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Project Management Introduces Pert/CPM as a tool for planning, scheduling, and controlling projects Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions Philip A. Vaccaro, PhD MGMT E-5050

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Project Management Overview History and ImportanceHistory and Importance The Two Pert / CPM ConventionsThe Two Pert / CPM Conventions Pert / CPM Building BlocksPert / CPM Building Blocks ES, EF, LS, LF, and SES, EF, LS, LF, and S Task Times Task Times Probabilistic PERTProbabilistic PERT

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Project Examples New Product Development & Manufacture New Product Promotion Campaign Broadway Shows Television Programs Corporate Restructure Software Conversion Weapons System Skyscraper Bridges & Highways Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions

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Lost revenues and profits Contract penalties Loss of clientele Higher costs due to overruns Reputation damage Resource waste Missed Deadline Consequences

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Project Prerequisites Tasks with clear start/finish points Tasks with alternate execution sequences Tasks with several possible time estimates Tasks that run parallel to each other THESE PREREQUISITES STRENGTHEN MANAGEMENT ACCOUNTABILITY AND PROVIDE FLEXIBILITY IN THE FACE OF FUNDING CHANGES, STAFFING, & TECHNICAL PROBLEMS

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Project Prerequisites Tasks with clear start/finish points Laying the foundation of a new home starts when the excavation crew and equipment arrive on the site and ends when the foundation has been poured. Framing starts when the carpenters arrive on site and ends when the frame has been built.

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Project Prerequisites Tasks with alternate execution sequences Tasks that can be reordered might result in overall shorter overall execution times and less cost.

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Project Prerequisites Tasks with several possible time estimates Identifying best case, worst case, and most likely time estimates for each project task allows us to better adopt to changes in funding, deadlines, and unforeseen technical problems. Flexibility

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Project Prerequisites Tasks that run parallel to each other It is vital that several tasks be scheduled at the same time, so that, if one of them is in danger of falling behind, the others will stand ready to assist with extra funds, personnel, equipment, and other resources. This will, in turn, save the entire project from falling behind schedule!

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PERT / CPM History The Critical Path Method (CPM) was developed in 1957 by J.E. Kelly of Remington Rand and M.R. Walker of DuPont. Originally, CPM was used to assist in building chemical plants, reducing completion time from 7 to 4 years. CPM requires only one time estimate for each project task

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PERT / CPM History Program Evaluation and Review Technique was developed in 1958 by the United States Navy Special Projects Office. Originally used to plan and control the Polaris submarine program, reducing completion time from 7 to 4 years ! In 1960, PERT and CPM were combined, hence the term PERT/CPM. PERT requires 3 time estimates for each project task

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U.S. Navy Special Projects Office Grace Murray Hopper 1906 - 1992 Ph.D, Yale University, 1934 Professor, Vassar College, 1931-1941 Developed the COBOL programming language and the compiler Worked on the Mark I & II computers at Harvard University Developed international standards for computer languages Lecturer, consultant, engineer, operations researcher Received 47 honorary degrees Naval reservist First women admiral, U.S. Navy (1984) Famous Staff Member

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Grace Murray Hopper Anecdote While she was working on the Mark II computer at Harvard University, her associates discovered a moth stuck on a relay, thereby impeding operation. Whereupon she remarked that they were “debugging” the system. The remains of the moth can be found at the Smithsonian Museum of American History in Washington, D.C.

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PERT / CPM PERT / CPM The Two Conventions Activity-on-Node Activity-on-Arc TASKS ARE SHOWN AS ARROWS ( ARCS ) NODES REPRESENT TASK START AND FINISH Activity-on-Node TASKS ARE SHOWN AS SQUARES ( NODES ) ARROWS REPRESENT TASK PREDECESSOR RELATIONSHIPS

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Activity-on-Node Convention The network is cleaner and uncluttered It is natural to view nodes as tasks It is easier to use than the activity-on-arc convention U.S. Government switched over to the AON convention in 2001 ADVANTAGES

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Activity-on-Node Building Blocks Nodes represent the tasks/activities Small nodes represent the start and finish of the project Arcs/arrows show the predecessor relationships among the tasks start 1 st Task 2 nd Task 3 rd Task end Here, the 2 nd task cannot begin until the 1 st task has been completed. The 3 rd task cannot begin until the 2 nd task has been completed.

