Risk and Uncertainty in Construction
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1 Is it really important to consider risk Risk and Uncertainty in Construction ? Outline The Impact of Uncertainty Risk Concepts Risk Management: Risk identification Risk Analysis (Qualitative and Quantitative) Risk Response Planning Risk Monitoring and Control Risk Management Techniques PERT, Monte Carlo Simulation, Decision Trees,… Sample Applications
Transcript of Risk and Uncertainty in Construction
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Is it really important to consider risk
Risk and Uncertainty in Construction
?
Outline
The Impact of Uncertainty Risk Concepts Risk Management:
Risk identification Risk Analysis (Qualitative and Quantitative) Risk Response Planning Risk Monitoring and Control
Risk Management Techniques PERT, Monte Carlo Simulation, Decision Trees,…
Sample Applications
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The Impact of Uncertainty
A (10)
B (9)
D (10)
C (10)
Consider the following small project
The Impact of Uncertainty
A (10)
B (9)
D (10)
C (10)
0
10
10
10
19
20
20 30
30 20
20
20 11
10
10 0
Total Project Duration = 30
What is the impact if you are uncertain about the durations?
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The Impact of Uncertainty
Consider small uncertainty in durations; Actual durations = + or – one day from given
Activity Theoretical Duration Actual Duration
A 10 9, 10, or 11
B 9 8, 9, or 10
C 10 9, 10, or 11
D 10 9, 10, or 11
An Excel Model
The Impact of Uncertainty
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The Impact of Uncertainty
The consequences of uncertainty represent risks
that might affect the project. This rises the need
for efficient
Risk Management
(Risk Identification, Analysis, Response, & Control)
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Concepts
Risk: The possibility of suffering loss (or harm) and the
impact of that loss on the involved party. Risk can be
characterized in terms of its Severity where:
Severity = Likelihood of Occurrence x Magnitude of the Impact.
Risk: Any event which is likely to affect (adversely) the
ability of project to achieve the defined objectives.
Concepts
Risk: A measure of the probability and consequence of not achieving a defined project goal (Kerzner 2001).
Risk = ƒ [Si, Pi, C] i = 1, 2, 3,……
Si: is a scenario of events that lead to hazard exposure (an unwanted change);
Pi: is the likelihood of scenario i; and
Ci: is the consequence of scenario.
Risk = ƒ [hazard, safeguard]
Risk increases with hazard but decreases with safeguard.
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Concepts
Opportunity: The possibility of realizing a favorable
outcome and the impact this outcome has on the
involved party. Opportunity is positive risk and can be
identified and managed in a similar way.
Uncertainty: The gap between the information required
to estimate an outcome and the information already
possessed by the decision maker.
Concepts
Risk Analysis: The process of identifying risk factors and
the quantification of those factors (estimating likelihood
and magnitude of impacts).
Risk Mitigation: The process of developing a plan to
respond or deal with risk on a project.
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Why Risk Analysis?
Minimize management by crisis
Minimize surprises and problems
Increase probability of project success
Better handling of true costs and schedules by properly estimating contingencies…
Risk Management
Definition: RM is the act or practice of dealing with risk. It is the
process by which risks to the project (e.g., to the scope,
deliverables, schedule, resources,…) are formally managed during
the project.
Processes: RM includes planning for risk, identifying and
analyzing risk, developing risk handling options, and monitoring
risks to determine how risks have changed.
Goal: minimizing potential risks while maximizing potential
opportunities and if properly conducted, reducing not
only the likelihood of an occurred event, but also the
magnitude of its impact.
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Risk Management
Risks Opportunities
Try to balance Risks and Opportunities
An orderly way of studying and
analyzing the project. More than
simply designing it…
Clear understanding of the project
objectives, all alternatives, and all
issues that need to be considered
during the design and
construction…
A comprehensive understanding of
all stakeholder issues, a probing of
internal experts and review of
similar projects…
Risk Management
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Characteristics of risk events
Risk is generally: “Magnitude dependent”.
The greater the payoff, the more the risk is acceptable…
“Value based”. Everyone sees risks differently.
Everyone has a different tolerance level for risk…
“Time dependent”. Risk is a future event, time affects its
perception. What is seen today as a risk may not be tomorrow…
More Characteristics
For risk to be an issue, the event and/or its outcome must be associated with a certain degree of uncertainty (the possibility).
In practice it is virtually impossible to avoid all risks.
Risks can be reduced and sometimes transferred (e.g. through contracts, financial agreements, allowances, insurance policies).
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Potential Risk & Knowledge Area
Risk Conditions Knowledge Area
Inadequate planning; poor resource allocation; poor integration management; lack of post – project review
Integration
Poor definition of scope or work packages; incomplete definitions of quality requirements; inadequate scope control.
Scope
Errors in estimating time or resource availability; poor allocation and management of float; early release of competitive product.
Time
Estimating errors; inadequate productivity, cost, change, or contingency control; poor maintenance, security, purchasing,…etc.
