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...COLUMNWIDT╚ 45 Programminτ the Performance Evaluation and Review ╘echnique (PERT) iε BASIC "┴ methoΣ fo≥ planninτ comple° activitie≤ wherσ n∩ precedent≤ exist." Origina∞ prograφ b∙ Steveε Zimmermaε anΣ Le∩ M« Conrad DevelopeΣ anΣ modifieΣ fo≥ thσ Osbornσ ▒ b∙ Douτ Hurst Tex⌠ anΣ prograφ listinτ reprinteΣ froφ BYT┼ Magazinσ witΦ permission. TABLE OF CONTENTS Osbornσ ▒ Prolog . . . . . . . . . . . 2 Introduction. . . . . . . . . . . . . 3 Origin≤ oµ PERT. . . . . . . . . . . . 3 Thσ Star⌠ oµ PER╘ Analysis. . . . . . 3 Thσ Bubblσ Diagram. . . . . . . . . . 4 Thσ Critica∞ Path. . . . . . . . . . . 4 Threσ Timσ Estimates. . . . . . . . . 5 Ou≥ PER╘ Program. . . . . . . . . . . 5 Runninτ thσ Program. . . . . . . . . . 6 Conclusion. . . . . . . . . . . . . . 8 Figurσ 1 . . . . . . . . . . . . . 9 Tablσ 1 . . . . . . . . . . . . . . 10 ┴ Glancσ a⌠ thσ Mathematic≤ oµ PERT 11 è Programminτ PER╘ iε BASIC "┴ methoΣ fo≥ planninτ comple° activitie≤ wherσ n∩ precedent≤ exist." Origina∞ prograφ b∙ Steveε Zimmermaε anΣ Le∩ M« Conrad DevelopeΣ anΣ modifieΣ fo≥ thσ Osbornσ ▒ b∙ Douτ Hurst Tex⌠ anΣ prograφ listinτ reprinteΣ froφ BYT┼ Magazinσ witΦ permission. ...T1 Osbornσ ▒ Prolog Thσ BYT┼ articlσ froφ whicΦ thi≤ librar∙ submissioε wa≤ ì extracteΣ appear≤ oε page≤ 465-47╕ oµ thσ Ma∙ 198▓ issuσ witΦ thσ ì themσ "Japanesσ Computers« Thi≤ wa≤ ß fairl∙ eas∙ prograφ t∩ conver⌠ t∩ ruε oε thσ O-▒ a≤ arσ mos⌠ program≤ writteε iε TRS-8░ Leve∞ I╔ o≥ Disδ ì Basic(als∩ b∙ MicroSoft)« Deletion≤ t∩ thσ prograφ includσ al∞ ì tapσ savσ anΣ loaΣ routines« Addition≤ includσ ß mean≤ b∙ whicΦ ì t∩ designatσ timσ unit≤ useΣ anΣ projec⌠ star⌠ date≤ a≤ wel∞ a≤ ì thei≥ appearancσ oε thσ harΣ cop∙ output« Also¼ anΣ mos⌠ ì important¼ i≤ thσ inclusioε oµ thσ abilit∙ t∩ displa∙ anΣ ì printou⌠ ß GANN╘ Char⌠ oµ thσ pertinen⌠ PER╘ elements. Thσ prograφ ha≤ grea⌠ practica∞ utility« A⌠ thσ Marinσ ì Corp≤ Communication-Electronic≤ School¼ Twentyninσ Palms¼ CA¼ wσ ì arσ involveΣ iε ß largσ numbe≥ oµ coursewarσ conversion≤ (t∩ ì Compute≥ AideΣ Instruction(CAI)⌐ tha⌠ arσ spreaΣ out¼ iε somσ ì cases¼ ove≥ period≤ a≤ largσ a≤ years« PER╘ ha≤ beeε instrumenta∞ ì iε botΦ thσ planninτ anΣ monitorinτ oµ thesσ projects. Therσ arσ no≈ │ maiε program≤ oε thσ diskette¼ PERTSAMP.COM¼ ì PERT80.BAS¼ anΣ PERT128.BAS« PERTSAMP.CO═ i≤ somethinτ I'φ reall∙ ì prouΣ of¼ althougΦ ╔ can'⌠ takσ ful∞ credi⌠ fo≥ thσ originality« ì ╔ pulleΣ ß prograφ calleΣ OSBOARD1.CO═ ofµ Kell∙ Smith'≤ CP/═ Ne⌠ ì ß whilσ back« I⌠ wa≤ reall∙ aε advertisemen⌠ fo≥ ß prograφ whicΦ ì make≤ thσ O-1'≤ graphic≤ eas∙ t∩ use« Iε doinτ s∩ i⌠ showeΣ thσ ì program'≤ capability« PERTSAMP.CO═ doe≤ mucΦ thσ same« Jus⌠ placσ ì thσ PER╘ diskettσ iε thσ ┴ drivσ anΣ hi⌠ thσ return« IMPORTAN╘ í Makσ surσ yo⌡ printe≥ i≤ u≡ wheε yo⌡ d∩ so« Wha⌠ yo⌡ wil∞ ge⌠ i≤ ß completσ samplσ ruε oµ thσ PER╘ prograφ ì includinτ printouts« Yo⌡ shoulΣ d∩ thi≤ righ⌠ awa∙ eveε thougΦ ì PER╘ hasn'⌠ eveε beeε explaineΣ yet« Thσ ┤ page≤ oµ outpu⌠ arσ ì Listing≤ 2,3,4,anΣ ╡ a≤ referreΣ t∩ iε thσ articlσ proper« ì PERTSAM╨ i≤ compileΣ BASIC« PERT80/128.BA╙ arσ nameΣ baseΣ oε ì thei≥ printe≥ requirements« TEM╨ i≤ merel∙ ß filσ whicΦ yo⌡ ma∙ ì read into the program