Ποσοτική Ανάλυση Επιχειρηματικών Αποφάσεων Προγραμματισμός – Διαχείριση Έργων

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  • , 2012-13

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    ( ) () , , , , , ,

    : , ( ) , , , , ( ).

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    , . , . Boeing Jumbo (project) . (Channel tunnel, London Eye, new drugs, Olympics etc). , . - .

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    (i) , (ii) (iii) ,, , , . . () .

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    , : ,, , , , , , , ..

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    PERT/CPM (1)PERTProgram Evaluation and Review TechniqueU.S. Navy (Polaris missile project)uncertain activity timesCPMCritical Path MethodDu Pont Company & Remington Rand UnivacIndustrial projects (activity times generally were known) ( PERT/CPM). .

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    PERT/CPM (2) PERT/CPM : ; ; ; ; ;

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    : Franks Fine Floats (1)Franks Fine Floats is in the business of building elaborate parade floats. Frank and his crew have a new float to build and want to (use PERT/CPM to help them) manage the project.

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    PERT/CPM (3) , . . ()

    : - . , - ( : - ).

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    : Franks Fine Floats (2) , () .

    ( / o).Frank wants to know the minimum total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

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    : Franks Fine Floats (3)

    Immediate Completion Activity Description Predecessors Time (days) A Initial Paperwork --- 3 B Build Body A 3 C Build Frame A 2 D Finish Body B 3 E Finish Frame C 7 F Final Paperwork B,C 3 G Mount Body to Frame D,E 68 H Install Skirt on Frame C 2Activities B, C must be finished before activity F can start.

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    , .K Activity On Node.( - Activity On Arrow).

    : . i . j, . i . j ( . i . j).

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    () (start) (finish)

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    : Franks Fine Floats (4) AON-StartFinish B3 D3 A3 C2 G6 F3 H2 E7 () Start Finish

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    T /. .T : , ( ) . ( PERT/CPM).

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    1 : (ES) (EF) .2 : (LS) (LF) .

    3 : 4 : . () . .

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    (ES) & (EF) forward Start. i, :Earliest Start Time = max {EF(k), k P}, P -= .Earliest Finish Time = ES + ( i ). () () Finish.

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    : Franks Fine Floats (5) Finish : F, G H() = 18 = max{9, 18, 7}StartFinish3 6B36 9D30 3A33 5C212 18G66 9F35 7H25 12E7max{6, 5}

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    : Franks Fine Floats (6) (ES) (EF)ESA = 0EFA = ESA + tA = 0 + 3 = 3ESB = EFA = 3EFB = ESB + tB = 3 + 3 = 6ESC = EFA = 3 EFC = ESC + tC = 3 + 2 = 5ESD = EFB = 6 EFD = ESD + tD = 6 + 3 = 9ESE = EFC = 5 EFE = ESE + tE = 5 + 7 = 12ESF = max{EFB, EFC} = max{6, 5} = 6 EFF = ESF + tF = 6 + 3 = 9ESG = max{EFD, EFE} = max{9, 12} = 12 EFG = ESG + tG = 12+6=18ESH = EFC = 5 EFH = ESH + tH = 5 + 2 = 7ESFINISH = max{EFF, EFG, EFH} = max{9, 18, 7} = 18

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    backward Finish. i, Latest Finish Time = min {LS(k), k S}, S i = .Latest Start Time = LF - ( i). (LS) (LF)

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    : Franks Fine Floats (7) StartFinish3 69B36 912D30 30 3A33 55C212 1818G66 918F35 718H25 1212E71216159563min{9, 15}

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    : Franks Fine Floats (8) (LS) (LF)LFG = 18LSG = LFG - tG = 18 - 6 =12LFH = 18LSH = LFH - tH = 18 - 2 =16LFF = 18LSF = LFF - tF = 18 - 3 = 15LFD = LSG = 12 LSD = LFD - tD = 12 - 3 = 9LFE = LSG = 12LSE = LFE - tE = 12 - 7 = 5LFB = min{LSD, LSF} = min{9, 15} = 9 LSB = LFB - tB = 9 - 3 = 6LFC = min{LSF, EFE} = min{15, 5} = 5 LSC = LFC - tC = 5 - 2 = 3LFA = min{LSB, EFC} = min{6, 3} = 3 LSA = LFA - tA = 3 - 3 = 0

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    (Slack)i = (Latest Start)i - (Earliest Start)i, or = (Latest Finish)i - (Earliest Finish)i.6 915 18F3

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    : Franks Fine Floats (9)Activity Slack Time

    Activity ES EF LS LF Slack A 0 3 0 3 0 (crit.) B 3 6 6 9 3 C 3 5 3 5 0 (crit.) D 6 9 9 12 3 E 5 12 5 12 0 (crit.) F 6 9 15 18 9 G 12 18 12 18 0 (crit.) H 5 7 16 18 11

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    ( )Example: Franks Fine Floats Start Finish, . For any network there will always be a path of critical activities from the initial node to final node.

    Critical Path: A C E G

    Project Completion Time: 18 days Note here that, we have (implicitly) assumed in calculating this figureof 18 days that we have sufficient resources to carried out the variousactivities.

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    Example: Franks Fine FloatsCritical PathStartFinish3 66 9B36 99 12D30 30 3A33 53 5C212 1812 18G66 915 18F35 716 18H25 125 12E7 A, C, E G B, D, F H , , 3, 3, 9 11

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    Example: Franks Fine Floats (winQSB)

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    , Henry Gantt, ( 1918). , () . . . Gantt

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    Example: Franks Fine Floats (winQSB)

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    Non-Critical Activities (..) [5, 16] H ! Making appropriate decisions to precisely when to start noncritical activities is a key feature of network analysis/project management.

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    (1)

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    (2)

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    . : (i) , (ii) (iii) . . :

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    = (a + 4m + b)/6

    2 = ((b-a)/6)2a = b = m = :

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    : .

    .. = SUM( . ) 2 = SUM( . ) :

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    : ABC Associates (1)

    Immed. Optimistic Most Likely Pessimistic Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -- 4 6 8 B -- 1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.511 K G,I 3 5 7

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    : ABC Associates (2)

    t = (a + 4m + b)/6 2 = ((b-a)/6)2Activity Expected Time Variance A 6 4/9 B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9

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    : ABC Associates (3) 64355241635

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    : ABC Associates (4) ES, EF LS, LF0 60 69 139 1313 1813 18 9 1116 1813 1914 2019 2220 2318 2318 23 6 712 136 96 90 45 9 6 1115 20 = max{22, 23} = 23

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    : ABC Associates (5)/ and SlackExpected Time Variance Activity ES EF LS LF Slack 64/9 A 0 6 0 6 0 *44/9 B 0 4 5 9 53 0 C 6 9 6 9 0 *51/9 D 6 11 15 20 911/36 E 6 7 12 13 641/9 F 9 13 9 13 0 *24/9 G 9 11 16 18 761/9 H 13 19 14 20 15 1 I 13 18 13 18 0 *31/9 J 19 22 20 23 154/9 K 18 23 18 23 0 *