Cost
Poor attitude toward quality; substandard; design / materials / workmanship; inadequate quality assurance program.
Quality
Poor conflict management; poor project organization and definition of responsibility; absence of leadership.
Human Resources
Carelessness in planning or communication; lack of consultation with key stakeholders.
Communication
Ignoring risk; unclear assignment of risk; poor insurance management. Risk
Unenforceable conditions or contract clauses; adversarial relations Procurement
Evaluating Impact of a risk on Major project Objectives
Very High
0.8
High
0.4
Moderate
0.2
Low
.1
Very low
.05
Project objective
>20% cost increase
10-20% cost increase
5-10% cost increase
<5% cost increase
Insignificant
Cost increase
Cost
overall Schedule
slips >20%
overall Schedule slippage
10-20%
overall Schedule slippage
5-10%
Schedule slippage
< 5%
Insignificant
Schedule slippage
Time
Project end items is
effectively useless
Scope reduction
unacceptable to the client
Major areas of scope are
affected
Minor Areas of scope are
affected
Scope Decrease
barely Noticeable
Scope
Project end item is
effectively unusable
Quality reduction
unacceptable to the client
Quality reduction requires
client approval
Only very demanding applications are affected
Quality degradation
barely noticeable
Quality
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Process of Risk Management
Generally involves the following steps:
Risk Management Planning
Risk Identification
Risk Analysis
Qualitative
Quantitative
Risk Response Planning
Risk Monitoring & Control
Process of Risk Management
Risk Management Planning: Deciding how to approach, plan and execute the
risk management activities for a project.
Risk Identification: Determining which risks might affect the project
and determining their characteristics.
Qualitative Risk Analysis: Prioritizing risks for further analysis by assessing
and combining their probability of occurrence & impact.
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Process of Risk Management
Quantitative Risk Analysis: Numerically analyzing the effect of identified risks on
overall project objectives.
Risk Response Planning: Developing options and actions to enhance
opportunities and reduce threats.
Risk Monitoring & Control: Tracing identified risks, monitoring residual risks,
identifying new risks, executing risk response plans, and evaluating their effectiveness throughout the project life.
Risk Management
Risk Management
Planning
Risk Identification
Qualitative Analysis
Quantitative Analysis
Response Planning
Monitoring and Control
Inputs
System
Tools & Techniques
Outputs
Inputs
Outputs
System (e.g., RI)
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1. Risk Management Planning
Project Charter (Definition)
is a statement of the scope, objectives and participants in a project.
It provides a preliminary delineation of roles and responsibilities, outlines the project objectives, identifies the main stakeholders, and defines the authority of the project manager.
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The purpose of the project charter is to document:
Project scope and justification (reasons for undertaking the project)
Objectives and constraints of the project
Identities of the main stakeholders
High level risk management plan
Communication plan
Target project benefits
Budget, key resources required and project schedule.
Tools & Techniques:
Planning Meeting & Analysis
Meetings to develop risk management plan
Attendees include:
Project manager,
Selected team members and stackholders,
Others involved in managing risk planning & executing the project.
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Methodology.
Roles & responsibilities.
Budgeting.
Timing.
Risk categories.
Definition of risk Probability & impact.
Probability and impact matrix.
Revised stakeholders tolerance.
Reporting formats.
Tracking.
Output: Risk Management Plan
Describes how risk management will be structured and performed in the project. It includes:
Project
Project management
Organizational External Technical
Estimating
Planning
Controlling
Communication
Project dependencies
Resources
Funding
Prioritization
Subcontractors & Suppliers
Regulations
Market
Customer
Weather
Requirement
Technology
Complexity & interfaces
Performances & reliability
Quality
Risk Categories
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2. Risk Identification
(Proj. description, WBS, Cost & dur.
Estimate, staffing & procurement plan)
(Sources)
(Symptoms)
Risk Factor Definition: Identify every possible event or
issue that may cause harm to the project (from the
organization view point).
Risk identification is not a one time event, but it is to be
performed on a regular basis throughout the project.
Risk factors can be stated in the form: “…… may happen during the execution of …. which may impact
……”, or “ If …… occurs, then an impact to ….. will be realized.”
e.g. “If rock occurs during excavation then production rates
will be low.”
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Two types of risks should be addressed:
- Internal Risk – can be controlled by the project team – (i.e staff assignment, cost estimate, …)
- External risk – beyond the control of the project team
– (i.e. government actions, market, weather, …)
Risk Identification is also concerned with opportunities (positive outcomes) as well as threats (negative outcomes).
Tools & Techniques: A number of approaches can be used including:
Documentation Review (a structured review of all proj. documents)
Standard Checklists (based on historical information)
Comparison to other projects
Expert Interviews
Facilitated brainstorming sessions (traditional, alternative)
Delphi Technique (A facilitator uses questionnaire to solicit ideas
about major project risks from experts, summarize their responses
and re-circulate them for further comment)
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Root cause identification (Inquiry into the essential
causes of a project risks)
SWOT Analysis (sample)
Assumption Analysis (Tool for exploring the validity of assumption as they apply to the project).
