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{"sheet":"11.1","index":0,"n_rows":18,"n_cols":9,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
["Example 11.1"]
[]
["Means","job",1,2]
[null,"a",4,5]
[null,"b",5,8]
[]
["Realizations",null,{"$f":"_xll.PsiExponential(C4)","v":1.583324192729455},{"$f":"_xll.PsiExponential(D4)","v":24.877745151012114}]
[null,null,{"$f":"_xll.PsiExponential(C5)","v":0.39411372344379914},{"$f":"_xll.PsiExponential(D5)","v":7.4082794923051409}]
[]
["Sequence"," ",1,2,null,2,1]
["Completions",null,{"$f":"C7","v":1.583324192729455},{"$f":"C11+D7","v":26.46106934374157},null,{"$f":"D7","v":24.877745151012114},{"$f":"F11+C7","v":26.46106934374157}]
[null,null,{"$f":"C11+C8","v":1.9774379161732543},{"$f":"MAX(D11,C12)+D8","v":33.869348836046711},null,{"$f":"F11+D8","v":32.286024643317255},{"$f":"MAX(G11,F12)+C8","v":32.680138366761057}]
[null,null,null,null,null,null,null,null,"pct"]
[null,null,"Expected makespan",{"$f":"_xll.PsiMean(D12)","v":19.507032564900619},null,null,{"$f":"_xll.PsiMean(G12)","v":19.336401238555663},null,{"$f":"(D14-G14)/G14","v":8.8243579681583986E-3}]
[null,null,"S.D. of makespan",{"$f":"_xll.PsiStdDev(D12)","v":10.520744465512214},null,null,{"$f":"_xll.PsiStdDev(G12)","v":10.397422114297603}]
[]
["Process time means",null,{"$f":"_xll.PsiMean(C7)","v":3.9999820231311776},{"$f":"_xll.PsiMean(D7)","v":4.9999809825308059}]
["(as simulated)",null,{"$f":"_xll.PsiMean(C8)","v":5.0000386481538301},{"$f":"_xll.PsiMean(D8)","v":7.9999632257040814}]

{"sheet":"11.2","index":1,"n_rows":18,"n_cols":11,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
["Example 11.2"]
[]
["Means","job",1,2,null,null,null,null,null,"Summary ","Table"]
[null,"a",1,1,null,null,null,null,null,"b2","pct"]
[null,"b",1,{"$f":"1+SQRT(7)","v":3.6457513110645907},null,"Treat b2 as a variable",null,null,null,2.5,4.3099999999999999E-2]
[null,null,null,null,null,null,null,null,null,3,4.5699999999999998E-2]
["Realizations",null,{"$f":"_xll.PsiExponential(C4)","v":4.1767724623651512},{"$f":"_xll.PsiExponential(D4)","v":0.1574607109072749},null,null,null,null,null,3.6457513110645907,4.65E-2]
[null,null,{"$f":"_xll.PsiExponential(C5)","v":1.9245623365871429},{"$f":"_xll.PsiExponential(D5)","v":0.33213290733050566},null,null,null,null,null,4,4.6300000000000001E-2]
[null,null,null,null,null,null,null,null,null,4.5,4.5600000000000002E-2]
["Sequence"," ",1,2,null,2,1,null,null,null,"based on"]
["Completions",null,{"$f":"C7","v":4.1767724623651512},{"$f":"C11+D7","v":4.334233173272426},null,{"$f":"D7","v":0.1574607109072749},{"$f":"F11+C7","v":4.334233173272426},null,null,null,"sample size"]
[null,null,{"$f":"C11+C8","v":6.1013347989522941},{"$f":"MAX(D11,C12)+D8","v":6.4334677062827996},null,{"$f":"F11+D8","v":0.48959361823778058},{"$f":"MAX(G11,F12)+C8","v":6.2587955098595689},null,null,null,"of 100,000"]
[null,null,null,null,null,null,null,null,"pct"]
[null,null,"Expected makespan",{"$f":"_xll.PsiMean(D12)","v":6.1460053505046197},null,null,{"$f":"_xll.PsiMean(G12)","v":5.8600782569865606},null,{"$f":"(D14-G14)/G14","v":4.8792367777199613E-2}]
[null,null,"S.D. of makespan",{"$f":"_xll.PsiStdDev(D12)","v":3.9430091858652165},null,null,{"$f":"_xll.PsiStdDev(G12)","v":3.7995184547704159}]
[]
["Process time means",null,{"$f":"_xll.PsiMean(C7)","v":0.99999155299627263},{"$f":"_xll.PsiMean(D7)","v":1.0000078683219771}]
["(as simulated)",null,{"$f":"_xll.PsiMean(C8)","v":1.0000109186134625},{"$f":"_xll.PsiMean(D8)","v":3.6457547583370293}]

