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**ELC 347 project management**

Week 10

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**Agenda Integrative Project**

2nd part Graded A few Minor problems 3nd part Due Outline of deliverables (posted in WebCT) Quiz 2 is postedand must be completed by Nov 9 Chapters 5-9, 20 short essays (4 from each chapter) Take home exam with 48 hours time limit Three will only be 3 Quizzes instead of the 4 mentioned in the syllabus Password is “CreepyScope” Today we will discuss Project Scheduling

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**Project Scheduling: Networks, Duration Estimation, and Critical Path**

Chapter 9 © 2007 Pearson Education

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**Project Scheduling Terms**

Successors Predecessors Network diagram Serial activities Concurrent activities Merge activities Burst activities Node Path Critical Path E D C B A F

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**Network Diagrams Help schedule resources Show interdependence**

Show start & finish dates Facilitate communication Determine project completion Identify critical activities

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**AOA Vs. AON The same mini-project is shown with activities on arc…**

D B F …and activities on node. E D B F C

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**Node Labels Basic math ES + DUR = EF LS + DUR = LF ES+AF=LS**

Early Start Activity Float Activity Descriptor Late Start ID Number Activity Duration Late Finish Early Finish Basic math ES + DUR = EF LS + DUR = LF ES+AF=LS

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**CPM versus PERT PERT was developed by US Navy in the 1950s’**

CPM was developed by Remington Rand and DuPont around the same time. Only difference is in durations estimating Pert uses 3 cases Most optimistic, most pessimistic and most likely and determines probability for each DoPo + DpOp +DePe = final duration CPM use only the most likely duration

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Duration Estimating Duration – the elapsed time from the start of an activity until it is finished Effort -- the actual time spent on the project Example Tony work on a project task for 20 hours at 4 hours per day starting Monday mourning. The project task was completed Late Friday Effort – 20 hours Duration – 5 days

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**Techniques for Estimating Duration**

Experience Historical data Research Modeling Experiments Breakdown/roll-up Delphi Method Panel of experts Consultants Three outside Estimates Ranging Other techniques

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**Duration Estimation Methods**

Past experience Expert opinion Mathematical derivation – Beta distribution Most likely (m) Most pessimistic (b) Most optimistic (a)

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**Sketch the network described in the table. **

Determine the expected duration and variance of each activity. Task Predecessor a m b Z -- 7 8 15 Y 13 16 19 X 14 18 22 W Y, X 12 V 1 4 T 6 10 S T, V 11 Task a b c Mean Variance Z Y X W V T S Task Early Start Early Finish Late Start Late Finish Slack Z Y X W V T S Project Length 64 Project Variance Project Std.dev Duration estimate.xls

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**Constructing the Critical Path**

Forward pass – an additive move through the network from start to finish Determines ES and EF using ES+DUR = EF If 2 (or more) EF from proceeding uses largest Backward pass – a subtractive move through the network from finish to start Determines LS and LF using LF- DUR = LS If 2 (or more) LS from succeeding use smallest Determine AF using LS-ES = AF Critical path – the longest path from end to end which determines the shortest project length

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**Rules for Forward/Backward Pass**

Forward Pass Rules (ES & EF) ES + Duration = EF EF of predecessor = ES of successor Largest preceding EF at a merge point becomes EF for successor Backward Pass Rules (LS & LF) LF – Duration = LS LS of successor = LF of predecessor Smallest succeeding LS at a burst point becomes LF for predecessor

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**Calculating a Project Duration**

Determine each activity and its predecessors Determine an estimated duration for each activity Find the “Critical Path” Add up the durations along the critical path

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**Whats the “Critical Path”**

The longest path based on precedence of activities and durations through a PERT/CPM network It’s critical because Its combined length determines the length of the project It has NO slack Delay of any activities on the critical path delays the entire project

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**Finding the critical path**

Use “forward pass” Calculations Each activity should have ES earliest possible Start time EF earliest possible finish time DUR duration EF = ES + DUR ES DUR EF Activity

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Example 3 4 7 A 7 5 12 B

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Special Case If an activity has more than one processor its EPS is set to the latest EPF of all its processors 3 4 7 A 7 5 12 C 5 B

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**An example of forward pass**

5 4 9 B 12 4 16 G 16 7 23 H 5 A 25 4 29 Finish 4 8 12 C 16 5 21 I Start 8 4 12 F 21 4 25 J 4 D 4 8 E

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**Backwards Pass Use to calculate Slack LS -> Latest start time**

LF -> Latest finish time TS -> total slack ES DUR EF Activity LS TS LF

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**An example of backward pass**

12 4 16 G 16 7 23 H 18 2 25 5 4 9 B 8 3 12 5 A 3 8 25 4 29 Finish 4 8 12 C 16 5 21 I Start 8 4 12 F 16 21 4 25 J 4 D 4 8 E 12

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**Sketch the network described in the table.**

Task Predecessor Time A -- 4 B 9 C 11 D 5 E 3 F 7 G D, F H E, G 2 K 1 Sketch the network described in the table. Determine the ES, LS, EF, LF, and slack of each activity Task ES EF LS LF Slack A B C D E F G H K SLACK.xls

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**Examine Critical Path for Reality Check**

Is the total duration typical? Are the durations of the CP activities typical? Reexamine all CP activity durations Reexamine assumptions

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Laddering Activities Project ABC can be completed more efficiently if subtasks are used ABC=18 days A(3) B(6) C(9) A1(1) A2(1) A3(1) B1(2) B2(2) B3(2) C1(3) C2(3) C3(3) Laddered ABC=12 days

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**Useful with a complex project or one that has a shared budget**

Hammock Activities Used as summaries for subsets of activities 0 A 5 B 15 15 C 18 0 Hammock 18 Useful with a complex project or one that has a shared budget

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**Reducing the Critical Path**

Eliminate tasks on the CP Convert serial paths to parallel when possible Overlap sequential tasks Shorten the duration on critical path tasks Shorten early tasks longest tasks easiest tasks tasks that cost the least to speed up

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Project Scheduling Prof. Jiang Zhibin Dept. of IE, SJTU.

Project Scheduling Prof. Jiang Zhibin Dept. of IE, SJTU.

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