrction trm. c = 1.04, c = 5.7. Arrivls to mchin r highly vribl. 41 Dignostic Exmpl (cont.) Stp 4: Why is c to mchin so lrg? Rcll tht c to mchin quls c d from mchin 1, nd cd = u c + (1 u ) c = (0.887 )(6.437) + ( )(1.0) = 5.7 c t mchin 1 is lrg. Stp 5: Why is c t mchin 1 lrg? Effctiv CV t mchin 1 is ffctd by filurs, c = c 0 mr + A(1 A) t 0 = = 6.43 Th infltion du to filurs is lrg. Rducing MTTR t mchin 1 would substntilly improv prformnc. 4 1

22 Procot Cs Sitution Problm: Currnt WIP round 1500 pnls Dsird cpcity of 3000 pnls/dy Typicl output of 1150 pnls/dy Outsid vndor bing usd to mk up slck Proposl: Expos is bottlnck, but in cln room Expnsion would b xpnsiv Suggstd ltrntiv is to dd bk ovn for touchups 43 Procot Cs Lyout IN Lodr Cln Cot 1 Cot Unlodr Unlodr Bk Touchup D&I Inspct Dvlop Lodr Mnufcturing Inspct Expos Cln Room OUT 44

23 Procot Cs Cpcity Clcultions Mchin Nm Procss or Lod Tim (min) Std Dv Procss Tim (min) Convyor Trip Tim (min) Numbr of Mchins MTTF MTTR Avil Stup Tim Rt (p/dy) Tim (min) Cl n Cot Cot Expos Dvlop Inspct Bk MI Touchup r b =,879 p/dy T 0 = 54 min = 0.46 dys W 0 = r b T 0 = 1,334 pnls 45 Procot Cs Bnchmrking TH Rsulting from PWC with WIP = 37,400: TH w = r w + W0 1 b 1,500 =,879 = 1,54 1, ,334 1 Highr thn ctul TH Conclusion: ctul systm is significntly wors thn PWC. Qustion: wht to do? 46 3

24 Procot Cs Fctory Physics Anlysis 1) Expos hs highst utiliztion: incrs cpcity vi brk splling ) Expos hs high V cofficint (nd limitd room for WIP): som is du to oprtor vribilty implmnt trining progrm mor is du to rrivl vribility look t cotr lin 3) Cotr lin hs long, infrqunt filurs: mintin fild rdy rplcmnts 47 Procot Cs Outcom TH (pnls/dy) Bst Cs 700 "Good" Rgion 400 Aftr Prcticl Worst Cs "Bd" Rgion 100 Bfor Worst Cs WIP (pnls) 48 4

25 Corrupting Influnc Tkwys Vrinc Cuss Congstion: mny sourcs of vribility plnnd nd unplnnd Vribility nd Utiliztion Intrct: congstion ffcts multiply utiliztion ffcts r highly nonlinr importnc of bottlnck mngmnt 49 Corrupting Influnc Tkwys (cont.) Vribility Propgts: flow vribility is s disruptiv s procss vribility non-bottlncks cn b mjor problms Vribility Must b Buffrd: invntory cpcity tim 50 5

Errata for Second Edition, First Printing

Errata for Second Edition, First Printing Errt for Scond Edition, First Printing pg 68, lin 1: z=.67 should b z=.44 pg 71: Eqution (.3) should rd B( R) = θ R 1 x= [1 G( x)] pg 1: Eqution (.63) should rd B( R) = x= R = θ ( x R) p( x) R 1 x= [1