Project scheduling pert cpm l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 65

Project Scheduling: PERT/CPM PowerPoint PPT Presentation


  • 327 Views
  • Uploaded on
  • Presentation posted in: General

Project Scheduling: PERT/CPM. Characteristics of a Project. A unique, one-time effort Requires the completion of a large number of interrelated activities Resources, such as time and/or money, are limited Typically has its own management structure. Project Management.

Download Presentation

Project Scheduling: PERT/CPM

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Project scheduling pert cpm l.jpg

Project Scheduling: PERT/CPM

M. En C. Eduardo Bustos Farias


Characteristics of a project l.jpg

Characteristics of a Project

  • A unique, one-time effort

  • Requires the completion of a large number of interrelated activities

  • Resources, such as time and/or money, are limited

  • Typically has its own management structure

M. En C. Eduardo Bustos Farias


Project management l.jpg

Project Management

  • A project manager is appointed to head the project management team

  • The team members are drawn from various departments and are temporarily assigned to the project

  • The team is responsible for the planning, scheduling and controlling the project to its completion

M. En C. Eduardo Bustos Farias


Pert and cpm l.jpg

PERT and CPM

  • PERT: Program Evaluation and Review Technique

  • CPM: Critical Path Method

    • Graphically displays project activities

    • Estimates how long the project will take

    • Indicates most critical activities

    • Show where delays will not affect project

M. En C. Eduardo Bustos Farias


Slide5 l.jpg

M. En C. Eduardo Bustos Farias


Project schedule l.jpg

Project Schedule

  • Converts action plan into operating timetable

  • Basis for monitoring & controlling project activity

  • More important for projects than for day-to-day operations

    • projects lack continuity of on-going functions

    • more complex coordination needed

  • One schedule for each major task level in WBS

  • Maintain consistency among schedules

  • Final schedule reflects interdependencies, departments.

M. En C. Eduardo Bustos Farias


Network model l.jpg

Network Model

  • Serves as a framework for:

    • planning, scheduling, monitoring, controlling

    • interdependencies and task coordination

    • when individuals need to be available

    • communication among departments and functions needed on the project

  • Identifies critical activities and slack time

  • Reduces interpersonal conflict

M. En C. Eduardo Bustos Farias


Pert cpm l.jpg

PERT / CPM

  • PERT:

    • Program Evaluation and Review Technique

    • estimates probability of on-time completion

  • CPM:

    • Critical Path Method

    • deterministic time estimates

    • control both time and cost

  • Similar purposes, techniques, notation

  • Both identify critical path and slack time

  • Time vs. performance improvement

M. En C. Eduardo Bustos Farias


Pert cpm definitions l.jpg

PERT / CPM Definitions

  • Activity: task or set of tasks

    • uses resources and takes time

  • Event: result of completing an activity:

    • has identifiable end state at a point in time

  • Network: combined activities & events in a project

  • Path: series of connected activities

  • Critical: activities, events, or paths which, if delayed, will delay project completion

  • Critical path: sequence of critical activities from start to finish

  • Node / Arrow (Arc) - PERT / CPM notation

M. En C. Eduardo Bustos Farias


The basics of using pert cpm l.jpg

The Basics of Using PERT/CPM

M. En C. Eduardo Bustos Farias


The project network model l.jpg

The Project Network Model

M. En C. Eduardo Bustos Farias


Pert cpm notations l.jpg

PERT / CPM Notations

  • EOT:

    • earliest occurrence time for event

    • time required for longest path leading to event

  • LOT: latest occurrence time for event

  • EST: earliest starting time for activity

  • LST: latest starting time for activity

  • Critical time: shortest time in which the project can be completed

  • Notation: AOA, AON, dummy activities

M. En C. Eduardo Bustos Farias


Slack time l.jpg

Slack Time

M. En C. Eduardo Bustos Farias


Project network l.jpg

Project Network

M. En C. Eduardo Bustos Farias


Example l.jpg

Example

M. En C. Eduardo Bustos Farias


Partial network l.jpg

Partial Network

How should activity K be added?

M. En C. Eduardo Bustos Farias


Slide17 l.jpg

This works, but there is a better way.

