Project Management

Lecture Outline

A. Project Management Process

B. Project Plan

-PERT Techniques

-CPM

C. Project Network: example 1

D. Project Network: example 2

E. Probabilistic Time Estimates in PERT

F. Probabilistic Network Analysis

G. Probabilistic Network Analysis: example 2

A. Project Management Process

Project: unique, one-time operational activity or effort

A. Project Management Process (cont.)

1

2

3

4

5

6

7

A. Project Management Process (cont.)

A. Introduction

• The project form of operations is used to produce the unique product, a single unit.

Projects include a wide range of manufacturing and service activities. Large objects such

as ships, passenger airplanes, and missile launchers are manufactured on a project basis

• A general sequence of management decisions required in all projects is planning (A),

Scheduling (B) and control decisions (C)

-A. Project planning establishes the major project objectives, the resources required, the

type of organization used, and the key people who will manage and implement the project

-B. In the scheduling phase the construction of a detailed list of project activities is done,

a time schedule for each activity is established and a time-phased budget of each activity

can be developed

-C. Project control is maintained, activities should be monitored for time, cost, and

performance in accordance with the project plan

• Almost all companies and public administrations are better prepared to master

managing the continuous and routine activities than to run special and complex

projects

• Experience demonstrates that discontinuous projects or activities suffer

problems in the preparation and implementation phase, unsatisfactory results being

obtained in periods, costs, quality, and results

• Projects can be efficiently managed with a complete and coherent methodologyvalid for any type of project

• But the technical and management aspects are not enough to reach the success

of projects. The human and behaviour aspects of people are also critical. The

project management that we apply will be successful if we combine the rigour of

project management with a suitable behaviour management

A. Project comprehensive management: introduction

B. Project plan: PERT techniques

• The PERT method was created in order to manage the Polaris Missiles Programme. In

this programme more than 3.000 external providers and subcontracted companies

collaborated. In order to facilitate its Management, it was subdivided into five sub-projects:

projectile, guidance system, propulsion system, submarine, and nuclear reactor

•The Special Project Office was responsible for the planning and coordination of the

different parts of the project. With its leadership and with the participation of other

participating companies, the method PERT was formulated. Thanks to this methodology, the

project was reduced from 4 years to 18 months

•After different modifications were introduced, it was arrived at CPM. All of these systems are

very similar and are generally known as PERT systems

Note: PERT = Progress Evaluation & Review Technique

Note: CPM = Critical Path Method

B. Project plan: CPM

•The essential technique for using CPM is to construct a model of the project that includes the following:-A list of all activities required to complete the project-The time (duration) that each activity will take to completion, and-The dependencies between the tasks

• Using these values, CPM calculates the longest path of planned activities to the end of the project, and the earliest and latest that each activity can start and finish without making the project longer. This process determines which activities are critical (i.e., on the longest path) and which have total float or slack (i.e., can be delayed without making the project longer). In project management a critical path is the sequence of project network activities which add up to the longest overall duration. This determines the shortest time possible to complete the project. Any delay of an activity on the critical path directly impacts the planned project completion date (there is no float on the critical path).

•These results allow managers to prioritize activities for the effective management of project completion, and to shorten the planned critical path of a project by pruning critical path activities, by "fast tracking" (i.e., performing more activities in parallel), and/or by "crashing the critical path" (i.e., shortening the durations of critical path activities by adding resources).

Time in months

Activity name Activity time Successor Predecessor

1. Design house and obtain financing 3 2,3 -

2. Lay foundations 2 4,5 1

3. Order and receive material 1 4,5 1

4. Build the house 3 7 2,3

5. Select Paint 1 6 2,3

6. Select Carpet 1 7 5

7. Finish work 1 - 4,6

Project activities

C. Example. Network for House Building Project

Copyright 2009 John Wiley & Sons, Inc.