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GENERAL FOUNDRY INC. GENERAL FOUNDRY INC. PROJECT TASKS TASK A TASK A – Build Internal Component TASK B TASK B – Modify Roof and Floor TASK C TASK C – Construct Collection Stack TASK D TASK D – Pour Concrete TASK E TASK E – Build Burner TASK F TASK F – Install Control System TASK G TASK G – Install Pollution Device TASK H TASK H – Inspect & Test EXAMPLE

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General Foundry Inc. THE PERT/CPM NETWORK STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS Time can be expressed in days, weeks, or months

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Task Interpretation EXAMPLE 2 A ES = 0EF = 2 TASK “A” EXPECTED DURATION TIME IS 2 WEEKS EARLIEST TIME TASK “A” CAN START IS AT THE END OF WEEK “0” THAT IS, THE START OF WEEK “1” EARLIEST TIME TASK “A” CAN FINISH IS AT THE END OF WEEK “2” THAT IS, THE START OF WEEK “3”

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Expected Task or Activity Time te = [ 1a + 4m + 1b ] 6 optimistic time estimate most likely time estimate pessimistic time estimate 67% Weights Sum of the Weights A WEIGHTED AVERAGE TIME FORMULA 17% Expected times are usually used for each task in the project

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Expected Task or Activity Time GIVEN: a = 1 week, b = 3 weeks, m = 2 weeks [ 1a + 4m + 1b ] [ 1(1) + 4(2) + 1(3) ] 6 6 12 = te = 2 weeks 6 == OPTIMISTIC TIME PESSIMISTIC TIME MOST LIKELY TIME EXAMPLE

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The BETA Distribution ( a skewed distribution) m tete a b Optimistic time Most likely time (mode) Pessimistic time Expected time TASK TIME IS NOT ASSUMED TO BE NORMALLY DISTRIBUTED The probability distribution commonly used to describe the inherent variability in task time estimates

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The BETA DISTRIBUTION Symmetrical, right, or left-skewed based on the nature of a particular task Unimodal with a high concentration of probability surrounding the most likely time estimate (m) No strong empirical reason for using the BETA distribution Attractive however, because the mean (μ) and the variance ( ) can be easily obtained from the three time estimates “a”, “m”, and “b” CHARACTERISTICS & COMMENTS

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The Critical Path ( CP ) The chain of tasks from project start to end that consumes the longest amount of time. Any delay in one or more of those tasks will delay the entire project. The critical path is equal to the project’s expected or mean completion time. start AB C end DE

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Critical Path Characteristics Several critical paths may exist within the project network at any given time. These critical paths may change or disappear entirely at any given time as the project progresses Management must monitor all critical paths closely.

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General Foundry Inc. THE NETWORK STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS

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General Foundry Inc. 1st Critical Path Candidate STARTFINISH A B C D E F G H 2 3 23 4 45 2 A-C-F-H Nine (9) Weeks

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General Foundry Inc. 2nd Critical Path Candidate STARTFINISH A B C D E F G H 2 3 23 4 45 2 A-C-E-G-H Fifteen (15) weeks

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General Foundry Inc. 3rd Critical Path Candidate STARTFINISH A B C D E F G H 2 3 23 4 45 2 B-D-G-H Fourteen (14) weeks

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The Critical Path A-C-F-H9 weeks A-C-E-G-H15 weeks B-D-G-H14 weeks The expected, mean, or average project completion time is 15 weeks

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General Foundry Inc. THE CRITICAL PATH STARTFINISH A B C D E F G H 2 3 23 4 45 2 Fifteen (15) Weeks

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E EE Expected, Mean, or Average Project Completion Time μ Here, 15 Weeks 50% CHANCE OF COMPLETION BEFORE μ (15 weeks) 50% CHANCE OF COMPLETION AFTER μ (15 weeks) THE CRITICAL PATH EQUALS MEAN PROJECT COMPLETION TIME

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EARLY START TIME ( ES ) The technique is called FORWARD PASS The earliest time that each task can begin. Computed from left to right, that is, from the network’s begin- ning node to the net- work’s finish node.

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EARLY START TIME FORMULA PREDECESSOR TASK ES PREDECESSOR TASK te FOLLOWER TASK ES =+ IF THERE ARE SEVERAL CANDIDATES FOR THE FOLLOWER TASK ES, THE LONGEST ES IS SELECTED THE VERY FIRST TASK IN A PROJECT HAS AN EARLY START TIME OF ZERO As we progress through the project, follower tasks will eventually become predecessor tasks themselves !