for practice. WitΦ thσ lates⌠ addition¼ tha⌠ is- thσ GANN╘ Chart¼ thi≤ ì PER╘ prograφ i≤ swiftl∙ approachinτ thσ qualit∙ oµ MILESTON┼ (oε ì thσ Osbornσ ApproveΣ Softwarσ list║ Organiπ Software¼ Retai∞ ì Pricσ $295.00)« è(Note║ M∙ friend¼ fo≥ thσ timσ being¼ Jerr∙ Lawson¼ ha≤ beeε ì ploddinτ awa∙ a⌠ PERT'≤ companioε prograφ "Programminτ thσ ì Critica∞ PatΦ MethoΣ iε BASIC"¼ (BYTE¼ Jul∙ 1982¼ page≤ 378-390⌐ ì fo≥ quitσ somσ timσ now« ╔ forceΣ hiφ t∩ d∩ i⌠ becausσ s∩ mucΦ ì caε bσ learneΣ abou⌠ programinτ froφ thσ copyinτ anΣ debugginτ ì process« It'≤ beeε ß slo≈ proces≤ anΣ beside≤ hσ ha≤ ß wifσ anΣ ì famil∙ t∩ whicΦ hσ i≤ morσ devoteΣ thaε hi≤ Osborne« Can'⌠ ì understanΣ that« Wheε hσ finishe≤ hi≤ part¼ thσ prograφ wil∞ bσ ì cleaneΣ up¼ modifieΣ anΣ submitted« Oncσ thi≤ i≤ done¼ MILESTON┼ ì wil∞ havσ beeε equaled.⌐ ...T1 Introduction. Thσ Performancσ Evaluatioε anΣ Revie≈ Techniquσ (PERT⌐ i≤ ß ì powerfu∞ methoΣ oµ planninτ comple° activities¼ especiall∙ ì pioneerinτ project≤ likσ thσ creatioε oµ ß ne≈ busines≤ o≥ thσ ì developmen⌠ oµ ß ne≈ machine« Thσ innovativσ naturσ oµ thesσ ì project≤ assure≤ tha⌠ fe≈ precedent≤ exis⌠ t∩ hel≡ estimatσ ì performancσ time. PER╘ give≤ manager≤ thσ tool≤ t∩ dea∞ witΦ uncertainty╗ PER╘ ì i≤ managemen⌠ iε action« I⌠ plans¼ schedules¼ anΣ control≤ ì activity« Usinτ PERT¼ contractors¼ builders¼ engineers¼ anΣ ì businessmeε caε improvσ planninτ iε thσ mids⌠ oµ uncertaint∙ anΣ ì savσ mone∙ a≤ ß result. Unti∞ now¼ onl∙ largσ businesse≤ witΦ acces≤ t∩ largσ ì computer≤ coulΣ usσ PERT« Thσ prograφ iε listinτ ▒ (Listinτ ▒ ma∙ ì bσ obtaineΣ b∙ loadinτ eithe≥ PERT80.BA╙ o≥ PERT128.BAS¼ settinτ ì WIDT╚ LPRIN╘ 80¼ anΣ theε doinτ ß LLIST.⌐ bring≤ PERT'≤ powe≥ t∩ ì microcompute≥ users« Beforσ presentinτ ou≥ program¼ however¼ we'l∞ givσ yo⌡ ß ì glimpsσ a⌠ PERT'≤ history¼ briefl∙ describσ thσ naturσ oµ PER╘ ì analysis¼ sugges⌠ onσ possiblσ PER╘ applicatioε fo≥ ß manager¼ ì anΣ examinσ thσ mathematic≤ behinΣ PERT. ...T1 Origin≤ oµ PERT. PER╘ date≤ bacδ t∩ ß teaφ createΣ b∙ thσ Nav∙ Specia∞ ì Project≤ Office¼ LockheeΣ Aircraf⌠ Corporation¼ anΣ managemen⌠ ì consultinτ firφ oµ Booz¼ Allen¼ anΣ Hamilton« Worδ durinτ WorlΣ ì Wa≥ ╔ oε thσ Gann⌠ schedulinτ char⌠ anΣ thσ Gann⌠ milestonσ char⌠ ì shoulΣ als∩ bσ noteΣ becausσ thesσ precipitateΣ thσ developmen⌠ ì oµ thσ networδ diagraφ (describeΣ later⌐ useΣ iε PERT. Manager≤ oµ man∙ differen⌠ kind≤ oµ task≤ havσ successfull∙ ì applieΣ PERT« Onσ particularl∙ spectacula≥ resul⌠ oµ thσ PER╘ ì approacΦ i≤ thσ Polari≤ missile¼ whicΦ als∩ occasioneΣ PERT'≤ ì development« (LockheeΣ Aircraf⌠ wa≤ thσ majo≥ contracto≥ fo≥ ì Polaris.⌐ Completioε timσ wa≤ critica∞ iε thσ Polari≤ program¼ ì bu⌠ therσ wa≤ considerablσ uncertaint∙ abou⌠ ho≈ lonτ thσ ì requireΣ activitie≤ woulΣ take« Moreover¼ thσ star⌠ oµ man∙ ì activitie≤ dependeΣ oε thσ completioε oµ others« Thesσ arσ thσ ì chieµ reason≤ wh∙ PER╘ employ≤ ß networδ schemσ anΣ focuse≤ oε ì thσ probabilit∙ oµ variou≤ activitie≤ finishinτ a⌠ specifieΣ ì times. ...T1 Thσ Star⌠ oµ PER╘ Analysis. PER╘ analysi≤ begin≤ b∙ reducinτ ß projec⌠ descriptioε t∩ ß ì lis⌠ oµ event≤ anΣ activities« Aε activit∙ i≤ ß par⌠ oµ ß ìèprojec⌠ tha⌠ consume≤ resource≤ o≥ timσ anΣ ha≤ ß definablσ ì beginninτ anΣ end« Aε even⌠ i≤ ß poin⌠ iε time¼ instant« Thσ ì beginninτ anΣ endinτ point≤ oµ aε activit∙ arσ events« T∩ appl∙ ì PER╘ t∩ ß comple° project¼ yo⌡ mus⌠ identif∙ al∞ thσ event≤ ì needeΣ t∩ completσ thσ projec⌠ anΣ al∞ thσ activitie≤ tha⌠ resul⌠ ì iε thσ identifieΣ events. A≤ aε example¼ we'l∞ usσ ß simplifieΣ versioε oµ aε actua∞ ì constructioε projec⌠ tha⌠ wσ jus⌠ completed« T∩ simplify¼ we'l∞ ì enΣ ou≥ examplσ witΦ thσ completioε oµ thσ building'≤ foundation« ì Wσ identifieΣ 1╕ activitie≤ needeΣ t∩ completσ thi≤ foundation« ì Tablσ ▒ list≤ thσ activities¼ assigneΣ letter≤ ┴ througΦ ╤ anΣ Z« ì EacΦ oµ thσ ninσ event≤ iε thσ projec⌠ consist≤ oµ thσ completioε ì oµ onσ o≥ morσ activities. ...T1 Thσ Bubblσ Diagram. Thσ seconΣ stagσ iε PER╘ analysi≤ i≤ thσ layou⌠ oµ ß ì "bubbleó diagraφ tha⌠ show≤ ho≈ thσ necessar∙ activitie≤ anΣ ì event≤ forφ ß sequencσ oµ steps« Figurσ ▒ i≤ thσ bubblσ diagraφ ì oµ ou≥ foundation-buildinτ example« WitΦ o≥ withou⌠ PERT¼ ì specifyinτ thσ sequencσ oµ ß project'≤ step≤ i≤ obviousl∙ aε ì importan⌠ planninτ activity« Mos⌠ contractor≤ la∙ ou⌠ thσ ì sequencσ oµ task≤ iε ß projec⌠ iε somσ fashion¼ bu⌠ PER╘ make≤ ì tasδ sequencinτ ß forma∞ activity« Formalizinτ thi≤ proces≤ lend≤ ì valuablσ structurσ t∩ essentia∞ planning« Iε particular¼ makinτ ß ì bubblσ diagraφ force≤ thσ planne≥ t∩ specif∙ whicΦ activitie≤ ì depenΣ oε thσ completioε oµ others. Diagram≤ likσ tha⌠ showε iε figurσ ▒ arσ als∩ calleΣ ì networks« ┴ PER╘ networδ ha≤ onσ initia∞ event¼ a⌠ thσ extremσ ì left¼ anΣ onσ termina∞ event¼ a⌠ thσ extremσ right« thσ circle≤ ì iε figurσ ▒ (afte≥ yo⌡ perforφ ß littlσ artwork⌐ arσ numbereΣ anΣ ì represen⌠ events« Thσ line≤ arσ lettereΣ anΣ represen⌠ ì activities╗ eacΦ linσ ha≤ aε arro≈ indicatinτ it≤ directioε iε ì timσ froφ beginninτ t∩ completion« Thσ networδ a≤ ß wholσ show≤ ì thσ serie≤ oµ activitie≤ tha⌠ mus⌠ bσ performeΣ t∩ completσ thσ ì project« thσ arrow≤ sho≈ whicΦ activitie≤ anΣ event≤ logicall∙ ì precedσ others. Aε even⌠ tha⌠ result≤ froφ completioε oµ morσ thaε onσ ì activit∙ i≤ calleΣ ß mergσ event╗ aε even⌠ tha⌠ represent≤ thσ ì join⌠ beginninτ oµ morσ thaε onσ activit∙ i≤ calleΣ ß burs⌠ ì event« Beforσ an∙ activit∙ caε start¼ al∞ precedinτ activitie≤ ì mus⌠ bσ completeΣ (bu⌠ no⌠ al∞ simultaneously)« Aε arrow'≤ lengtΦ ì anΣ it≤ compas≤ directioε arσ insignificant. DasheΣ line≤ iε networδ diagram≤ represen⌠ ì "dummy"activities« ┴ dumm∙ activit∙ exist≤ wheε thσ completioε oµ ì onσ even⌠ depend≤ oε thσ completioε oµ anothe≥ bu⌠ require≤ n∩ ì additiona∞ worδ o≥ activity« PER╘ handle≤ dumm∙ activitie≤ likσ ì an∙ other≤ bu⌠ assign≤ thσ activit∙ zer∩ timσ anΣ zer∩ costs. ...T1 Thσ Critica∞ Path. Thσ longes⌠ routσ froφ thσ beginninτ oµ thσ networδ oε thσ ì lef⌠ t∩ it≤ enΣ oε thσ righ⌠ determine≤ thσ timσ requireΣ t∩ ì completσ thσ project« thi≤ linσ i≤ thσ critica∞ path¼ whicΦ ì determine≤ thσ minimuφ timσ requireΣ t∩ completσ ß job« AlthougΦ ìèthσ concep⌠ oµ ß critica∞ patΦ ma∙ sounΣ complex¼ i⌠ i≤ simplσ ì oncσ you'vσ laiΣ ß projec⌠ ou⌠ iε ß bubblσ diagram. Critical-patΦ analysi≤ caε revea∞ way≤ t∩ shorteε thσ ì critica∞ patΦ anΣ t∩ contro∞ thσ tota∞ lengtΦ oµ ß job« Becausσ ì oµ thσ sizσ oµ ou≥ computer¼ thi≤ prograφ analyze≤ thσ critica∞ ì patΦ bu⌠ doe≤ no⌠ attemp⌠ t∩ shorteε it. ...T1 Threσ Timσ Estimates. Alonτ eacΦ activit∙ linσ iε figurσ 1¼ yo⌡ seσ threσ decima∞ ì numbers« Thesσ number≤ represen⌠ aε optimistic¼ likel∙ anΣ ì pessimistiπ estimatσ oµ thσ timσ requireΣ t∩ completσ thσ ì activity« EacΦ timσ thσ activit∙ i≤ no⌠ oε thσ critica∞ path¼ ß ì manager'≤ decisioε t∩ authorizσ expenditure≤ fo≥ overtimσ woulΣ ì bσ foolisΦ anΣ wasteful« Al∞ activitie≤ no⌠ oε thσ critica∞ patΦ ì havσ "slacδ time,ó thσ differencσ betweeε thσ earlies⌠ anΣ lates⌠ ì expecteΣ finish« B∙ definition¼ onl∙ thσ activitie≤ oε thσ ì critica∞ patΦ havσ zer∩ slacδ time« We'l∞ elaboratσ later. ...T1 Ou≥ PER╘ Program. Ou≥ PER╘ Prograφ i≤ showε iε listinτ 1« ┴ dimensioε (DIM⌐ ì statemen⌠ a⌠ linσ 16░ provide≤ place≤ t∩ storσ datß oε ì activities« Thσ samσ DI═ statemen⌠ als∩ provide≤ storagσ fo≥ ß ì dumm∙ variable,SV¼ t∩ bσ useΣ late≥ durinτ sorts. Oε ß systeφ witΦ 32╦ (remembe≥ thσ articlσ wa≤ writteε fo≥ ß ì TRS-80⌐ byte≤ oµ memor∙ anΣ tw∩ disδ drives¼ ou≥ prograφ caε ì handlσ morσ thaε 20░ activities« Wσ havσ ye⌠ t∩ neeΣ morσ thaε ì 10░ activities« You≥ machine'≤ memor∙ capacit∙ anΣ thσ limit≤ oµ ì you≥ DI═ statemen⌠ wil∞ determinσ thσ sizσ oµ thσ probleφ tha⌠ ì ou≥ prograφ caε handlσ fo≥ you« Yo⌡ caε finΣ thσ limit≤ b∙ ì experimentation. Onσ wa∙ t∩ savσ memor∙ i≤ t∩ carefull∙ omi⌠ remarδ (REM⌐ ì statements(Thesσ statement≤ arσ lef⌠ iε iε fn.f⌠ PERTSAMP.BA╙ bu⌠ ì havσ beeε removeΣ froφ PERT80.BA╙ anΣ PERT128.BA╙ iε thσ Osbornσ ì ▒ version)« A≤ noteΣ before¼ thσ critica∞ patΦ consist≤ oµ ß serie≤ oµ ì activitie≤ tha⌠ havσ zer∩ slacδ time« T∩ finΣ thσ critica∞ path¼ ì yo⌡ mus⌠ identif∙ activitie≤ tha⌠ havσ zer∩ slacδ time« Thσ ì prograφ output¼ consistinτ oµ tw∩ tables¼ i≤ designeΣ t∩ identif∙ ì thesσ activities. Thσ firs⌠ tablσ (seσ listinτ 2⌐ show≤ thσ program'≤ input¼ ì listinτ al∞ thσ activitie≤ iε thσ project¼ thei≥ beginninτ anΣ ì endinτ events¼ anΣ thσ threσ estimate≤ oµ thσ timσ eacΦ activit∙ ì requires« Yo⌡ shoulΣ checδ you≥ inpu⌠ wheneve≥ yo⌡ usσ thi≤ ì prograφ becausσ otherwisσ yo⌡ ma∙ ge⌠ craz∙ results. Thσ seconΣ tablσ (seσ listinτ 3⌐ i≤ thσ program'≤ output« ì Noticσ thσ las⌠ column¼ "Slacδ Time.ó Zero≤ iε thi≤ columε ì identif∙ thσ critica∞ path« Yo⌡ can¼ oµ course¼ tracσ thσ ì activitie≤ iε thσ critica∞ patΦ b∙ lookinτ iε thσ firs⌠ column¼ ì "Code,ó fo≥ eacΦ activit∙ witΦ zer∩ slacδ time« Bu⌠ ou≥ prograφ ì als∩ provide≤ ß men⌡ optioε CRITICA╠ PAT╚ AN─ TIME¼ whicΦ permit≤ ì botΦ thσ critica∞ patΦ anΣ thσ timσ requireΣ t∩ completσ it« Familiarit∙ witΦ thσ projec⌠ anΣ thσ prograφ wil∞ probabl∙ ì makσ listing≤ ▓ anΣ │ al∞ yo⌡ wil∞ neeΣ t∩ full∙ monito≥ yo⌡ ì program« Unfortunately¼ man∙ time≤ therσ wil∞ bσ ß neeΣ t∩ makσ ì thσ schedulinτ oµ you≥ projec⌠ understandablσ t∩ supervisor≤ o≥ ìèother≤ withou⌠ detaileΣ explanation« Thi≤ i≤ wherσ listinτ ┤ ì become≤ invaluable« Listinτ ┤ i≤ ß GANN╘ char⌠ fo≥ thσ project« ì Thi≤ char⌠ caε bσ headeΣ iε eithe≥ onσ oµ tw∩ way≤ dependinτ oε ì thσ timσ estimate≤ iε you≥ DAT┴ statements« Thi≤ wil∞ bσ eithe≥ ì WEEK╙ o≥ MONTHS« Thσ GANN╘ char⌠ heade≥ i≤ triggereΣ b∙ yo⌡ inpu⌠ ì oε linσ 150« Iµ yo⌡ ente≥ WEEK╙ you≥ heade≥ wil∞ sho≈ 1╡ month≤ ì oµ ┤ week≤ eacΦ oε PERT8░ anΣ ▓ year≤ oµ week≤ oε PERT128« Iµ yo⌡ ì picδ MONTHS¼ yo⌡ ge⌠ ╡ year≤ oµ month≤ oε eithe≥ PERT8░ o≥ ì PERT128« Thσ GANN╘ Char⌠ list≤ eacΦ activit∙ simila≥ t∩ listing≤ ì ▓ anΣ │ anΣ actuall∙ merel∙ provide≤ ß graphiπ representatioε oµ ì listinτ 3« Thσ ┼ represent≤ thσ earl∙ star⌠ time« Thσ └ and/o≥ ├ ì symbo∞ represen⌠ thσ expecteΣ timσ fo≥ thσ activit∙ (C'≤ iµ thσ ì activit∙ i≤ oε thσ Critica∞ Path)« Thσ ╠ i≤ fo≥ thσ las⌠ finish« ì B∙ default¼ an∙ spacσ betweeε thσ las⌠ └ fo≥ aε activit∙ anΣ thσ ì ╠ represent≤ slacδ timσ iµ thσ activit∙ i≤ starteΣ a⌠ thσ earl∙ ì star⌠ anΣ i≤ finisheΣ iε thσ expecteΣ time« Therσ wil∞ bσ n∩ ì spacσ betweeε thσ las⌠ ├ anΣ thσ ╠ fo≥ an∙ activity« A≤ stated¼ ì thesσ liσ oε thσ critica∞ patΦ anΣ therσ i≤ n∩ slacδ time« ┴ worΣ oµ cautioε abou⌠ usinτ thσ program║ round-ofµ ì problem≤ iε calculatioε thσ critica∞ patΦ forceΣ u≤ t∩ definσ ì zer∩ slacδ timσ a≤ 0.00▒ insteaΣ oµ truσ zero« Wherσ smal∞ ì difference≤ arσ important¼ thi≤ approximatioε oµ zer∩ caε causσ ì problems« Thσ valuσ 0.00▒ i≤ entereΣ iε linσ 1490╗ perhap≤ yo⌡ ì caε changσ thσ valuσ t∩ truσ zer∩ fo≥ somσ oµ you≥ applications« ì Furthermore¼ sincσ wσ useΣ statistica∞ method≤ t∩ determinσ thσ ì probabilit∙ oµ ß project'≤ beinτ completeΣ oε time¼ giveε ß ì scheduleΣ completioε date¼ yo⌡ shoulΣ remembe≥ tha⌠ datß ì generateΣ b∙ thσ prograφ i≤ baseΣ oε estimate≤ anΣ i≤ itselµ aε ì estimate. ...T1 Runninτ thσ Program. Thσ easies⌠ wa∙ t∩ inpu⌠ datß i≤ t∩ usσ DAT┴ statement≤ a⌠ ì thσ enΣ oµ thσ prograφ startinτ alway≤ a⌠ linσ numbe≥ 4000« ì Enterinτ datß froφ thσ keyboarΣ take≤ timσ anΣ increase≤ thσ ì numbe≥ oµ errors« Thσ bes⌠ wa∙ d∩ thσ DAT┴ statement≤ i≤ t∩ boo⌠ ì u≡ WordSta≥ iε drivσ ┴ anΣ thσ PER╘ diskettσ iε drivσ B« Creatσ ß ì filσ oε drivσ ┬ iε thσ "Nó non-documen⌠ modσ tha⌠ prett∙ wel∞ ì discribe≤ you≥ project« Likσ "BUILDING.BAS"« Simpl∙ star⌠ usinτ ì linσ 400░ witΦ thσ numbe≥ oµ activitie≤ anΣ thσ numbe≥ oµ events« ì Theε adΣ eacΦ activit∙ letter¼ description,startinτ anΣ endinτ ì even⌠ anΣ lastl∙ thσ optimistic¼ likely¼ anΣ pessimestiπ times¼ ì a≤ below: 400░ DAT┴ 18,9 401░ DAT┴ A,ACCT« PAPERS,1,2,1,2,3 402░ DAT┴ B,SHO╨ BANKERS,1,3,2,4,6 403░ DAT┴ C,SHO╨ REA╠ EST.,1,4,1,13,17 ETC...... Oncσ thi≤ i≤ done¼ savσ thσ program« No≈ boo⌠ u≡ MBASI├ anΣ LOA─ ì "x:PERT80ó o≥ "x:PERT128"« MERG┼ "x:BUILDINGó t∩ appenΣ you≥ DAT┴ ì line≤ t∩ thσ prograφ theε SAV┼ "x:BUILDINGó (x║ ╜ thσ disδ drivσ ì oµ choice)« Thi≤ save≤ thσ entirσ prograφ unde≥ thσ namσ formerl∙ ì useΣ b∙ you≥ DAT┴ line≤ anΣ leave≤ PERT80/12╕ intac⌠ withou⌠ datß ì line≤ anΣ availablσ fo≥ futurσ projects« Thσ followinτ ìèdescriptioε oµ ß prograφ ruε assume≤ tha⌠ DAT┴ statement≤ werσ ì useΣ fo≥ input. Whethe≥ yo⌡ inpu⌠ datß froφ DAT┴ statement≤ o≥ thσ keyboard¼ ì thσ prograφ begin≤ b∙ givinτ thσ identificatioε messagσ anΣ theε ì displays: **¬ NOT┼ BEGINNIN╟ EVENT╙ WIL╠ B┼ SORTE─ INT╧ ì NUMERICA╠ ORDE╥ *** wheε asking DIMENSION╙ FO╥ ACTIVITIES?_ (NOTE║ Thi≤ wil∞ onl∙ appea≥ iµ datß i≤ t∩ bσ entereΣ froφ ì keyboard or disk file.) TIM┼ UNIT╙ WIL╠ B┼ MEASURE─ IN?_ and PROJECT START DATE?