Chapter 8- Project Management

8/13/2019 Chapter 8- Project Management

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Chapter 8: Project Management

Dr. Angela de Oliveira

RES EC 313

QUANTITATIVE METHODS


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HOUSEKEEPING

You will get exams back on Thursday

Where we are in the term:

Exam 1: Linear and Nonlinear programming. Some of ourmost powerful analytical tools!

New Material: We will cover a number of popular ways

numbers help managers to make better decisions.

Our 1stway: Project management using networks.


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TODAYS GAME PLAN

The Elements of Project Management

CPM/PERT

Probabilistic Activity Times

Project Crashing and Time-Cost Trade-Off

Formulating the CPM/PERT Network as a Linear

Programming Model


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Network representation is useful for project analysis.

Networks show how project activities are organized and are used

to determine time duration of projects.

Network techniques used are:

CPM (Critical Path Method) PERT (Project Evaluation and Review Technique)

Now called CPM/PERT

Developed independently during late 1950s.

Build upon the Gantt Chart

Overview


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Elements of Project Management

Management is generally perceived as concerned withplanning, organizing, and control of an ongoingprocess

or activity.

Project management is concerned with control of an

important activity for a relatively short per iod of time

after which management effort ends.


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Project Planning

Objectives

Project scope

Contract requirements

Schedules

Resources

Personnel

Control

Risk and problem analysis


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Project Planning

Objectives

Detailed project statement

Include what will be accomplished

How it feeds into the strategic plan Time, cost, and return estimates

Project scope


Schedules

Resources

Personnel

Control



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Project Planning

Objectives

Project scope

Approach to the project

Project justification & benchmark for success

Technological and resource feasibility

Major tasks and schedule


Schedules

Resources

Personnel

Control



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Project Planning

Objectives

Project scope


Structure of managerial, reporting, & performance

responsibilities

Include staff, suppliers, subcontractors,

Include projected organizational structure

Schedules

Resources

Personnel

Control



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Project Planning

Objectives

Project scope


Schedules

List of all major tasks, events and subschedulesuse to make a

master schedule

Resources

Personnel Control



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Project Planning

Objectives

Project scope


Schedules

Resources Project budget

Procedures for budget control

Personnel

Control



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Project Planning

Objectives Project scope


Schedules

Resources

Personnel

Identify and recruit project team

Be sure to list special skills and training needed

Control



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Project Planning



Schedules

Resources

Personnel

Control

Procedures for monitoring and evaluating progress and

performance

Include schedules and cost



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Project Planning



Schedules

Resources

Personnel

Control


Anticipate uncertainties, potential problems


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Project Return

Lots of projects could be chosen. They are often selected based on ROI Return on investment (ROI) is a measure used to evaluate

projects calculated by dividing the dollar gain minus the

dollar cost by the dollar cost.

gain from project - cost of projectROI

cost of project

ROI can be used to rank projects

Caution: Not all project benefits can be measured in dollars


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Project team typically consists of a group of individuals from various

areas in an organization and often includes outside consultants.

Project team may include workers.

Members of engineering staff often assigned to project work.

Most important member of project team is theproject manager.

Project manager is often under great pressure because of

uncertainty inherent in project activities and possibility of failure.

Potential rewards, however, can be substantial.

Project manager must be able to coordinate various skills of team

members into a single focused effort.

The Project Team


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Scope Statement

Scope Statement Document providing common understanding of project.

Justification describing the factors giving rise to need forproject.

Expected results and what constitutes success.

List of necessary documents and planning reports.

Statement of work (SOW)

Planning document for individuals, team members, groups,

departments, subcontractors and suppliers

Describes what is required for successful, on time

completion.


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ELEMENTS OF PROJECT MANAGEMENT

WORK BREAKDOWN STRUCTURE (WBS)

Organizational chart

WBS breaks down project into major components (modules).

Modulesare further broken down into activitiesand, finally, into

individual tasks.

Identifies activities, tasks, resource requirements and relationships

between modules and activities. Helps avoid duplication of effort.

Basis for project development, management, schedule, resources and

modifications.

Approaches for WBS development:

1. Top down process

What components constitute this level?

2. Brainstorm entire project

Put everything on sticky notes and then organize.


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Sample Work Breakdown Structure


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Responsibility Assignment Matrix

WBS is very big. It gives you the big picture, but not very

manageable.

Use an organizational breakdown structure (OBS).

OBS is a table or a chart showing which organizational units

are responsible for work items. OBS leads to the responsibility assignment matrix (RAM)

RAM helps organize smaller elements

RAM shows who is responsible for doing the necessary work in

the project

This can include overall responsibility, who actually does the

work, and who acts in a support capacity

Project manager assigns work elements to organizational units,

departments, groups, individuals or subcontractors.