9-11

C. Network for House Building Project (1)

1

3

2

2

4

3

3

1 5

1

6

1

7

1Start

Design house

and obtain

financing

Order and receive

materials Select paint

Select carpet

Lay foundations Build house

Finish work


9-12

C. Activity Start Times

1

3

2

2

4

3

3

1 5

1

6

1

7

1Start

Start at 3 monthsStart at 6 months

Start at 5 months

Finish at 9 months

Finish

Finish at 9 months

Finish at 7 monthsFinish at 8 months


9-13

1

3

2

2

4

3

3

1 5

1

6

1

7

1Start

C. Critical Path. Network for the House Building Project

Critical path

Longest path through a network

Minimum project completion time

A: 1-2-4-73 + 2 + 3 + 1 = 9 months

B: 1-2-5-6-73 + 2 + 1 + 1 + 1 = 8 months

C: 1-3-4-73 + 1 + 3 + 1 = 8 months

D: 1-3-5-6-73 + 1 + 1 + 1 + 1 = 7 months


9-14

C. Activity Scheduling

• Earliest start time (ES)– earliest time an activity can start

– ES = maximum EF of immediate predecessors

• Forward pass– starts at beginning of CPM/PERT network to determine

earliest activity times

• Earliest finish time (EF)– earliest time an activity can finish

– earliest start time plus activity time

– EF= ES + t


9-15

C. Activity Scheduling (cont.)

• Latest start time (LS)– Latest time an activity can start without delaying critical

path time

– LS= LF - t

• Latest finish time (LF)– latest time an activity can be completed without delaying

critical path time

– LF = minimum LS of immediate predecessors

• Backward pass– Determines latest activity times by starting at the end of

CPM/PERT network and working forward

22

13

31 5

1

43

61

71

0 3

3 5 5 8

8 9

3 45 6

6 70 3

4 56 7

7 8

8 9

3 5 5 8

C. Network for House Building Project (2)Earliest start

Earliest finish

Lateststart

Latestfinish


9-17

* Critical Path

09988*7

178676

167565

08855*4

145343

05533*2

03300*1

Slack SEFLFESLSActivity

C. Activity Slack

1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

Months

Activity

C. Gantt chart

1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

Months

Activity

C. Gantt chart, critical path


9-20

C. Node Configuration. Network for the House Building Project

1 0 3

3 0 3

Activity number

Activity duration

Earliest start

Latest start

Earliest finish

Latest finish


9-21

C. Earliest Activity Start and Finish Times

1 0 3

1

2 3 5

2

3 3 4

1 5 5 6

1

4 5 8

3

6 6 7

1

7 8 9

1

Start

Design house

and obtain

financing

Select pain

Lay foundations

Select carpet

Build house

Finish work

Order and receive

materials


9-22

C. Latest Activity Start and Finish Times

1 0 3

1 0 3

2 3 5

2 3 5

3 3 4

1 4 5 5 5 6

1 6 7

4 5 8

3 5 8

6 6 7

1 7 8

7 8 9

1 8 9

Start

Design house

and obtain

financing

Select pain

Lay foundations

Select carpet

Build house

Finish work

Order and receive

materials

D. Problem solving (2)

• Suppose a project that is composed of 9 activities. It has been established the sequence of the different activities and the duration of each.

• Obtain the project net, the critical path, draw the Gantt Chart. Obtain and the most optimal costs and resources management.

D. Problem solving (2), Project costs

Total project time : 10 months

TotalActivityname

Activitytime Succesor Predeccesor Activity Cost

A 1 B,D,F,G 60

B 2 C A 40

C 3 I B 120

D 2 E A 20

E 4 I D,F 160

F 1 E A 35

G 2 H A 90

H 5 I G 150

I 2 C,E,H 90

TOTAL 9 22 765

• we have adopted the CPM approach of assuming that all activity times are known and fixed constants. That is, there is no variability in activity times. However, in practice, it is likely that activity completion times vary depending on various factors

• This means that we cannot ignore the impact of variability in activity times when deciding the schedule for a project. PERT addresses this issue


• In PERT we employ a probability distribution based on three time estimates for each activity, as follows:

a = Optimistic time estimatem = Most likely time estimateb = Pessimistic time estimate

• Assumes that the actual activity times are distributed according the beta probability distribution


m b

Times estimates that are more likely to exceed the average than to be less than the average

a

Probability of 1 in 100 of < a occuring

Probability of 1 in 100 that the activity time will be of > b occuring

Most realistic estimate of the time required to complete an activity

• According to beta distribution the average or expected time of the three time estimates can computed as follows:


Mean (expected time): t =a + 4m + b

6

Using the expected time the ES, EF, LS and LF can be computed

• To compute the dispersion or variance of activity completion time we use the formula:

Variance: 2 =b - a

6

2

The project completion time can be computed by adding the variance along the critical path