M. En C. Eduardo Bustos Farias


Slide18 l.jpg

M. En C. Eduardo Bustos Farias


Earliest time for an event l.jpg

Earliest Time for an Event

M. En C. Eduardo Bustos Farias


Earliest time for each event l.jpg

Earliest Time for Each Event

Expected time to complete the project is 44 days.

M. En C. Eduardo Bustos Farias


Latest time for an event l.jpg

Latest Time for an Event

M. En C. Eduardo Bustos Farias


Latest time for each event l.jpg

Latest Time for Each Event

Expected time to complete the project is 44 days.

M. En C. Eduardo Bustos Farias


Slack time23 l.jpg

Slack Time

M. En C. Eduardo Bustos Farias


Critical activities l.jpg

Critical Activities

M. En C. Eduardo Bustos Farias


Probabilistic time estimation l.jpg

Probabilistic Time Estimation

M. En C. Eduardo Bustos Farias


Slide26 l.jpg

  • Expected completion time:

  • Based on optimistic, pessimistic, most likely

  • Take weighted average of the 3 times

    • TE = (a + 4m + b)/6

  • Uncertainty = variance (range of values)

  • Probability of completion of project in desired time D

  • M. En C. Eduardo Bustos Farias


    Transforming plan to network l.jpg

    Transforming Plan to Network

    M. En C. Eduardo Bustos Farias


    Slide28 l.jpg

    • Know activities which comprise project

    • Determine predecessor and successor activities

    • Time and resources for activities

    • Interconnections depend on technical interdependencies

    • Expected completion time

      • as soon as possible versus as late as possible

    M. En C. Eduardo Bustos Farias


    Gantt chart l.jpg

    GANTT Chart

    M. En C. Eduardo Bustos Farias


    Gantt charts l.jpg

    Gantt Charts

    Henry Laurence Gantt (1861-1919)

    M. En C. Eduardo Bustos Farias


    Slide31 l.jpg

    • Planned and actual progress

    • for multiple tasks on horizontal time scale

    • easy to read, easy to construct

    • effective monitoring and control of progress

    • requires frequent updating

    M. En C. Eduardo Bustos Farias


    Components of gantt chart l.jpg

    Components of GANTT Chart

    • Activities - scheduled and actual

    • Precedence relationships

    • Milestones (identifiable points in project)

      • usually represents reporting requirements

      • usually corresponds to critical events

    • Can add budget information

    • Does not show technical interdependencies

    • Need PERT network to interpret, control, and compensate for delays

    M. En C. Eduardo Bustos Farias


    Planning and scheduling l.jpg

    Planning and Scheduling

    M. En C. Eduardo Bustos Farias


    Gantt basics l.jpg

    Gantt Basics

    • Basically, a timeline with tasks that can be connected to each other

    • Note the spelling!

    • It is not all-capitals!

    • Can be created with simple tools like Excel, but specialised tools like Microsoft Project make life easier

    M. En C. Eduardo Bustos Farias


    Making a gantt chart l.jpg

    Making a Gantt chart

    • Step 1 – list the tasks in the project

    M. En C. Eduardo Bustos Farias


    Making a gantt chart36 l.jpg

    Making a Gantt chart

    • Step 2 – add task durations

    M. En C. Eduardo Bustos Farias


    Making a gantt chart37 l.jpg

    Making a Gantt chart

    • Step 3 – add dependencies (which tasks cannot start before another task finishes)

    M. En C. Eduardo Bustos Farias


    Notes l.jpg

    Notes

    • The arrows indicate dependencies.

    • Task 1 is a predecessor of task 2 – i.e. task 2 cannot start before task 1 ends.

    • Task 3 is dependent on task 2. Task 7 is dependent on two other tasks

    • Electrics, plumbing and landscaping are concurrent tasks and can happen at the same time, so they overlap on the chart. All 3 can start after task 4 ends.

    • Painting must wait for both electrics and plumbing to be finished.

    • Task 9 has zero duration, and is a milestone

    M. En C. Eduardo Bustos Farias


    Making a gantt chart39 l.jpg

    Making a Gantt chart

    • Step 4 – find the critical path

    The critical path is the sequence of tasks from beginning to end that takes the longest time to complete.