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Sample Responsibility Assignment Matrix

j S i


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Project Scheduling

Project schedule evolves from planning documents, with focus on

timely completion.

Critical element in project managementsource of most conflicts and

problems.

Schedule development steps:

1. Define activities,

2. Sequence activities,

3. Estimate activity times,4. Develop schedule.

Gantt chart and CPM/PERTtechniques can be useful.

Computer software packages available, e.g. Microsoft Project.

G Ch


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Gantt Chart

Popular, traditional technique, also known as a bar chart -developed

by Henry Gantt (1914).

A visual display of project schedule showing activity start and finish

times and where extra time is available.

Suitable for projects with few activities and precedence

relationships.

Drawback: precedence relationships are not always discerniblewhich limits charts use to smaller projects

S l G Ch


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Sample Gantt Chart

Takes 3 months. Nothing else can happen until completed.

Start at same time Slack

P j t C t l


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Project Control

Process ofensuring progress toward successful completion.

Monitoring project to minimize deviations from project plan and

schedule.

Corrective actions necessary if deviations occur.

Key elements of project control

Time managementfrequent monitoring and updates

Cost managementsome cost estimates are wrong. May have

extra costs if behind schedule Performance managementmonitoring progress and

developing status updates

Earned value analysis (EVA)standard for numerically

measuring a projects progress

CPM/PERT


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There are two main presentation styles:

1stPresentation style: Activity-on-Arc (AOA) Network

2ndPresentation style: Activity-on-Node (AON) Network

I will follow the conventions used in your text

BUTeven with just these two styles, you can see these networks

drawn a LOT of different ways.

They will all contain the same pieces of information But they may look very different from each other

CPM/PERT

Th P j t N t k


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Copyright 2013 Pearson Education, Inc. Publishing as Prentice Hall

1stPresentation style: Activity-on-Arc (AOA) Network

A branch reflects an activityof a project.

A node represents the beginning and end of activities, referred to as

events.

Branches in the network indicate precedence relationships. When an activity is completed at a node, it has been realized.

The Project Network

CPM/PERT


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EXAMPLE PROJECT NETWORK:

HOUSE BUILDING PROJECTNumber Activity Predecessor Duration

1 Design house and obtain financing -- 3 months

2 Lay foundation 1 2 months

3 Order and receive materials 1 1 month

4 Build house 2,3 3 months

5 Select paint 2, 3 1 month

6 Select carpet 5 1 month7 Finish work 4, 6 1 month

Activity on Arc (AOA) : The Project Network


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Activities can occur at the same time (concurrently).

Network aids in planning and scheduling.

Time duration of activities shown on branches.

Activity-on-Arc (AOA) : The Project Network

Activities are located on

the arrows, known as

branches

Time

The nodes are events

They indicate the beginning and

end of activities

Dummy activities are

placeholders: see next slide

Dummy Activities


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Two or more activities cannot share the same start and end nodes.

So, how do you handle two separate activities that start and end at

the same time??

Use a dummy activity

A dummy activity shows a precedence relationshipbut reflectsno passage of time.

It is represented on the network with a dashed line.

Dummy Activities

A ti it N d (AON) P j t N t k


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Activity-on-Node (AON) - Project Network

for the House Building Project

2nd

Presentation style: Activity-on-Node (AON) Network A node represents an activity, with its label andtime shown

on the node

The branches show the precedence relationships

Convention used in Microsoft Project software

Activity on Node (AON) Project Network


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Activity-on-Node (AON) - Project Network

for the House Building Project

Everything is on the node: Branches (arrows) only show precedence

Label,

Not always included

Activity number

from the table

Timeneeded

This says that activity 5, which is to

select paint, can begin after both

activity 2&3 are finished. It will take1 period.

The Project Network


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The Project Network

Paths Through a Network

Path Events

A 1247

B 12567

C 1347

D 13567

We need to identify the paths through the network Helps figure out how long the project will take

Also identify the most crucial activities to finishing on time

What to do:

Trace out all of the ways you can get from start to finish

Then, figure out how long it takes (next slide).

The Project Network


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Add up the times (the bottom number on each node) along the path

The cri tical pathis the longest path through the network; the

minimum time needed to complete the network.

Path A: 1 2 4 7 3 + 2 + 3 + 1 = 9 months ***

Path B: 1 2 5 6 7 3 + 2 + 1 + 1 + 1= 8 months

Path C: 1 3 4 7 3 + 1 + 3 + 1 = 8 months

Path D: 1 3 5 6 7 3 + 1 + 1 + 1 + 1 = 7 months

The Project Network

The Critical Path


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ACTIVITY SCHEDULING IN ACTIVITY-ON-NODE

CONFIGURATION

This part is

what we had

before:

This is new:

Helps with overall planning

The Project Network


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ES (Earliest start) is the earliest time an activity can start:

(Earliest finish) is the earliest start time plus the activity time:

The Project Network

Activity Scheduling : Earliest Times

EF ES t

{ }ES Maximum EF immediate predecessors

ES=0 since this is the

1stactivity

EF = 0 + 3 = 3

ES=3 since that is EF of

activity 1EF = 3 + 1 = 4

ES = 5 because that is the longest EF

time of the activities before this one (2

& 3)

EF = 5 + 3 = 8

The Project Network


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WorkBACKWARDS

LS is the latest time an activity can start without delayingcritical path time:

LF is the latest finish time:

The Project Network

Activity Scheduling : Latest Times

LS LF t

{ }LF Minimum LS following activities

LF=9, no later

activities.LS = 9-1 = 8LF = min{8} = 8LS = 8-1 = 7

LF = min{8} = 8

LS = 8-3 = 5

LF = min{5, 6} = 5

LS = 5-2 = 3

On the critical path, the

ES & LS times will be

the same!

The Project Network


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Slackis the amount of time an activity can be delayed without

delaying the project: S = LSES = LF - EF Slack Time exists for those activities not on the critical path for

which the earliest and latest start times are not equal.

Shared Slack is slack available for a sequence of activities.

The Project Network

Activity Slack Time (1 of 2)

*Critical path

Activity LS ES LF EF Slack, S*1 0 0 3 3 0

*2 3 3 5 5 0

3 4 3 5 4 1

*4 5 5 8 8 0

5 6 5 7 6 1

6 7 6 8 7 1

*7 8 8 9 9 0



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Activity time estimates usually cannot be made with certaintyhow

to we account for this?

PERT used for probabil istic activity times.

In PERT, threetime estimates are used:

most l ikelytime (m), the optimistictime (a), and the pessimistictime (b).

You will write out the nodes of your network with all 3 times

instead of 1 time (next slide)


Probabilistic Activity Times:


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Probabilistic Activity Times:

Southern Textile Company example

Activity #

3 Activity

times



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To get mean and variance, we need a distribution: Beta distribution.

1streason: convention

2nd reason: can approximate mean and variance with only 3

estimates

3rdreason: continuous distribution but no predetermined shape(takes on shape of our estimates)

Recall: most likely(m), optimistic (a), &pessimistic(b).

To estimate the mean and variance of a Beta PERTdistribution:

Mean (expected time):

Variance:

a 4m bt6

2b - a

6v


Calculating Probabilistic Activity Times


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Calculating Probabilistic Activity Times

=(6 + (4*8) + 10)/6

=(3 + (4*6) + 9)/6

=((5-3)/6)2

= (2/6)2

= (1/3)2= 1/9

=((7-1)/6)2

= (6/6)2

= (1)2= 1



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Activity #

MEAN time

ES & EF

LS & LF

Indicates slack

EXPECTED completion time



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Expected project time is the sum of the expected times of the

critical path activities. Project var iance is the sum of the critical path activities variances

This assumes activity times are statistically independent

The expected project time is assumed to be normally distr ibuted

(based on central limit theorem: caution warranted here).

For our example, expected project time (tp) and variance (vp)

interpreted as the mean () and variance (2) of a normal

distribution:

= 25 weeks

2= 62/9

= 6.9 weeks2


Expected Project Time and Variance

Probability Analysis of a Project Network


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We can use this information to figure out our chances of

finishing within a specified timeframe

Use the normal distribution

probabilities are determined by computing the number

of standard deviations (Z) a value is from the mean.

A standard deviation, , is the square root of variance

You get the Z by: =

The Z value is used to find the corresponding

probability in Table A.1, Appendix A.

This should be VERY familiar from stats!! Here is one

wa it is useful for mana ers!


Example 1: What is the probability that the


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We will use the table to find this part.Then, add them together to get our answer.

Example 1: What is the probability that the

network will be completed in 30 weeks or less

This is p = 0.5000



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What is the probability that the new order processing

system will be ready by 30 weeks?


Example 1

2

25

6.9

6.9 2.63

30 251.90

2.63

weeks

xZ

Z

Z value of 1.90 corresponds to

probability of .4713 in Table A.1,

Appendix A. Go down to the 1.9 row and over

to the 0.00 column

The probability of completing

project in 30 weeks or less:(.5000 + .4713) = .9713.

Example 2: What is the probability the network


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Example 2: What is the probability the network

will be completed in 22 weeks or less?