{"sheet":"11.3a","index":2,"n_rows":21,"n_cols":6,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Example 11.3 ",null,"Deterministic Counterpart Sequence"]
[]
["Job j",1,2,3,4,5]
["Mean A",9.94,10.14,10.15,10.3,10.45]
["StDev A",0.32,0.02,0.73,0.91,0.27]
["Mean B",10.16,10.16,10.26,10.45,10.46]
["StDev B",0.74,0.11,0.76,0.2,0.05]
[]
["Expected differences based on the comparison in Theorem 11.1."]
[null,"Calculations made in VBA from the user-defined function ExpDiff"]
[]
[null,1,2,3,4,5]
[1,{"$f":"ExpDiff(MA,MB,SA,SB,$A13,B$12)","v":0},{"$f":"ExpDiff(MA,MB,SA,SB,$A13,C$12)","v":3.2872111177088215E-2},6.2681413805503183E-3,0.16586657492656975,-3.7117112287729626E-2]
[2,-3.2872111177088215E-2,0,3.2471207904581689E-2,0.27459185380602946,4.5369547268983013E-3]
[3,-6.2681413805503183E-3,-3.2471207904581689E-2,0,0.16789135719971071,-3.7074653218112985E-2]
[4,-0.16586657492656975,-0.27459185380602946,-0.16789135719971071,0,-0.30512677672190058]
[5,3.7117112287729626E-2,-4.5369547268983013E-3,3.7074653218112985E-2,0.30512677672190058,0]
[]
["Sequence",1,2,3,4,5]
[null,null,{"$f":"INDEX($B$13:$F$17,B19,C19)","v":3.2872111177088215E-2},{"$f":"INDEX($B$13:$F$17,C19,D19)","v":3.2471207904581689E-2},{"$f":"INDEX($B$13:$F$17,D19,E19)","v":0.16789135719971071},{"$f":"INDEX($B$13:$F$17,E19,F19)","v":-0.30512677672190058}]
[{"$f":"IF(C21<0,\"stable\",\"not stable\")","v":"not stable"},"max",{"$f":"MAX(C20:F20)","v":0.16789135719971071}]

{"sheet":"11.3b","index":3,"n_rows":21,"n_cols":11,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Example 11.3 ",null,"An API-Stable Sequence"]
[null,null,null,null,null,null,null,"Calculations for Array(1,2)"]
["Job j",1,2,3,4,5,null,"StDev A2",{"$f":"C5","v":0.02},{"$f":"I3^2","v":4.0000000000000002E-4}]
["Mean A",9.94,10.14,10.15,10.3,10.45,null,"StDev B1",{"$f":"B7","v":0.74},{"$f":"I4^2","v":0.54759999999999998}]
["StDev A",0.32,0.02,0.73,0.91,0.27,null,null,null,{"$f":"J3+J4","v":0.54799999999999993},{"$f":"_xlfn.NORM.S.DIST(J7,TRUE)","v":0.48922302312558252}]
["Mean B",10.16,10.16,10.26,10.45,10.46,null,null,null,{"$f":"SQRT(J5)","v":0.74027022093286987},{"$f":"_xlfn.NORM.S.DIST(J7,FALSE)","v":0.39879670759502001}]
["StDev B",0.74,0.11,0.76,0.2,0.05,null,null,"z",{"$f":"(C4-B6)/J6","v":-2.7017161347914383E-2}]
[]
["Expected differences based on the comparison in Theorem 11.1.",null,null,null,null,null,null,null,null,{"$f":"J6*(K6+J7*K5)","v":0.28543286637615511},{"$f":"C4-J9","v":9.8545671336238456}]
[null,"Calculations made in VBA from the user-defined function ExpDiff"]
[]
[null,1,2,3,4,5]
[1,{"$f":"ExpDiff(MA,MB,SA,SB,$A13,B$12)","v":0},{"$f":"ExpDiff(MA,MB,SA,SB,$A13,C$12)","v":3.2872111177088215E-2},6.2681413805503183E-3,0.16586657492656975,-3.7117112287729626E-2,null,null,null,null,9.8874392448009338]
[2,-3.2872111177088215E-2,0,3.2471207904581689E-2,0.27459185380602946,4.5369547268983013E-3,null,null,null,null,9.8545671336238456]
[3,-6.2681413805503183E-3,-3.2471207904581689E-2,0,0.16789135719971071,-3.7074653218112985E-2,null,null,null,null,{"$f":"K13-K14","v":3.2872111177088215E-2}]
[4,-0.16586657492656975,-0.27459185380602946,-0.16789135719971071,0,-0.30512677672190058]
[5,3.7117112287729626E-2,-4.5369547268983013E-3,3.7074653218112985E-2,0.30512677672190058,0]
[]
["Sequence",4,3,2,1,5]
[null,null,{"$f":"INDEX($B$13:$F$17,B19,C19)","v":-0.16789135719971071},{"$f":"INDEX($B$13:$F$17,C19,D19)","v":-3.2471207904581689E-2},{"$f":"INDEX($B$13:$F$17,D19,E19)","v":-3.2872111177088215E-2},{"$f":"INDEX($B$13:$F$17,E19,F19)","v":-3.7117112287729626E-2}]
[{"$f":"IF(C21<0,\"stable\",\"not stable\")","v":"stable"},"max",{"$f":"MAX(C20:F20)","v":-3.2471207904581689E-2}]

