INSE6230_L7
Transcript of INSE6230_L7
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INSE 6230: Total Quali ty Project Managemen t
Lectu re #7
Project Time Management 3
Project Cost Management
Nov. 5, 2012
Instruc tor: Dr. Zhigang (Wil l) Tian
CIISE, Faculty of Eng ineering and Comp uter Science
Conco rdia Univers i ty
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Presenting the Scheduling Results
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Gant Chart
Lists activities and shows
their scheduled start, finish
and duration.
Monitoring a project: indicate
the current state of each
activity.
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Percentage Complet ion versus Time
Early start schedule:
- each activity was
scheduled at its earliest start
time, ES(i,j)
Late start schedule:
- based on latest possible
start times for each activity,
LS(i,j)
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Ac tual Percentage Complet ion versus Time
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CPM with Complex Precedence Relationship
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Complex precedence relationsh ip
There are 4 precedence relationships between predecessor activity (A)
and successor activity (B), which provide flexibility for modeling differentreal situations.
Finish-to-Start (FS): (Finish of predecessor A to Start of successor B)
- B can NOT start until A finishes.
- The most common precedence relationship.
Start-to-Start (SS):
- B can NOT start until A starts.
Finish-to-Finish (FF):
- B can NOT finish until A finishes.
Start-to-Finish (SF):
- B can NOT finish until A starts.
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Lags, Leads and Window s
For each of the 4 precedence relationships between predecessor activity
(A) and successor activity (B), a lag time (or lead time) can be specified.
Lag time:
- A delay between the predecessor event (start or finish) and the
successor event (start or finish).
- Example: A Finish-to-Start relationship between A and B with a 2 days
lag, means B can not start until A has finished for 2 days
In this example, FS = 2 days.
Lead time:
- The successor event (start or finish) can occur before the predecessor
event (start or finish) within a certain time frame.
- Example: A Finish-to-Start relationship between A and B with a 2 dayslead, means B can not start until it is 2 days before A finishes
In this example, FS = - 2 days.
Window:
- A certain time window for an activity to be performed.
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Microsof t Project
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Project Time Management: Advanced Top ics
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Schedul ing w ith Uncertain Durat ions
In previous discussions, it is assumed that activity
durations are fixed and known. However, there may be a significant amount of
uncertainty associated with the actual durations:
Examples:
external events such as adverse weather
the time required to gain regulatory approval for projectsmay vary tremendously
Two simple methods for dealing with uncertainty
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Simple method 1
Ignoring the uncertainty, and schedule the project
using the expected or most likely duration for eachactivity.
Drawbacks:
Typically results in overly optimistic schedules
the use of single activity durations often produces a rigid,inflexible mindset on the part of schedulers. As a result,
field managers may loose confidence in the realism of aschedule based upon fixed activity durations.
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Simple method 2
Include a contingency allowance in the estimate of
activity durations. For example, an activity with an expected duration of two
days might be scheduled for a period of 2.2 days,
including a 10% contingency.
Systematic use of contingency factors can result in moreaccurate schedules
However, formal scheduling methods that incorporateuncertainty more formally are useful as a means of
obtaining greater accuracy
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PERT (Project Evaluation and Review Technique)
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PERT (Project Evaluat ion and Review Techn ique)
PERT is a commonly used formal method for dealing
with uncertainty in project scheduling.
Apply the critical path scheduling process and thenanalyze the results from a probabilistic perspective.
Procedure:
Using expected activity durations and critical pathscheduling, a critical path of activities can be identified
This critical path is then used to analyze the duration ofthe project incorporating the uncertainty of the activity
durations along the critical path.
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PERT: Project duration measu res
The expected project duration:
The expected project duration is equal to the sum of theexpected durations of the activities along the critical path.
The variance in the duration of this critical path:
the variance or variation in the duration of this critical path iscalculated as the sum of the variances along the critical path.
Assuming that activity durations are independent random
variables
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The mean and variance for each activ i ty du rat ion
The mean and variance for each activity duration are typically
computed from the following three estimates (using AOArepresentation as an example):
"optimistic" (ai,j)
"most likely" (mi,j),
"pessimistic" (bi,j)
Mean:
Variance:
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Examp le 6.1: A so ftware developm ent pro ject
(Source: Nahmias, Production and
operations analysis, McGraw-Hill, 2005)
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Example 6.1: CPM resu lt
The critical path: A C E G - I
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Example 6.1: PERT
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Example 6.2: An swer the fol lowing quest ions
Answer the following questions about the project scheduling
problem described in Example 6.1.
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Example 6.2
1. The probability that the project can be completed within 22 weeks:
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Example 6.2
2. The probability that the project requires more than 28 weeks:
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Example 6.2
3. The number of weeks required to complete the project with probability 0.90:
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Use of 95 percenti le
Absolute limits on the optimistic and pessimistic activity
durations are difficult to estimate from historical data A common practice is to use the ninety-fifth percentile of activity
durations for these points.
The optimistic time would be such that there is only 5% chance
that the actual duration would be less than the estimatedoptimistic time.
The calculation of the expected duration is the same.
Variance:
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Example 6.3: 95 percenti le variance estimation
Project: nine-activity construction project
Critical path: A C- F - I
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Example 6.3
Activity durations estimation
The sum of the means for the critical activities is 4.0 + 8.0 + 12.0 + 6.0 = 30.0 days,
and the sum of the variances is 0.4 + 1.6 + 1.6 + 1.6 = 5.2
leading to a standard deviation of 2.3 days.
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Problems w ith using PERT method
1. The procedure focuses upon a single critical path, when
many paths might become critical due to random fluctuations. As a result of the focus on only a single path, the PERT method
typically underestimates the actual project duration.
2. Assume that most construction activity durations areindependent random variables.
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Monte Carlo simulation
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Monte Car lo s imu lat ion
Objective: obtain information about the distribution of project completion
time (as well as other schedule information)
Input: Duration distribution of each activity; Network diagram.
Procedure:
1. In each iteration, generate a set of activity durations, based on theircorresponding duration distributions.
2. Use CPM to compute the project completion time and other scheduling
information.
3. Repeat 1 and 2 until the maximum iteration Nis reached. Thus, Nprojectcompletion times can be obtained.
4. Determine the project completion time distribution based on the data
obtained in 3.
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Monte Car lo s imu lat ion
A number of different indicators of the project schedule can be
estimated from the results of a Monte Carlo simulation: Estimates of the expected time and variance of the project completion.
An estimate of the distribution of completion times, so that the probabilityof meeting a particular completion date can be estimated.
The probability that a particular activity will lie on the critical path. This isof interest since the longest or critical path through the network may
change as activity durations change.
Monte Carlo simulation is more accurate than PERT Dependency among duration distributions of activities can be modeled.
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Examp le 6.4: A Three-Activ i ty Project Example
A simple project involving
three activities in series.
The actual project duration
has a mean of 10.5 days, and
a standard deviation of 3.5
days.
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Example 6.5
Nine-activity project:
Run the simulation 500 times.
The average project duration is found to be 30.9 days with astandard deviation of 2.5 days.