    It is also the shortest possible time that the project can be finished in.

    Any task on the critical path is called a critical task.

    No critical task can have its duration changed without affecting the end date of the project.

    M. En C. Eduardo Bustos Farias


    Slide40 l.jpg

    • MS Project can work out the critical path for you!

    • The length of the critical path is the sum of the lengths of all critical tasks (the red tasks 1,2,3,4,5,7) which is 2+3+1+1.5+2+1 = 10.5 days.

    • In other words, the minimum amount of time required to get all tasks completed is 10.5 days

    • The other tasks (6,8) can each run over-time before affecting the end date of the project

    M. En C. Eduardo Bustos Farias


    Slide41 l.jpg

    • The amount of time a task can be extended before it affects other tasks is called slack (or float).

    • Both tasks 6 and 8 can take one extra day before they affects a following task, so each has one day’s slack.

    M. En C. Eduardo Bustos Farias


    Slide42 l.jpg

    Critical tasks, by definition, can have NO slack.

    Tip:

    If ever asked Can task X’s duration be changed without affecting the end date of the project?, if it is a critical task the answer is always NO!

    M. En C. Eduardo Bustos Farias


    Benefits of cpm pert l.jpg

    Benefits of CPM/PERT

    • Useful at many stages of project management

    • Mathematically simple

    • Give critical path and slack time

    • Provide project documentation

    • Useful in monitoring costs

    M. En C. Eduardo Bustos Farias


    Advantages of pert cpm l.jpg

    Advantages of PERT/CPM

    • useful at several stages of project management

    • straightforward in concept, and not mathematically complex

    • uses graphical displays employing networks to help user perceive relationships among project activities

    • critical path and slack time analyses help pinpoint activities that need to be closely watched

    • networks generated provide valuable project documentation and graphically point out who is responsible for various project activities

    • applicable to a wide variety of projects and industries

    • useful in monitoring not only schedules, but costs as well

    M. En C. Eduardo Bustos Farias


    Limitations to cpm pert l.jpg

    Limitations to CPM/PERT

    • Clearly defined, independent and stable activities

    • Specified precedence relationships

    • Subjective time estimates

    • Over emphasis on critical paths

    M. En C. Eduardo Bustos Farias


    Limitations of pert cpm l.jpg

    Limitations of PERT/CPM

    • project activities must be clearly defined, independent, and stable in their relationships

    • precedence relationships must be specified and networked together

    • time activities in PERT are assumed to follow the beta probability distribution -- this may be difficult to verify

    • time estimates tend to be subjective, and are subject to fudging by managers

    • there is inherent danger in too much emphasis being placed on the critical path

    M. En C. Eduardo Bustos Farias


    Probabilistic pert cpm l.jpg

    Probabilistic PERT/CPM

    M. En C. Eduardo Bustos Farias


    Mean and standard deviation of project duration l.jpg

    Mean and Standard Deviation of Project Duration

    • Once the expected time te for all activities has been computed, proceed to use te in place of the single activity duration in CPM to work out the critical path and the project duration

    • The resulting project duration is the mean project duration TE

    • We also need to work out the standard deviation of the project duration  as follows:

      • Project Duration = (Summation of i2 f all the activities on the critical path)

    M. En C. Eduardo Bustos Farias


    Probability of different project durations l.jpg

    Probability of Different Project Durations

    • From statistics, once we know the mean project duration, TE, and the standard deviation of the project duration,  we can work out the probability that the project duration will be shorter than any specific time, T (i.e. the project will take T days or less) through the following formula:

      • Z=(T- TE )/  , where Z is the quantity called the Normal variate

      • Knowing Z, we can read off the probability from Normal Distribution Tables which are provided in nest slides