_ A≤ yo⌡ seσ iε listinτ 2¼ event≤ arσ arrangeΣ accordinτ t∩ ì thσ earlies⌠ startinτ even⌠ iε eacΦ activity¼ anΣ tie≤ arσ brokeε ì b∙ referencσ t∩ thσ earlies⌠ endinτ even⌠ fo≥ eacΦ activity. No≈ thσ prograφ present≤ thσ inpu⌠ menu: INPU╘ MENU ╦ KEYBOARD ─ DIS╦ FILE Optioε ╥ cause≤ thσ prograφ t∩ reaΣ DAT┴ statement≤ a⌠ thσ ì enΣ oµ thσ program« Afte≥ ß brieµ delay¼ thσ prograφ wil∞ displa∙ ì fo≥ verificatioε thσ inpu⌠ oµ wha⌠ wa≤ read. Thσ vide∩ displa∙ oµ thσ inpu⌠ wil∞ looδ slightl∙ differen⌠ ì thaε thσ tablσ iε listinτ ▓ becausσ oµ thσ difference≤ iε thσ ì screeε anΣ printe≥ sizes« Iµ ß singlσ screeε won'⌠ accommodatσ ì al∞ thσ input¼ thσ prograφ wil∞ asδ yo⌡ t∩ pagσ through. Afte≥ listinτ al∞ thσ input¼ thσ prograφ wil∞ say: -▓ ADD¼ -▒ T╧ CONTINU┼ O╥ NUMBE╥ T╧ CHANGE?_ Thσ numbe≥ referreΣ t∩ i≤ thσ numbe≥ oµ an∙ activit∙ tha⌠ yo⌡ ì wisΦ t∩ change« Assuminτ yo⌡ wan⌠ t∩ continuσ anΣ ente≥ -1¼ thσ ì prograφ wil∞ ask: HAR─ COP┘ O╞ INPU╘ DAT┴ (Y/N)?_ Iµ yo⌡ reques⌠ harΣ copy¼ thσ prograφ wil∞ prin⌠ │ line≤ oµ EG╧ ì datß anΣ theε asks: TITLE?_ DATE?_ anΣ wil∞ prin⌠ you≥ responses¼ a≤ wel∞ a≤ thσ measurσ oµ timσ ì unit≤ a⌠ thσ to≡ oµ thσ page« Ou≥ samplσ se⌠ oµ datß useΣ thσ ì titlσ PER╘ SAMPL┼ anΣ thσ datσ 11/26/82. è Afte≥ thσ inpu⌠ i≤ printed¼ thσ screeε wil∞ displa∙ thσ ì results¼ a≤ showε iε listinτ 3« Fo≥ eacΦ activity¼ yo⌡ wil∞ seσ ì computation≤ oµ ho≈ lonτ i⌠ shoulΣ bσ expecteΣ t∩ take¼ thσ ì earlies⌠ weeδ (yo⌡ ma∙ usσ month≤ also⌐ i⌠ caε start¼ thσ ì earlies⌠ i⌠ caε finish¼ anΣ thσ slacδ timσ (thσ differencσ ì betweeε thσ earlies⌠ anΣ lates⌠ possiblσ finish)« Yo⌡ ma∙ havσ t∩ ì pagσ througΦ ß screeε displa∙ oµ thi≤ data« Thσ prograφ wil∞ ì agaiε asδ iµ yo⌡ wan⌠ harΣ copy. Nex⌠ thσ GANN╘ Char⌠ wil∞ bσ displayeΣ witΦ paginτ agaiε iµ ì necessar∙ anΣ ß promp⌠ fo≥ harΣ copy« Line≤ 8╡ anΣ 9░ se⌠ screeε ì anΣ printe≥ widtΦ t∩ accomodatσ al∞ requirements. Theε yo⌡ wil∞ see: OUTPU╘ MENU ├ CRITICA╠ PAT╚ AN─ TIME ─ DISK ┼ END ╥ RECYCLE SELECTION?_ Optioε C¼ fo≥ ou≥ example¼ result≤ iε ß displa∙ likσ thσ ì following: CRITICA╠ PATH ├ ╔ ╦ ╬ P TIM┼ O╞ CRITICA╠ PATH 42.33 SCHEDULE─ PROJEC╘ TIM┼ (US┼ SAM┼ TIM┼ UNIT╙ A╙ DATA)?_ Fo≥ ou≥ example¼ thσ critica∞ patΦ consist≤ oµ shoppinτ fo≥ ì ß real-estatσ agent¼ obtaininτ land¼ gettinτ architectura∞ plans¼ ì gettinτ ß detaileΣ layou⌠ fo≥ construction¼ anΣ actuall∙ buildinτ ì thσ foundation« Thσ timσ oµ thσ critica∞ patΦ i≤ expecteΣ t∩ bσ ì 42.3│ weeks« Yo⌡ caε no≈ inpu⌠ thσ scheduleΣ timσ fo≥ thσ project¼ anΣ ì thσ prograφ wil∞ usσ thσ ┌ calculation≤ explaineΣ iε thσ textbo° ì "┴ Glancσ a⌠ thσ Mathematic≤ oµ PERTó t∩ tel∞ yo⌡ ß probabilit∙ ì oµ meetinτ thσ schedule« A≤ showε iε listinτ 3¼ therσ i≤ ß ì 0.012385▓ probabilit∙ oµ finishinτ iε 3╡ week≤ anΣ ß 0.99053╢ ì probabilit∙ oµ finishinτ iε 5░ weeks« A≤ noteΣ earlier¼ therσ i≤ ì als∩ ß .50░ probabilit∙ oµ finishinτ iε thσ expecteΣ timσ oµ thσ ì critica∞ patΦ - 42.3│ weeks. ...T1 Conclusion. Iµ yo⌡ neeΣ hel≡ planninτ anΣ schedulinτ comple° projects¼ ì thi≤ PER╘ prograφ caε providσ it« Yo⌡ caε usσ i⌠ withou⌠ knowinτ ì ho≈ t∩ perforφ thσ calculation≤ involved« AlthougΦ wσ repea⌠ ou≥ ì cautioε abou⌠ relyinτ oε estimate-baseΣ estimates¼ wσ stil∞ ì believσ PER╘ ha≤ proveΣ itselµ ß valuablσ manageria∞ too∞ anΣ ì tha⌠ ou≥ prograφ accuratel∙ represent≤ PERT. è ▀ _ |2ⁿ |7| ▀ |8ⁿ _ ▀ ▀ ▀ |9| |1ⁿ |3ⁿ |5| ▀ _ |4ⁿ |6ⁿ (NOTE║ Sincσ i⌠ i≤ impossiblσ t∩ dra≈ ß ful∞ fledgeΣ bubblσ diagraφ witΦ ì WordStar¼ perforφ thσ followinτ upoε printinτ thi≤ documentation« Connec⌠ thσ ì bubble≤ anΣ labe∞ thσ resultan⌠ line≤ a≤ showε below. 