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General Foundry Inc. EARLY START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS ES = 0 ES = 2 ES = 3 ES = 4 ES = 8 ES = 13

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EARLY START TIME SELECTED CALCULATIONS PREDECESSOR TASK ES A ( 0 ) PREDECESSOR TASK te A ( 2 ) FOLLOWER TASK ES C ( 2 ) =+ IF THERE ARE SEVERAL CANDIDATES FOR THE FOLLOWER TASK ES, THE LONGEST ES IS SELECTED THE VERY FIRST TASK IN A PROJECT HAS AN EARLY START TIME OF ZERO

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General Foundry Inc. EARLY START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS ES = 0 ES = 2 ES = 3 ES = 4 ES = 8 ES = 13

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EARLY START TIME SELECTED CALCULATIONS PREDECESSOR TASK ES B ( 0 ) PREDECESSOR TASK te B ( 3 ) FOLLOWER TASK ES D ( 3 ) =+ IF THERE ARE SEVERAL CANDIDATES FOR THE FOLLOWER TASK ES, THE LONGEST ES IS SELECTED THE VERY FIRST TASK IN A PROJECT HAS AN EARLY START TIME OF ZERO

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General Foundry Inc. EARLY START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS ES = 0 ES = 2 ES = 3 ES = 4 ES = 8 ES = 13

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ES Candidate Selection 4 E 4 D G 5 ES=4 ES=3 ES=8 COMING IN FROM TASK “E” EARLY START TIME FOR TASK “G” WOULD BE “8” ( 4 + 4 = 8 ) COMING IN FROM TASK “D” EARLY START TIME FOR TASK “G” WOULD BE “7” ( 3 + 4 = 7 ) THEHIGHER EARLY START CONTROLS

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General Foundry Inc. EARLY START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS ES = 0 ES = 2 ES = 3 ES = 4 ES = 8 ES = 13

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ES Candidate Selection 3 F 5 G H 2 ES=4 ES=8 ES=13 COMING IN FROM TASK “F” EARLY START TIME FOR TASK “H” WOULD BE “7” ( 4 + 3 = 7 ) COMING IN FROM TASK “G” EARLY START TIME FOR TASK “H” WOULD BE “13” ( 8 + 5 = 13 ) THEHIGHER EARLY START CONTROLS

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EARLY FINISH TIME ( EF ) This technique is also called FORWARD PASS The earliest time that each task can finish. Computed from left to right, that is, from the network’s beginning node to the network’s finish node.

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EARLY FINISH TIME FORMULA TASK EARLY START TIME ES TASK EXPECTED TIME te TASK EARLY FINISH TIME EF =+ NEEDLESS TO SAY, EARLY FINISH TIMES CANNOT BE COMPUTED UNTIL EARLY START TIMES ARE IDENTIFIED

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General Foundry Inc. EARLY FINISH TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS ES=0EF=2 ES=0EF=3 ES=2EF=4 ES=3EF=7 ES=4EF=7 ES=4EF=8 ES= 8 EF=13 ES=13EF=15

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EARLY FINISH TIME SELECTED CALCULATIONS TASK EARLY START TIME ES = 0 A TASK EXPECTED TIME te = 2 A TASK EARLY FINISH TIME EF = 2 A =+ NEEDLESS TO SAY, EARLY FINISH TIMES CANNOT BE COMPUTED UNTIL EARLY START TIMES ARE IDENTIFIED

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General Foundry Inc. EARLY FINISH TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS ES=0EF=2 ES=0EF=3 ES=2EF=4 ES=3EF=7 ES=4EF=7 ES=4EF=8 ES= 8 EF=13 ES=13EF=15

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EARLY FINISH TIME SELECTED CALCULATIONS TASK EARLY START TIME ES = 2 C TASK EXPECTED TIME te = 2 C TASK EARLY FINISH TIME EF = 4 C =+ NEEDLESS TO SAY, EARLY FINISH TIMES CANNOT BE COMPUTED UNTIL EARLY START TIMES ARE IDENTIFIED

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General Foundry Inc. EARLY FINISH TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS EF=2 EF=3 EF=4 EF=7 EF=7 EF=8 EF=13 EF=15

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LATE FINISH TIME ( LF ) This technique is called BACKWARD PASS The latest time that each task can finish without jeopardizing the project’s expected completion time. Computed from right to left, that is, from the network’s finish node to the network’s start node.