    M. En C. Eduardo Bustos Farias


    Normal distribution table for negative values of z l.jpg

    Normal Distribution Table for Negative Values of Z

    M. En C. Eduardo Bustos Farias


    Normal distribution table for positive values of z l.jpg

    Normal Distribution Table for Positive Values of Z

    Z | Probability

    ---------------------

    0.0 | 0.5000

    0.1 | 0.5398

    0.2 | 0.5793

    0.3 | 0.6179

    0.4 | 0.6554

    0.5 | 0.6915

    0.6 | 0.7257

    0.7 | 0.7580

    0.8 | 0.7881

    0.9 | 0.8159

    1.0 | 0.8413

    1.1 | 0.8643

    1.2 | 0.8849

    1.3 | 0.9032

    1.4 | 0.9192

    1.5 | 0.9332

    Z | Probability

    ---------------------

    1.6 | 0.9452

    1.7 | 0.9554

    1.8 | 0.9641

    1.9 | 0.9713

    2.0 | 0.9772

    2.1 | 0.9821

    2.2 | 0.9861

    2.3 | 0.9893

    2.4 | 0.9918

    2.5 | 0.9938

    2.6 | 0.9953

    2.7 | 0.9965

    2.8 | 0.9974

    2.9 | 0.9981

    3.0 | 0.9987

    >3.0| 1

    M. En C. Eduardo Bustos Farias


    Example52 l.jpg

    Example

    • Consider a project with TE = 5days and =2 days.If we wish to find out the probability that the project will take 7 days or less. Thus T=7days. First, work out a value (calles the normal variate) Z, as follows:

      • Z=(T- TE )/ =(7-5)/2=1

      • Read off the Normal Distribution Tables, the probability for Z=1. We get the value 0.8413. Thus the probability that the project will take 7 days or less is 0.8413

      • If we need to find the probability that the project takes more than 7 days, we make use of the fact that:

        • Probability that project takes more than x days= 1-Probability that project takes x days or less

        • Probability that project takes more than 7 days= 1-Probability that project takes 7 days or less = 1-0.8413=0.1587

    M. En C. Eduardo Bustos Farias


    Interpolating from the normal distribution table l.jpg

    Interpolating from the Normal Distribution Table

    • In the previous example, the ‘Z’ value was 1.0 and could be read off directly. If you had a value like 1.01, you could still round it off to 1.0

    • However there will be instances when you will get a value like 1.275, in which case you will need to interpolate from the table

    • From the table Z1=1.2, P1=0.8849

      Z2=1.3, P2=0.9039

      Use the interpolation formula:

      P=P1+Z-Z1 *(P2-P1)

      Z2-Z1

      Thereforeat Z=1.275,

      P=0.8849 + 1.275 -1.2 * (0.9039-0.8849) = 0.8992

      1.3-1.2

    M. En C. Eduardo Bustos Farias


    Crash and normal times and costs l.jpg

    Crash and Normal Times and Costs

    Activity

    Cost

    Crash

    Crash Cost - Normal Cost

    $34,000

    $33,000

    $32,000

    $31,000

    $30,000

    Crash Cost/Week =

    Normal Time - Crash Time

    Crash

    Cost

    $34,000 - $30,000

    =

    3 - 1

    $4,000

    =

    = $2,000/Week

    2 Weeks

    Normal

    Normal

    Cost

    1

    2

    3

    Time (Weeks)

    Crash Time

    Normal Time

    M. En C. Eduardo Bustos Farias


    Crash costing l.jpg

    CRASH COSTING

    • 1. Find critical path.

    • 2. Find cheapest act. in critical path

    • 3. Reduce time until:

      • a. Can’t be reduced

      • b. Another path becomes critical

      • c. Increase in direct costs exceeds savings from shortening project

    • 4. Return to Step 1, as longas savings.

    M. En C. Eduardo Bustos Farias


    Slide56 l.jpg

    Total Costs

    Indirect/Penalty Costs

    Cost

    Costs of Crashing

    Time

    Time-Cost Trade-Off

    M. En C. Eduardo Bustos Farias

    10-9


    Beta probability distribution with three time estimates l.jpg

    Beta Probability Distribution with Three Time Estimates

    Probability

    Probability of

    1 in 100

    (a) Occuring

    Probability of

    1 in 100

    (b) Occuring

    Optimistic

    Time

    (a)

    Most

    Likely

    Time

    (m)

    Pessimistic

    Time

    (b)

    Activity Time

    M. En C. Eduardo Bustos Farias


    Time estimates in weeks for project l.jpg

    2

    b - a

    a + 4m + b

    Variance =

    )

    (

    t =

    6

    6

    2

    3 - 1

    6

    4

    36

    (

    )

