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Project Scheduling: PERT/CPM

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Project Scheduling: PERT/CPM

M. En C. Eduardo Bustos Farias

- 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

- 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: 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

M. En C. Eduardo Bustos Farias

- 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

- 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:
- 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

- 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

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

- 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

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

How should activity K be added?

M. En C. Eduardo Bustos Farias

This works, but there is a better way.

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

Expected time to complete the project is 44 days.

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

Expected time to complete the project is 44 days.

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

M. En C. Eduardo Bustos Farias

Probabilistic Time Estimation

M. En C. Eduardo Bustos Farias

- Expected completion time:
- Based on optimistic, pessimistic, most likely
- Take weighted average of the 3 times
- TE = (a + 4m + b)/6

M. En C. Eduardo Bustos Farias

Transforming Plan to Network

M. En C. Eduardo Bustos Farias

- 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

M. En C. Eduardo Bustos Farias

Henry Laurence Gantt (1861-1919)

M. En C. Eduardo Bustos Farias

- 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

- 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

M. En C. Eduardo Bustos Farias

- 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

- Step 1 – list the tasks in the project

M. En C. Eduardo Bustos Farias

- Step 2 – add task durations

M. En C. Eduardo Bustos Farias

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

M. En C. Eduardo Bustos Farias

- 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

- 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

- 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

- 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

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

- 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

- 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

- Clearly defined, independent and stable activities
- Specified precedence relationships
- Subjective time estimates
- Over emphasis on critical paths

M. En C. Eduardo Bustos Farias

- 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

M. En C. Eduardo Bustos Farias

- 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

- 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

M. En C. Eduardo Bustos Farias

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

- 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

- 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

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

- 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

Total Costs

Indirect/Penalty Costs

Cost

Costs of Crashing

Time

Time-Cost Trade-Off

M. En C. Eduardo Bustos Farias

10-9

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

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

(

)

=

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

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 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

- 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

- Consider the following PERT network:

M. En C. Eduardo Bustos Farias

- 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

- 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

- 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