{"sheet":"11.3 Sim","index":4,"n_rows":22,"n_cols":10,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
["Example 11.3 ",null,"Simulation Model"]
[]
["Job j",1,2,3,4,5]
["Mean A",9.94,10.14,10.15,10.3,10.45,{"$f":"SUM(MA)","v":50.980000000000004}]
["StDev A",0.32,0.02,0.73,0.91,0.27]
["Mean B",10.16,10.16,10.26,10.45,10.46]
["StDev B",0.74,0.11,0.76,0.2,0.05]
[null,null,null,null,null,null,null,null,"Results"]
[]
["Sequence",1,2,3,4,5,null,"Sequence","Mean","St. Dev."]
["Mean A",{"$f":"INDEX(MA,B10)","v":9.94},{"$f":"INDEX(MA,C10)","v":10.14},{"$f":"INDEX(MA,D10)","v":10.15},{"$f":"INDEX(MA,E10)","v":10.3},{"$f":"INDEX(MA,F10)","v":10.45},null,"4-3-2-1-5",62.065726951218657,1.2574891510874799]
["StDev A",{"$f":"INDEX(SA,B10)","v":0.32},{"$f":"INDEX(SA,C10)","v":0.02},{"$f":"INDEX(SA,D10)","v":0.73},{"$f":"INDEX(SA,E10)","v":0.91},{"$f":"INDEX(SA,F10)","v":0.27},null,"1-2-3-4-5",62.110790530373265,0.95743636807671451]
["Mean B",{"$f":"INDEX(MB,B10)","v":10.16},{"$f":"INDEX(MA,C10)","v":10.14},{"$f":"INDEX(MA,D10)","v":10.15},{"$f":"INDEX(MA,E10)","v":10.3},{"$f":"INDEX(MA,F10)","v":10.45}]
["StDev B",{"$f":"INDEX(SB,B10)","v":0.74},{"$f":"INDEX(SB,C10)","v":0.11},{"$f":"INDEX(SB,D10)","v":0.76},{"$f":"INDEX(SB,E10)","v":0.2},{"$f":"INDEX(SB,F10)","v":0.05}]
[]
["Times",{"$f":"_xll.PsiNormal(B11,B12)","v":9.9041368591862504},{"$f":"_xll.PsiNormal(C11,C12)","v":10.151352891151033},{"$f":"_xll.PsiNormal(D11,D12)","v":10.379106951693608},{"$f":"_xll.PsiNormal(E11,E12)","v":9.7963043659714852},{"$f":"_xll.PsiNormal(F11,F12)","v":10.933349132406299}]
[null,{"$f":"_xll.PsiNormal(B13,B14)","v":10.890727894127011},{"$f":"_xll.PsiNormal(C13,C14)","v":10.219802541780503},{"$f":"_xll.PsiNormal(D13,D14)","v":10.707733707047458},{"$f":"_xll.PsiNormal(E13,E14)","v":10.262525290327764},{"$f":"_xll.PsiNormal(F13,F14)","v":10.434623526412878}]
[]
["Completions",{"$f":"B16","v":9.9041368591862504},{"$f":"B19+C16","v":20.055489750337284},{"$f":"C19+D16","v":30.434596702030891},40.230901068002375,51.164250200408674,"Mean","St. Dev"]
[null,{"$f":"B19+B17","v":20.794864753313263},{"$f":"MAX(B20,C19)+C17","v":31.014667295093766},{"$f":"MAX(C20,D19)+D17","v":41.722401002141225},51.984926292468991,{"$f":"MAX(E20,F19)+F17","v":62.419549818881869},{"$f":"_xll.PsiMean(F20)","v":62.110790530373265},{"$f":"_xll.PsiStdDev(F20)","v":0.95743636807671451}]
[]
[null,null,null,null,null,"Total on Mch A, as a check on G4:",{"$f":"_xll.PsiMean(F19)","v":50.980000675293688}]