1-▓ A-1,2,│ 4-╡ I-8,11,13 1-│ B-2,4,╢ 5-╢ J-2,3,4 1-┤ C-2,13,1╖ 5-╖ K-2,5,12 2-│ D-2,4,╡ 5-╕ L-1,2,4 2-╡ G-1.4,2.2,6.╖ 6-╕ M-2,3,4 2-╢ F-.4,1.3,1.╡ 6-╣ O-1,2,5 2-╖ Z-4,5,╕ 7-╕ N-9,11,12 3-┤ E-3,4,╡ 7-╣ Q-1,2,3 3-╡ H-2,4,╢ 8-╣ P-1,3,6 ...T2 Figurσ 1 Thσ PER╘ networδ diagraφ oµ thσ activitie≤ requireΣ t∩ builΣ ß foundation« ì EacΦ circlσ represent≤ aε even⌠ anΣ eacΦ linσ betweeε circle≤ represent≤ onσ oµ ì thσ activitie≤ listeΣ iε tablσ 1« Thσ threσ number≤ giveε fo≥ eacΦ activit∙ ì represen⌠ humaε estimate≤ oµ thσ optimistic(minimum)¼ likely¼ anΣ ì pessimistic(maximum⌐ timσ iε week≤ tha⌠ eacΦ activit∙ wil∞ take« Thσ networδ ha≤ ì onσ initia∞ event¼ even⌠ ▒ a⌠ thσ extremσ lef⌠ anΣ onσ termina∞ event¼ even⌠ ╣ ì a⌠ thσ extremσ right« Thσ critica∞ patΦ i≤ thσ onσ tha⌠ take≤ thσ mos⌠ timσ t∩ ì ge⌠ froφ even⌠ ▒ t∩ even⌠ 9. èLette≥ Activit∙ Beginninτ End Even⌠ Event ┴ assemblσ accountinτ datß ▒ 2 ┬ looδ fo≥ banδ ▒ 3 ├ looδ fo≥ real-estatσ agen⌠ ▒ 4 ┌ seeδ permit≤ ▓ 7 ─ makσ marke⌠ stud∙ oµ areß ▓ 3 ╟ looδ fo≥ contracto≥ ▓ 5 ╞ seeδ insurancσ fo≥ con- ▓ 6 struction ╚ ge⌠ basiπ architectura∞ plan≤ │ 5 ┼ makσ cos⌠ stud∙ │ 4 ╔ bu∙ lanΣ ┤ 5 ╩ lis⌠ material≤ ╡ 6 ╦ ge⌠ morσ detaileΣ architec- ╡ 7 tura∞ plans ╠ havσ surve∙ madσ ╡ 8 ═ bu∙ firs⌠ batcΦ oµ material≤ ╢ 8 ╧ bu∙ seconΣ batcΦ oµ ╢ 9 materials ╬ completσ detaileΣ interna∞ ╖ 8 layou⌠ oµ foundation ╤ hirσ cre≈ ╖ 9 ╨ builΣ foundatioε ╕ 9 ...T2 Tablσ 1 Thσ activitie≤ requireΣ t∩ builΣ ß foundation« thσ prograφ iε listinτ ▒ use≤ thσ ì letter≤ a⌠ lef⌠ t∩ identif∙ thσ activities« Thσ tw∩ column≤ a⌠ righ⌠ lis⌠ thσ ì firs⌠ anΣ las⌠ even⌠ durinτ eacΦ activity« Aε even⌠ i≤ thσ completioε oµ onσ o≥ ì morσ activities. è...T2 ┴ Glancσ a⌠ thσ Mathematic≤ oµ PERT Thσ mathematic≤ oµ PER╘ involve≤ somσ interestinτ ì statistica∞ concepts« Yo⌡ don'⌠ havσ t∩ understanΣ thσ ì mathematic≤ t∩ usσ PERT¼ bu⌠ i⌠ help≤ yo⌡ t∩ understanΣ ho≈ ou≥ ì prograφ works. First¼ wσ mus⌠ refresΦ you≥ recollectioε oµ somσ basiπ ì statistica∞ terms« thσ meaε oµ ß se⌠ oµ occurence≤ oµ somσ ì variablσ i≤ thσ arithmetiπ averagσ oµ thσ value≤ oµ thσ ì occurences╗ thσ standarΣ deviatioε i≤ thσ squarσ roo⌠ oµ thσ meaε ì oµ thσ square≤ oµ thσ deviation≤ oµ individua∞ occurence≤ froφ ì thσ mean)╗ thσ variancσ i≤ thσ squarσ oµ thσ standarΣ deviation. Fo≥ example¼ iµ wσ havσ threσ value≤ 9.1▓ anΣ 15¼ thei≥ meaε ì i≤ 36/3=12¼ thei≥ variancσ is (9-12)▓ ½ (12-12)▓ ½ (15-12)▓ ╜ 18 anΣ thσ standarΣ deviatioε i≤ thσ squarσ roo⌠ oµ 18¼ whicΦ i≤ ì approximatel∙ 4.24. I⌠ i≤ ß commoε statistica∞ assumptioε tha⌠ thσ standarΣ ì deviatioε iε unimoda∞ distribution≤ (distribution≤ tha⌠ havσ onl∙ ì ß singlσ most-likel∙ occurrinτ value⌐ i≤ roughl∙ ß sixtΦ oµ thσ ì rangσ oµ distributioε lie≤ witΦ threσ standarΣ deviation≤ oµ thσ ì mean╗ anΣ fo≥ thσ norma∞ distribution¼ 99.