This is p = 0.5000 The table tells us this probability.So, take 0.5000the probability in the table



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A customer will trade elsewhere if the new ordering system is notworking within 22 weeks. What is the probability that she will be

retained?

First, convert the problem to a Z:

=

Z = (22 - 25)/2.63 = -1.14

Z value of 1.14 (ignore negative) corresponds to probability of .3729in Table A.1, Appendix A.

1.1 row, 0.04 column

Probability that customer will be retained is .1271= .5000 - .3729


Example 2

Project Crashing and


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What if you are in a hurry? Project duration can be reducedby assigning more

resources to project activities.

However, doing this increases project cost. Decision is based on analysis of trade-off between time

and cost.

Project crashingis a method for shortening projectduration by reducing one or more cr itical activities to a

time less than normal activity time.

Project Crashing and

Time-Cost Trade-Off Overview



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Project Crashing and Time Cost Trade Off

Example: Building a House (from start of lecture)

Activity #

Time in weeks

Lets assume that activity 1 costs $3000 for a 12 week completion time

It can be completed in 7 weeks (crash time) for $5000 (crash cost).

So, 5 weeks costs us $2000.



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Project Crashing and Time Cost Trade Off

$2000 $400 / 5

Total Crash Costweek

Total Crash Time weeks

127 = 5

50003000 = 2000

Project Crashing and Time-Cost Trade-Off:


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Project Crashing and Time Cost Trade Off:

You can do the same thing for each activity

You get these estimates from a contractor, someone else

=12-7 =2000/5

Network with normal activity times and weekly


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Ne wo w o c v y es d wee y

crashing costs

As activities are crashed, the critical path may change and several pathsmay become critical.

Here we can crash activity 1 without changing the path because all paths

will be equally affected.

This is normally done using a computer.



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j g

General Relationship of Time and Cost (1 of 2)

Another reason to crash a project is to lower indirectcosts

Project crashing costs and indirect costs have an inverse

relationship.

Crashing costs are highest when the project is

shortened.

Indirect costs increase as the project duration

increases.

The optimal project time is at the minimum point on the

total cost curve.

General Relationship of Time and Cost


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p

The CPM/PERT Network


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General linear

programming model

with AOA convention

Lets look at an

example

The objective is to minimize the project duration (critical path time).

Formulating as a Linear Programming Model

minimize

subject to

, for all activities

, 0

earliest event time of node

earliest event time of node

time of activity

i

i

j i ij

i j

i

j

ij

Z x

x x t i j

x x

where

x i

x j

t i j

Example Problem Formulation and Data


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p

AOA Network

Recall: The activity is on the arc (arrow/branch) Activity 1 2: The activity starting at 1 and ending at 2

ET: EarliestEvent Time. The earliest a node can be realized.

We know ET of last node equals critical path time

Letxibe the ET at each node. Then, set up the LPM.

ET = max(12 + 4, 12 + 8)

=max(16, 20) = 20

ET = max(20 + 12, 24 + 4)

=max(32, 28) = 32

ET = 32 + 4 = 36



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Minimize Z = x1+ x2 + x3+ x4+ x5 + x6+ x7subject to:

x2 - x112

x3- x2 8x4- x2 4

x4- x30

x5- x44

x6- x

412

x6- x54

x7- x64

xi, xj0

Example Problem Formulation and Data (2 of 2)

This is the sum of all the earliest event times

It does not have a useful interpretation

It is used because it will give us the earliest event

time at each node, which is what we want.

We have a minimum time for each activity Look at Activity 12

ET at node 2, x2= 12

ET at node 1, x1= 0 (it is the beginning)

Minimum time for 12 = x2x1= 12 - 0 = 12

To formulate the constraint, we realize that it is

possible to go over time, but not under time.

Do the same thing for each activity, including

dummy activities

Dont forget to include the non-negativity

constraints

You can then use solver or QM for Windows

Exhibit 8.10: Example Problem Solution with


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p

Excel

B6:B12 =B7-B6

Decision variables,

B6:B12



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Exhibit 8.11

Example Problem Solution with Excel (2 of 4)

Set dummy activities = 0



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This is the total project duration



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A shadow price of 1 indicates an activity is on the

critical path: Just refer back to the referenced cells

to get the activities


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FOR THURSDAY

Read Chapter 8


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NOTE ON VARIANCE:

Variance for the Beta PERT distribution is based on thestatistical concept that there are +-3 standard deviations

from the mean, or 6 standard deviations

Since b=most pessimistic and a = most optimistic, b-a is =

6 standard deviations

So, (b-a)/6 is one standard deviation

Then, just square it to get the variance

v = ((b-a)/6)^2

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Chapter 8- Project Management