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LATE FINISH TIME FORMULA FOLLOWER TASK LATE FINISH TIME (LF) FOLLOWER TASK EXPECTED TIME (te) PREDECESSOR TASK LATE FINISH TIME (LF) = - IF THERE ARE SEVERAL CANDIDATES FOR THE PREDECESSOR TASK LF, SELECT THE SHORTEST LF

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General Foundry Inc. LATE FINISH TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS LF = 2 LF = 4 LF = 8 LF = 13 LF = 8 LF = 13 LF = 15

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LATE FINISH TIME SELECTED CALCULATIONS FOLLOWER TASK LATE FINISH TIME (LF = 15) H FOLLOWER TASK EXPECTED TIME (te = 2) H PREDECESSOR TASK LATE FINISH TIME (LF = 13) F = - IF THERE ARE SEVERAL CANDIDATES FOR THE PREDECESSOR TASK LF, SELECT THE SHORTEST LF

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General Foundry Inc. LATE FINISH TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS LF = 2 LF = 4 LF = 8 LF = 13 LF = 8 LF = 13 LF = 15

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LF Candidate Selection 2 C 4 E F 3 LF=4 LF=8 LF=13 COMING IN FROM TASK “F”. THE LATE FINISH TIME FOR TASK “C” IS “10” (13-3=10) COMING IN FROM TASK “E”, THE LATE FINISH TIME FOR TASK “C” IS “4” (8-4=4) THE SMALLER LATE FINISH TIMECONTROLS

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LATE START TIME ( LS ) This technique is also called BACKWARD PASS The latest possible time that each task can start without jeopardizing the project’s expected completion time. Computed from right to left, that is, from the network’s finish node to the network’s start node.

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LATE START TIME FORMULA TASK LATE FINISH TIME (LF) TASK EXPECTED TIME (te) TASK LATE START TIME (LS) = - NEEDLESS TO SAY, TASK LATE START TIMES CANNOT BE COMPUTED UNTIL TASK LATE FINISH TIMES ARE IDENTIFIED

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General Foundry Inc. LATE START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS LS=0LF=2 LS=1LF=4 LS=2LF=4 LS=4LF=8 LS=10LF=13 LS=4LF=8 LS= 8 LF=13 LS=13LF=15

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LATE START TIME SELECTED CALCULATIONS TASK LATE FINISH TIME (LF = 15) H TASK EXPECTED TIME (te = 2) H TASK LATE START TIME (LS = 13) H = - NEEDLESS TO SAY, TASK LATE START TIMES CANNOT BE COMPUTED UNTIL TASK LATE FINISH TIMES ARE IDENTIFIED

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General Foundry Inc. LATE START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS LS=0LF=2 LS=1LF=4 LS=2LF=4 LS=4LF=8 LS=10LF=13 LS=4LF=8 LS= 8 LF=13 LS=13LF=15

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LATE START TIME LATE START TIME SELECTED CALCULATIONS TASK LATE FINISH TIME (LF = 4) B TASK EXPECTED TIME (te = 3) B TASK LATE START TIME (LS = 1) B = - NEEDLESS TO SAY, TASK LATE START TIMES CANNOT BE COMPUTED UNTIL TASK LATE FINISH TIMES ARE IDENTIFIED

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General Foundry Inc. LATE START TIMES STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS LS=0 LS=1 LS=2 LS=4 LS=10 LS=4 LS=8 LS=13

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SLACK TIME ( S ) The time each task may be postponed without jeopardizing the project’s expected completion time. The chain of zero slack tasks in the network will also identify the critical path. ALSO KNOWN AS PRIMARY SLACK

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SLACK TIME FORMULAE TWO VERSIONS S = Task LS – Task ES S = Task LF – Task EF

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General Foundry Inc. ALL SLACK TIME CALCULATIONS STARTFINISH A B C D E F G H 2 3 23 4 45 2 ES=0 EF=3 LS=1 LF=4 S=1 S=1 ES=2 EF=4 LS=2 LF=4 S=0 S=0 ES=3 EF=7 LS=4 LF=8 S=1 S=1 ES= 4 EF= 7 LS=10 LF=13 S=6 S=6 ES=4 EF=8 LS=4 LF=8 S=0 S=0 ES=8 EF=13 LS=8 LF=13 S=0 S=0 ES=13 EF=15 LS=13 LF=15 S=0 S=0 ES = 0 EF = 2 LS = 0 LF = 2 S = 0