{"sheet":"11.4","index":5,"n_rows":17,"n_cols":7,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["Example 11.4",null,"Simulation Model"]
[]
[null,null," epsilon =",1E-3]
["Means","job",1,2]
[null,"a",{"$f":"1-$D$3","v":0.999},1]
[null,"b",1,{"$f":"1-$D$3","v":0.999}]
[]
["Realizations",null,{"$f":"C5","v":0.999},{"$f":"_xll.PsiExponential(D5)","v":0.42084681698174486}]
[null,null,{"$f":"_xll.PsiExponential(C6)","v":0.96073122346283679},{"$f":"D6","v":0.999}]
[]
["Sequence"," ",1,2,null,2,1]
["Completions",null,{"$f":"C8","v":0.999},{"$f":"C12+D8","v":1.4198468169817449},null,{"$f":"D8","v":0.42084681698174486},{"$f":"F12+C8","v":1.4198468169817449}]
[null,null,{"$f":"C12+C9","v":1.9597312234628368},{"$f":"MAX(D12,C13)+D9","v":2.9587312234628369},null,{"$f":"F12+D9","v":1.4198468169817449},{"$f":"MAX(G12,F13)+C9","v":2.3805780404445818}]
[]
[null,null,"Expected makespan",{"$f":"_xll.PsiMean(D13)","v":3.4981089827224001},null,"Optimum -->",{"$f":"_xll.PsiMean(G13)","v":2.99899074530471}]
[]
[null,null,"    Deterministic counterpart",{"$f":"3-2*D3","v":2.9980000000000002},"<-- Optimum",null,{"$f":"3.5-2*D3","v":3.4980000000000002}]

{"sheet":"11.5a","index":6,"n_rows":9,"n_cols":7,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["Example 11.5",null,"Deterministic counterpart"]
[]
["Means","job",1,2]
[null,"a",1,1.5]
[null,"b",1.5,1]
[]
[null,null,1,2,null,2,1]
["Completions",null,{"$f":"C4","v":1},{"$f":"C8+D4","v":2.5},null,{"$f":"D4","v":1.5},{"$f":"F8+C4","v":2.5}]
[null,null,{"$f":"C8+C5","v":2.5},{"$f":"MAX(C9,D8)+D5","v":3.5},null,{"$f":"F8+D5","v":2.5},{"$f":"MAX(F9,G8)+C5","v":4}]

{"sheet":"11.5b","index":7,"n_rows":21,"n_cols":10,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Example 11.5",null,"Simulation with Uniform Distributions"]
[]
["Means","job",1,2]
[null,"a",1,{"$f":"_xll.PsiUniform(0,3)","v":1.9243832989577334}]
[null,"b",{"$f":"_xll.PsiUniform(0,3)","v":2.9498480204350126},1]
[]
[null,null,1,2,null,2,1]
["Completions",null,{"$f":"C4","v":1},{"$f":"C8+D4","v":2.9243832989577334},null,{"$f":"D4","v":1.9243832989577334},{"$f":"F8+C4","v":2.9243832989577334}]
[null,null,{"$f":"C8+C5","v":3.9498480204350126},{"$f":"MAX(C9,D8)+D5","v":4.949848020435013},null,{"$f":"F8+D5","v":2.9243832989577334},{"$f":"MAX(F9,G8)+C5","v":5.874231319392746},null,"Here, the means"]
[null,null,"mean",{"$f":"_xll.PsiMean(D9)","v":3.9988882551970262},null,"mean",{"$f":"_xll.PsiMean(G9)","v":3.9999999736370406},null,"are the same."]
[]
[null,null,"S.L.",null,"Makespan for S.L."]
[null,null,0.55000000000000004,{"$f":"_xll.PsiPercentile(D$9,$C13)","v":4.2246314257012099},null,null,{"$f":"_xll.PsiPercentile(G$9,$C13)","v":4.1522817301610528},"2-1 lies above 1-2"]
[null,null,0.6,{"$f":"_xll.PsiPercentile(D$9,$C14)","v":4.322610923853758},null,null,{"$f":"_xll.PsiPercentile(G$9,$C14)","v":4.3190808846189164},"lines cross near SL = 0.60"]
[null,null,0.65,{"$f":"_xll.PsiPercentile(D$9,$C15)","v":4.4170426502537365},null,null,{"$f":"_xll.PsiPercentile(G$9,$C15)","v":4.4911624103213788},"1-2 lies above 2-1"]
[null,null,null,"corresponds to Figure 11.1"]
[]
["Uncertain Function Summary Information"]
[null,"Cell","Formula","Mean","Std Dev","Minimum","Maximum","25th Pctlle","50th Pctle","75th Pctle"]
[null,"11.5b'!$D$9","MAX(C9,D8)+D5",3.9988882551970262,0.70757739814921072,2.0124156175529651,4.999992849153565,3.4992388087311461,4.1214314679816875,4.5968778988647303]
[null,"11.5b'!$G$9","MAX(F9,G8)+C5",3.9999999736370406,1.2263591538871979,1.0195064180786455,6.9938245913502444,3.121854311225146,3.9963013476004985,4.8775496380411862]