This formula is based on the statistical concept that from one end of the beta distribution to the other is 6 standard deviations (+- standard deviation from the mean). Since (b-a) is 6 standard deviations, the variance is ((b-a)/6)2

t =a + 4m + b

6 2 =

b - a6

2

E. Activity Time Estimates in PERT, example for House Building Project

a = Optimistic time estimatem = Most likely time estimateb = Pessimistic time estimate

Time Estimates Mean Time Variance

Activity a m b t б2

1 2 3 5 3 0,25

2 1 2 3 2 0,11

3 1 1 3 1 0,11

4 1 5 7 5 1,00

5 1 1 3 1 0,11

6 1 1 4 2 0,25

7 1 1 3 1 0,11

The variance is higher when thespreadbetween the pessimistic and the optimistic value is higher

21,2,3

12,3,5

31,1,3 5

1,1,3

41,5,7

61,1,4

71,1,3

E. Project Network with Probabilistic Time Estimated, example for House Building Project

a m b

a = Optimistic time estimate

m = Most likely time estimate

b = Pessimistic time estimate

21,2,3

12,3,5

31,1,3 5

1,1,3

41,5,7

61,2,4

71,1,3

0 3

0 3

3 5 5 10

3 4

10 11

5 66 8

4 5

10 11

5 10

8 107 8

3 5

E. Project Network with Probabilistic Time Estimated, example for House Building Project

Earliest start

Earliest finish

Lateststart

Latestfinish

E. Probabilistic Time Estimated, Activity Early, Late Times, and Slack, example for House Building Project

Total Project Variance = б21 +б2

2 +б2

4 +б27 = 0,25 + 0,11 + 1 + 0,11 = 1,47

Project standard deviation = Project variance = 1,47 = 1,21 months

Activity t б2 ES EF LS LF Slack

1 3 0,25 0 3 0 3 0

2 2 0,11 3 5 3 5 0

3 1 0,11 3 4 4 5 1

4 5 1,00 5 10 5 10 0

5 1 0,11 5 6 7 8 2

6 2 0,25 6 8 8 10 2

7 1 0,11 10 11 10 11 0


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E. Probabilistic Time Estimates, Gantt Chart, example for House Building Project

1 2 3 4 5 6 7 8 9Months

10

1

2

3

4

5

6

7

Activity

11


9-33


Determine probability that project is

completed within specified time

where

tp = project mean time

= project standard deviation

x = proposed project time

Z = number of standard deviations xis from mean

Z =x - t


9-34


• Variation in activities that are on the critical path can affect the overall project completion time. PERT uses the variance of the critical path activities to help determine the variance of the overall project.

• PERT makes two more assumptions:1. The total project completion times follow a normal probability distribution2. Activity times are statistically independent

• With this assumptions the bell-shaped normal curve can be used to represent project completion dates. • This normal curve implies that there is a 50% chance that the project completiontime will be less than the complexion date and a 50% chance that it will exceed the completion date


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F. Normal Distribution of Project Time

= tp Timex

Z

Probability


9-36

F. Project Example

What is the probability that the project is completed within 14

months? t =11 and 2 = 1.47 months

2 = 1.47 months

= 1.47

= 1.21 months

Z =

=

= 2.48

x - t

14 - 11

1.21

From Table a Z score of 2.48 corresponds to a probability of 0.4934.

Thus P(14) = 0.5000 + 0.4934 = 0.9934 or 99,34%

t = 11 Time (months)x = 14

P(x 14 months)


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F. Project Example

t = 11 Time (months)x = 9

P(x 9 months)

What is the probability that the project is completed within 9

months?

2 = 1,47 months

= 1.47

= 1,21 months

Z =

=

= -1,65

x - t

9 - 11

1.21

From Table a Z score of -0,76 corresponds to a probability of 0,2764.

Thus P(9) = 0,5000 – 0,4 = 0,049 or 4,9%

G. Problem solving (2). Project Network with Probabilistic Time Estimated in PERT

Compute the ES, EF, LS and LF, the variance of each activity, the variance of the project and draw the Gantt Chart. What is the probability that the project is completedWithin 16 months? And within 12 months?

Time Estimates

Activity Succesor Predecessor a m b

A B,D,F,G 1 1 2

B C A 1 2 3

C I B 1 3 5

D E A 2 7 8

E I D, F 3 4 5

F E A 1 1 3

G H A 1 2 4

H I G 3 5 6

I C,E,H 1 2 4

Project Management

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