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General Foundry Inc. PRIMARY SLACK TIMES FOR ALL TASKS STARTFINISH A B C D E F G H 2 3 23 4 45 2 TIME in WEEKS S=0 S=1 S=0 S=1 S=6 S=0 S=0 S=0

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General Foundry Inc. CRITICAL PATH VIA ZERO SLACK TIME TASKS STARTFINISH A B C D E F G H 2 3 23 4 45 2 A-C-E-G-H S=0 S=1 S=0 S=1 S=6 S=0 S=0 S=0

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Probabilistic PERT 1.Critical path time ( CP or μ ) 2. CP tasks’ optimistic times ( a ) 3. CP tasks’ pessimistic times ( b ) 4. CP tasks’ time variances ( ) REQUIRES 4 STATISTICS Generates probabilities for completing a project before and after its expected completion date.

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Task Time Variance Formula OF THE BETA DISTRIBUTION 2 where: a = optimistic time b = pessimistic time 6 = constant ( k ) MUCH EASIER FORMULA THAN THE ONE FOR THE NORMAL PROBABILITY DISTRIBUTION ! = b - a 6

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EXAMPLE EXAMPLE ALL NEW - VARIANCES FABRICATED Assume the critical path is 36.33 days ( CP = μ ) Assume the tasks along the critical path are: C,D,E,F,H,K Assume that the critical path task time variances ( σ ) in days are: C =.11 C =.11 D =.11 D =.11 E =.44 E =.44 F = 1.78 F = 1.78 H = 1.00 H = 1.00 K = 1.78 K = 1.78 2

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Requirements I.What are the chances of finishing the project in 30 days or less? In other words, P ( t =< 30 ) = ? II.What are the chances of finishing the project in 40 days or less? In other words, P ( t =< 40 ) = ?

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Solution Project Variance = ∑ CP Task Variances ( σ ).11.44 1.78 1.00 1.78 5.22 days = Project 5.22 Std Dev = √5.22 = 2.28 days ( σ ) 2

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Solution μ = 36.33 days σ = 2.28 days X = 30 days Project completion time is normally distributed. Therefore, a normal curve can be drawn with a μ and σ. Z = X – μ = 30.00 – 36.33 = Z = X – μ = 30.00 – 36.33 = - 2.78 σ 2.28 σ 2.28 The no. of standard deviates between the mean ( μ ) and the value of interest ( X ) Z.08 2.7 2.7.99728 The percentage of the normal curve covered to a point that is “2.78” standard deviates to the left of the mean = 99.728% -2.78 z.99728.00272

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Solution Therefore, the probability of finishing the project in 30 days or less is: 1 -.99728 =.00272 P( t =< 30 ) ≈ 0% Conversely, the probability of finishing the project in more than 30 days is:.99728 P( t > 30 ) ≈ 100%

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Solution μ = 36.33 days σ = 2.28 days X = 40 days Project completion time is normally distributed. Therefore, a normal curve can be drawn with a μ and σ. Z = X – μ = 40.00 – 36.33 = Z = X – μ = 40.00 – 36.33 = +1.61 σ 2.28 σ 2.28 The no. of standard deviates between the mean (μ) and the value of interest (X) Z.01 1.6 1.6.94630 The percentage of the normal curve covered to a point that is “1.61” standard deviates to the right of the mean = 94.630% + 1.61 Z.94630.0537

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Solution Therefore, the probability of finishing the project in 40 days or less is:.94630 P( t=<40 ) ≈ 95% Conversely, the probability of finishing the project in more than 40 days is:.0537 P( t>40 ) ≈ 5%

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PERT / CPM with QM for WINDOWS

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We scroll to PROJECT MANAGEMENT ( PERT / CPM ) Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions

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We have only one time estimate for each task in this project We select the SINGLE TIME ESTIMATE program

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There are 8 tasks in the project “Precedence List” is another term for Activity-on-Node Convention The tasks are labeled A, B, C, D, etc.

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The Data Input Table “Prec” is an abbreviation for “Predecessor Task”. Here, the program provides for listing as many as 7 predecessor tasks for each task.

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Project Estimated Completion Time ( Critical Path ) Zero Slack Time Tasks Are Highlighted In Red

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The 2 nd Solution Is “CHARTS” Four Different Charts Can Be Brought Up By Clicking Their Titles Early Start Early Finish Late Start Late Finish Critical Path Tasks

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Here, the program displays a precedence relationship diagram based on what we entered in the “predecessor” columns The Critical Path Tasks Are Shown In Red

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Template and Sample Data

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Template and Sample Data

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Project Management

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