    =

    2

    4 - 2

    6

    4

    36

    (

    )

    =

    2

    3 - 1

    6

    4

    36

    (

    )

    =

    2

    6 - 2

    6

    16

    36

    (

    )

    =

    2

    7 - 1

    6

    36

    36

    (

    )

    =

    2

    9 - 1

    6

    64

    36

    (

    )

    =

    2

    11 - 3

    6

    64

    36

    (

    )

    =

    2

    3 - 1

    6

    4

    36

    (

    )

    =

    Time Estimates (in weeks) for project

    Optimistic

    a

    Most

    Probable- m

    Pessimistic

    b

    Expected Time

    t = [(a + 4m + b)/6]

    Variance

    [(b - a)/6]2

    Activity

    A

    B

    C

    D

    E

    F

    G

    H

    1

    2

    1

    2

    1

    1

    3

    1

    2

    3

    2

    4

    4

    2

    4

    2

    3

    4

    3

    6

    7

    9

    11

    3

    2

    3

    2

    4

    4

    3

    5

    2

    M. En C. Eduardo Bustos Farias

    Total 25 weeks


    Probability of project meeting the deadline l.jpg

    Probability of Project Meeting the Deadline

    Project Standard

    Deviation, T

    =

    Project Variance

    Due Date - Expected Completion Date

    Z

    =

    T

    16 - 15

    =

    =

    0.57

    1.76

    .57 Standard Deviations

    Probability

    (T  16 Weeks)

    is 71.6%

    15

    Weeks

    16

    Weeks

    Time

    M. En C. Eduardo Bustos Farias


    Pert cost l.jpg

    PERT/Cost

    • PERT/Cost is a technique for monitoring costs during a project.

    • Work packages (groups of related activities) with estimated budgets and completion times are evaluated.

    • A cost status report may be calculated by determining the cost overrun or underrun for each work package.

    • Cost overrun or underrun is calculated by subtracting the budgeted cost from the actual cost of the work package.

    • For work in progress, overrun or underrun may be determined by subtracting the prorated budget cost from the actual cost to date.

    M. En C. Eduardo Bustos Farias


    Pert cost61 l.jpg

    PERT/Cost

    • The overall project cost overrun or underrun at a particular time during a project is determined by summing the individual cost overruns and underruns to date of the work packages.

    M. En C. Eduardo Bustos Farias


    Example how are we doing l.jpg

    Example: How Are We Doing?

    • Consider the following PERT network:

    M. En C. Eduardo Bustos Farias


    Example how are we doing63 l.jpg

    Example: How Are We Doing?

    • Earliest/Latest Times

      ActivityESEFLSLFSlack

      A 0 9 0 9 0

      B 0 8 5 13 5

      C 0 10 7 17 7

      D 8 11 22 25 14

      E 8 12 13 17 5

      F 9 13 13 17 4

      G 9 12 9 12 0

      H 12 17 12 17 0

      I 12 16 21 25 9

      J 17 25 17 25 0

    M. En C. Eduardo Bustos Farias


    Example how are we doing64 l.jpg

    Example: How Are We Doing?

    • Activity Status (end of eleventh week)

      ActivityActual Cost% Complete

      A $6,200 100

      B 5,700 100

      C 5,600 90

      D 0 0

      E 1,000 25

      F 5,000 75

      G 2,000 50

      H 0 0

      I 0 0

      J 0 0

    M. En C. Eduardo Bustos Farias


    Example how are we doing65 l.jpg

    Example: How Are We Doing?

    • Cost Status Report

      (Assuming a budgeted cost of $6000 for each activity)

      ActivityActual CostValueDifference

      A $6,200 (1.00)x6000 = 6000 $200

      B 5,700 (1.00)x6000 = 6000 - 300

      C 5,600 (.90)x6000 = 5400 200

      D 0 0 0

      E 1,000 (.25)x6000 = 1500 - 500

      F 5,000 (.75)x6000 = 4500 500

      G 2,000 (.50)x6000 = 3000 -1000

      H 0 0 0

      I 0 0 0

      J 0 0 0

      Totals $25,500 $26,400 $- 900

    M. En C. Eduardo Bustos Farias


  • Login