Lecture Notes 2-19

# Lecture Notes 2-19 - Cycle Time CTs(M/M/1) a (\$3.; Em WM

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Unformatted text preview: Cycle Time CTs(M/M/1) a (\$3.; Em WM ‘ﬂﬁMﬂﬂe=(e;Ewmﬁa+Em WSW/MW Eel (" “:*’“’)+E[sa 0T8(GI/G/1) '= EM + Em Gee/arc) = (ﬁe) (1—2;) Em ('1 2+2”) mm WIP given throughput A, 0T5, use Littles’ Law WI P3 = ACTS. Imperfect Servers 5‘ normal service time and T is imperfect service time a = availability E T] = Elsi/a _ ' [T] = 02\$] + “(1 - a)(1 + C2[RDEIRUELS'I Expectations Eh): + b] = GElX] + b VlaX + b] = a2V[X] + 0 V X] ='E[X3] ~— ELY]2 LM=VHMM 2 E[X2] = (02[X]'+ 1mm? Imperfect Servers 6' normal service time and T is imperfect service time a = availability ' -En=emm_ [T] = Gals] +..a(lk - a)(1‘+ CzIRDElel-EB] Expectations E[aX + b] = aE[X] + b V[aX +b] 2 2V[X] +0 V X] =’E[X3] — E[X]2 [X1 e VIXI/EIXP ' EIX’J = (02[X1_+ DEIXF - EXponentiai random variable T ~ ﬁt) = Ae’“, t z 0 BIT] =1/2\, WT] = 1N, GRIT] = 1 Poisson random variable N ~ p(t) = 95%;?- t > 0 n a 0 - EfN] = A, V[T] = A, 02m] =1 Departures E Ta] = 1/). ' [le -_= 0; .—= (1 — u2)09[Ta] +u202[ , for capacity 0 = 1 0%le :04 = 1+(1 " “2)(02ETBI _ 1) + “2(02[S] _ 1)/\/5: c > 1 2@ W717 : mix/[771+ vow 37:7 WMMW . 5:, ﬁxo 1.) £312.56] M l + Va» [WEDGE Z Vii]: EZNJVMZDIJ+ meNZEZbJ ‘34 :2 I [g + “L'LEEZ’DJZ' C%:V[T .3: im + ﬁg 1 {a a if L rzg/ - ‘ I?) i WW m H ' " ' “‘ WMWV,...-rw.. ClsNonSerialExmle 2-19—2010 Data: Arrivals: 1am: 4 SCVaI: 0.750 Data: Service at WS's WSI:ES1; 0.200 SCVsl: 2.000 W82: E82: 0.400 SCVSZ: 1.500 WS3: E33: 0.420 SCVs3: 3.000 W34: ES4: 0.220 SCVs4: 1.000 Factory Analysis ws1 WSlel: 0.800 CTsl: 1.300 WIPsl: 5.200 SCle: 1.550 W82 WS2: U2: 0.800 CT32: 2.620 WIPsz: 5.240 scvaz: 1.419 WS3 WS 3:U3: 0.840 CTs3: 5.133 WIPs3: 10.266 scva3: 2.492 W84 WS4:U4: 0.880 CTs4: 2.604 WIPs4: 10.417 SCVd4: 1.216 Measures for the Factory in hrs Thsys: 4.000 CTsys: 7.781 WIPsys: 31.123 I Model ---------------------------------------------- -- Print["ClsNonSerialEx.mIe 2-19-2010"]; RealFormat[8,3}; hltegerFormatB]; [* time units hours *] lam] = 4; SCVal = 3/4; ESI = 0.20; SCVsl = 2.0; BS2 = 0.40; SCVs2 = 1.5; ES3 = 0.42; SCVs3 = 3.0; ES4 = 0.22; SCVs4 = 1.0; Print["Data: Arrivals: 1am: ",1am1," SCVaI: ",SCVaI]; Print["Data: Service at WS's"]; Print["WSl: ESI: ",ESI," SCVSI: ",SCVsl}; Print["WS2: E82: ",ESZ," SCVSZ: ",SCVs2]; Print["WS3: ES3: ",ES3," SCVS3: ",SC-Vs3]; Print["WS4: ES4: ",ES4," SCVS4: ",SCVs4]; Print[" "]; Print["Fact0ry Analysis "]; Print[" II]; Print["—---- WS 1"]; U1 = 1am1*ESI; CTsl = O.S(SCVa1+SCVsl)(Ul/(1-Ul))ES1+ESl; WIPsl =1am1*CTsl; SCle = (I—(U1"‘2))SCVa1+(U1"2)SCVs1; Print["WS 1: U1: ",U1," CTsl: ",CTsl," WIPsl: ",WIPSI," SCle: ",SCle]; Print[" "]; [* 1/2 output of WS 1 goes to WS 2 *] lam2 = (1/2)1am1; SCVa2 =(1/2)SCVd1 + 1/2; Print["----- WS 2"]; U2 = lam2*ES2; CTSZ = 0.5(SCVa2+SCV82)(U2/(1-U2))E32+ES2; WIPSZ = 1am2*CT52; SCVd2 = (1-(U2"2))SCVa2+(U2"2)SCV52; Print["WS 2: U2: ",U2," CTSZ: ",CTs2," WIPs2: ",WIPs2," SCVd2: ",SCVd2]; Print[" 11]; [* 1/2 output of WS 1 goes to WS 3 *] 1am3 = (l/2)lam1; SCVa3 = (1/2)SCle + 1/2; Print["--——- WS 3"]; U3 = lam3*ES3; CTs3 = 0.5(SCVa3+SCVs3)(U3/(1-U3))ES3+ES3; WIPs3 =1am3*CTs3; SCVd3 = (1-(U3"2))SCVa3+(U3"2)SCVs3; Print["WS 3: U3: ",U3," CTs3: ",CTs3," WIPS3Z ",WIPs3," SCVd3: ",SCVd3]; Print[ll II]; [* output of WS 2 and WS 3 goes to WS 4 *] lam4 = lam2+lam3; SCVa4 = (lam2/lam4)SCVd2+(1am3/lam4)SCVd3; Print["----— WS 4"]; U4 = lam4*ES4; CTS4 = 0.5(SCVa4+SCVs4)(U4/(1-U4))ES4+ES4; WIPS4 = lam4*CTs4; SCVd4 = (1-(U4A2))SCVa4+(U4A2)SCVs4; Print["WS 4: U4: ",U4," CTs4: ",CTs4," W]Ps4: ",WIPS4," PrintEH II]; Print["Measures for the Factory in hrs"]; CTs = CTs1+(1/2)CT52+(1/2)CT53+ CTs4; WIPsys = WIPsl+WIP32+WIPs3+ WIPs4; Thsys = Iam4; [* general way to compute CTsys *] CTsys = WIPsys/Thsys; Print["Thsys: ",Thsys," CTsys: ",CTsys," WIPsys: ",WIPsys]; SCVd4: ",SCVd4]; ...
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## This note was uploaded on 03/24/2010 for the course ISEN 316 taught by Professor Staff during the Spring '08 term at Texas A&M.

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Lecture Notes 2-19 - Cycle Time CTs(M/M/1) a (\$3.; Em WM

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