╖ percen⌠ oµ thσ ì distributioε lie≤ withiε threσ standarΣ deviation≤ oµ thσ mean. Sincσ wσ havσ estimate≤ oµ thσ minimuφ timσ ß anΣ thσ ì maximuφ timσ Γ requireΣ t∩ completσ aε activity¼ wσ havσ ì establisheΣ aε estimateΣ rangσ oµ actua∞ times« Wσ caε estimatσ ì thσ standarΣ deviatioε oµ thσ actua∞ timσ as (b-a) 6 Sincσ PER╘ assume≤ tha⌠ chance¼ o≥ randoφ factor≤ wil∞ ì influencσ thσ actua∞ timσ needeΣ t∩ completσ aε activity¼ wσ caε ì expec⌠ thσ actua∞ time≤ t∩ bσ distributeΣ alonτ somσ curve« PER╘ ì assume≤ tha⌠ thσ meaε actua∞ timσ wil∞ follo≈ thσ distributioε ì knowε a≤ thσ betß distribution¼ whicΦ i≤ containeΣ iε ß finitσ ì interva∞ anΣ ma∙ bσ eithe≥ symmetriπ o≥ skewed« Ou≥ mos⌠ likel∙ ì timσ oµ completioε φ i≤ thσ modσ oµ thσ curvσ fo≥ eacΦ ì activity« thσ followinτ equation¼ baseΣ oε thσ assumptioε tha⌠ ì ou≥ formulß fo≥ thσ standarΣ deviatioε i≤ correct¼ i≤ linea≥ ì approximatioε oµ thσ valuσ oµ thσ expecteΣ value¼ EV¼ oµ thσ meaε ì time: (a+4xm+b) E╓ ╜ ---------- 6 A≤ yo⌡ caε see¼ thi≤ i≤ jus⌠ ß weighteΣ average¼ countinτ thσ ì minimuφ anΣ maximuφ eacΦ oncσ anΣ thσ modσ fou≥ times¼ theε ì dividinτ thσ tota∞ b∙ 6« Oε linσ 99░ oµ listinτ 1¼ samσ equatioε ì i≤ expresseΣ as: A(I,6)=(A(I,3)+4*A(I,4)+A(I,5)/6 è Thσ followinτ equatioε give≤ thσ variancσ oµ thσ betß ì distributioε fo≥ eacΦ activity: VA╥ =((b-a)/6)2 Fo≥ eacΦ activity¼ thσ prograφ applie≤ thσ statistica∞ ì principle≤ describeΣ abovσ anΣ calculate≤ thσ timσ thσ activit∙ ì shoulΣ last¼ thσ earlies⌠ timσ a⌠ whicΦ i⌠ caε start¼ thσ ì earlies⌠ finish¼ thσ lates⌠ start¼ anΣ thσ lates⌠ finish« ì Calculatioε oµ thσ earlies⌠ star⌠ anΣ finisΦ time≤ i≤ calleΣ thσ ì "forwarΣ passó anΣ take≤ placσ iε ou≥ prograφ a⌠ line≤ 97░ t∩ ì 1080« Calculatioε oµ thσ lates⌠ star⌠ anΣ finisΦ i≤ calleΣ thσ ì "backwarΣ passó anΣ take≤ placσ a⌠ line≤ 109░ t∩ 1230. Thσ differencσ betweeε thσ earlies⌠ anΣ lates⌠ projecteΣ ì finisΦ fo≥ eacΦ activit∙ i≤ calleΣ "slacδ time"« A⌠ line≤ 124░ t∩ ì 1290¼ thσ prograφ calculate≤ slacδ timσ fo≥ eacΦ activity« Thσ ì even⌠ tha⌠ havσ zer∩ slacδ timσ forφ thσ critica∞ path. T∩ obtaiε thσ approximatσ variancσ fo≥ thσ critica∞ path¼ ì adΣ thσ variance≤ oµ thσ activitie≤ oε thσ path: VAR(Path)=VAR(1)+VAR(2⌐ ....+VAR(n) I⌠ happen≤ tha⌠ thσ Centra∞ Limi⌠ theoreφ enable≤ us¼ baseΣ oε ì thσ foregoing¼ t∩ assumσ tha⌠ thσ distributioε oµ thσ timσ ì requireΣ t∩ completσ thσ critica∞ patΦ i≤ normal« BaseΣ oε thi≤ ì assumption¼ wσ caε calculatσ thσ probabilit∙ oµ thσ project'≤ ì beinτ oε time¼ giveε somσ specifieΣ targe⌠ completioε time« Thσ ì calculation'≤ basi≤ i≤ thσ deviatioε oµ thσ scheduleΣ completioε ì timσ froφ thσ estimateΣ meaε completioε witΦ thσ deviatioε ì measureΣ iε unit≤ oµ standarΣ deviations« Thi≤ deviatioε i≤ ì calleΣ Z« Thσ ┌ calculatioε fo≥ thσ standarΣ norma∞ tablσ is: (scheduleΣ timσ oµ ) ¿ timσ critica∞ path) ┌ ╜ ---------------------------------- VAR(Path) Rathe≥ thaε requirσ yo⌡ t∩ usσ norma∞ table≤ witΦ ou≥ ì program¼ wσ havσ buil⌠ iε ß Taylo≥ serie≤ t∩ approximatσ thσ ì tables« (┴ Taylo≥ serie≤ i≤ ß powe≥ serie≤ tha⌠ give≤ thσ ì expansioε oµ ß functioε f(x⌐ iε thσ neighborhooΣ oµ ß poin⌠ a¼ ì provideΣ al∞ derivative≤ exis⌠ anΣ ß serie≤ converges.⌐ Thσ ì Taylo≥ serie≤ i≤ locateΣ a⌠ linσ 244░ anΣ followinτ iε ou≥ ì program. Thσ expecteΣ timσ oµ thσ critica∞ patΦ i≤ thσ suφ oµ thσ ì expecteΣ time≤ oµ al∞ thσ activitie≤ oε thσ path« Iµ thσ ì scheduleΣ timσ oµ thσ projec⌠ equal≤ thσ expecteΣ timσ oµ thσ ì critica∞ path¼ yo⌡ havσ ß 5░ percen⌠ chancσ oµ completinτ thσ ì projec⌠ oε time.