{"sheet":"11.5c","index":8,"n_rows":16,"n_cols":7,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["Example 11.5",null,"Minimize d subject to service level floor"]
[]
["Means","job",1,2,null,"d",4.32]
[null,"a",1,{"$f":"_xll.PsiUniform(0,3)","v":1.5787536945741039}]
[null,"b",{"$f":"_xll.PsiUniform(0,3)","v":1.1518006712965574},1]
[]
[null,null,1,2,null,2,1]
["Completions",null,{"$f":"C4","v":1},{"$f":"C8+D4","v":2.5787536945741039},null,{"$f":"D4","v":1.5787536945741039},{"$f":"F8+C4","v":2.5787536945741039}]
[null,null,{"$f":"C8+C5","v":2.1518006712965576},{"$f":"MAX(C9,D8)+D5","v":3.5787536945741039},null,{"$f":"F8+D5","v":2.5787536945741039},{"$f":"MAX(F9,G8)+C5","v":3.7305543658706615}]
[null,null,"on time?",{"$f":"IF(D9<=G3,1,0)","v":1},null,null,{"$f":"IF(G9<=G3,1,0)","v":1}]
[null,null,"S.L.",{"$f":"_xll.PsiMean(D10)","v":0.59802999999999995},null,null,{"$f":"_xll.PsiMean(G10)","v":0.60092999999999996}]
[]
[null,null,null,"corresponds to Figure 11.1"]
[null,null,null,"For a target of S.L. = 0.6, 1-2 lies above 2-1"]
[null,null,null,"so it reaches the target at a smaller due date."]
[null,null,null,"2-1 minimizes d."]

{"sheet":"11.5d","index":9,"n_rows":15,"n_cols":7,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Example 11.5",null,"Minimize d + gE(T)"]
[]
["Means","job",1,2,null,"d",4.3167516213368753]
[null,"a",1,{"$f":"_xll.PsiUniform(0,3)","v":1.5540710882751099},null,"g",2.5]
[null,"b",{"$f":"_xll.PsiUniform(0,3)","v":1.81353224477105},1]
[]
[null,null,1,2,null,2,1]
["Completions",null,{"$f":"C4","v":1},{"$f":"C8+D4","v":2.5540710882751099},null,{"$f":"D4","v":1.5540710882751099},{"$f":"F8+C4","v":2.5540710882751099}]
[null,null,{"$f":"C8+C5","v":2.81353224477105},{"$f":"MAX(C9,D8)+D5","v":3.81353224477105},null,{"$f":"F8+D5","v":2.5540710882751099},{"$f":"MAX(F9,G8)+C5","v":4.3676033330461603}]
[null,null,"Tardiness",{"$f":"MAX(0,D9-G3)","v":0},null,null,{"$f":"MAX(0,G9-G3)","v":5.0851711709285041E-2}]
[null,null,"E[T]",{"$f":"_xll.PsiMean(D10)","v":0.14401180361562504},null,null,{"$f":"_xll.PsiMean(G10)","v":0.3547562171002161}]
[]
[null,null,"d  +gE[T]",{"$f":"G3+G4*D11","v":4.6767811303759377},null,null,{"$f":"G3+G4*G11","v":5.203642164087416}]
[null,null,"optimal",4.6764448787344888,null,"<-- opt",5.2132237713979208]
[null,null,"d*",4.3237961213234763,null,null,4.3167516213368753]