7/29/2019 INSE6230_L7

1/33

1

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

7/29/2019 INSE6230_L7

2/33

2

Presenting the Scheduling Results

7/29/2019 INSE6230_L7

3/33

3

Gant Chart

Lists activities and shows

their scheduled start, finish

and duration.

Monitoring a project: indicate

the current state of each

activity.

7/29/2019 INSE6230_L7

4/33

4

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)

7/29/2019 INSE6230_L7

5/33

5

Ac tual Percentage Complet ion versus Time

7/29/2019 INSE6230_L7

6/33

6

CPM with Complex Precedence Relationship

7/29/2019 INSE6230_L7

7/337

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.

7/29/2019 INSE6230_L7

8/338

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.

7/29/2019 INSE6230_L7

9/339

Microsof t Project

7/29/2019 INSE6230_L7

10/3310

Project Time Management: Advanced Top ics

7/29/2019 INSE6230_L7

11/3311

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

7/29/2019 INSE6230_L7

12/3312

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.

7/29/2019 INSE6230_L7

13/3313

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

7/29/2019 INSE6230_L7

14/33

14

PERT (Project Evaluation and Review Technique)

7/29/2019 INSE6230_L7

15/33

15

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.

7/29/2019 INSE6230_L7

16/33

16

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

7/29/2019 INSE6230_L7

17/33

17

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:

7/29/2019 INSE6230_L7

18/33

18

Examp le 6.1: A so ftware developm ent pro ject

(Source: Nahmias, Production and

operations analysis, McGraw-Hill, 2005)

7/29/2019 INSE6230_L7

19/33

19

Example 6.1: CPM resu lt

The critical path: A C E G - I

7/29/2019 INSE6230_L7

20/33

20

Example 6.1: PERT

7/29/2019 INSE6230_L7

21/33

21

Example 6.2: An swer the fol lowing quest ions

Answer the following questions about the project scheduling

problem described in Example 6.1.

7/29/2019 INSE6230_L7

22/33

22

Example 6.2

1. The probability that the project can be completed within 22 weeks:

7/29/2019 INSE6230_L7

23/33

23

Example 6.2

2. The probability that the project requires more than 28 weeks:

7/29/2019 INSE6230_L7

24/33

24

Example 6.2

3. The number of weeks required to complete the project with probability 0.90:

7/29/2019 INSE6230_L7

25/33

25

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:

7/29/2019 INSE6230_L7

26/33

26

Example 6.3: 95 percenti le variance estimation

Project: nine-activity construction project

Critical path: A C- F - I

7/29/2019 INSE6230_L7

27/33

27

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.

7/29/2019 INSE6230_L7

28/33

28

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.

7/29/2019 INSE6230_L7

29/33

29

Monte Carlo simulation

7/29/2019 INSE6230_L7

30/33

30

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.

7/29/2019 INSE6230_L7

31/33

31

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.

7/29/2019 INSE6230_L7

32/33

32

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.

7/29/2019 INSE6230_L7

33/33

33

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.