Diagramming Techniques:
Cause & effect Diagrams.
Process flow Charts.
Influence Diagrams.
Causes and Effect diagram
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Check List of Construction Risk Drivers
Financial/economical Legal Political Environmental Communication Technological Construction Geotechnical Geographical
Output: Risk Register (check risk register sample)
List of identified risks.
List of potential responses.
Root cause of risk.
Updated risk categories.
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3. Qualitative Risk Analysis
Includes methods for prioritizing the identified risks for
further action such as Quantitative Analysis or Risk
response planning.
Assess the priority of identified risks using their
probability of occurrence and their corresponding impact
on project objectives if they occur.
Gets outputs from Risk Management Planning and Risk
identification process.
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Tools & Techniques: Interviews or meetings
Step1:Assess the Risk Probability and Impact.
Risk probability investigates the likelihood that a risk will occur, while risk impact investigates the effect on project objectives if the risk event occurs.
Risks with obviously low ratings of probability & impact will not be rated, but will be included on a watch list for future monitoring.
Step 2: Create Probability and Impact matrix.
Risk are prioritized for further quantitative analysis & response based on their risk rating.
The matrix specified combination of probability and impact that lead to rating the risks as low, moderate or high priority.
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ــــــــــ
ــــــــــ
ــــــــــ
high Medium low
Prob. Risk
ــــــــــ
ــــــــــ
ــــــــــ
high Medium low
impact
Risk
0.05 0.13 0.20 0.4 0.80 0.80 0.4 0.20 0.10 0.05 Impact
0.01 0.01 0.02 0.04 0.08 0.08 0.04 0.02 0.01 0.01 0.10
0.02 0.03 0.06 0.12 0.24 0.24 0.12 0.06 0.03 0.02 0.30
0.03 0.05 0.10 0.2 0.40 0.40 0.2 0.10 0.05 0.03 0.50
0.04 0.07 0.14 0.28 0.56 0.56 0.28 0.14 0.07 0.04 0.70
0.05 0.09 0.18 0.36 0.72 0.72 0.36 0.18 0.09 0.05 0.90
Opportunities Threats Probability
Probability and Impact Matrix
Impact (Ratio Scale) on an objective (e.g., cost, time, scope and quantity)
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Step 3: Check/Refinement
Data Quality (Risk Data Quality Assessment).
Is a technique to evaluate the degree of usefulness of risk data for risk management
Involves examining the degree to which the risk is understood and the accuracy, quality and reliability of the data about risk.
Risk Categories (by sources of risks, area of project affected, project phase,…etc).
Urgency (Risk Urgency Assessment)
Risks requiring near – term response may be considered more urgent to address
Output: Risk Register (Updates), includes:
Relative ranking or priority list of project risks. Risks grouped by categories. List of risk requiring response in the near term. List of risks for additional analysis and response. Watch lists of low priority risks. Trends in qualitative risk analysis results.
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4. Quantitative Risk Analysis
Performed on risks that have been prioritized during the Qualitative Risk Analysis.
Analyzes the effect of those risk events and assigns a numeric rating to those risks.
Risk Quantification should also be repeated after Risk Response Planning as well as Risk Monitoring & Control to determine if the overall project risk has been decreased.
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The process uses techniques such as: Monte Carlo Simulation & decision tree analysis to:
Quantify the possible outcomes for the project & their probabilities.
Assess the probability of achieving specific objectives.
Identify the most influential risks on the project & their relative impact.
Identify project cost, schedule, quality and scope given the project risks.
Tools & Techniques
1. Data Gathering & Representation Techniques
Interviewing
(Used to quantify the probability and impact of risks on project objectives).
Probability distributions
(Continuous probability distributions or discrete distributions can be used to represent uncertainty).
Common distribution types include the uniform, normal, Triangular, Beta distribution.
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Highest
(Pessimistic)
Most Likely
Lowest
(Optimistic)
WBS Element
10 6 4 Design
35 20 16 Build
23 15 11 Test
41 Total Project
Range of Project Cost Estimate ($)
0.1 0.1
0.0 0.0
Beta Distribution Triangular Distribution
Example of Commonly Used
Probability Distributions
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Expert Judgment
(Internal or external to the organization)
2. Quantitative Risk Analysis and Modeling Techniques
Sensitivity Analysis
Helps to determine which risks have the most potential impact on the project
Examines the extent to which the uncertainty of each project element affects the objective being examined when all other uncertain elements are held at their base line value.
Is carried out by identifying a project variable and giving that variable limits within which it is likely to vary.
Limitations: when changing a variable it assumes ceteris paribus (i.e. that all other things remain the same.
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Energy Cost
Design Changes
Operating efficiency
Construction Period
Exchange Rate
10 20 30 0 -10 -20 -30
Ca
sh
Ba
lan
ce
Change in variable (%)
Sensitivity Diagram
Expected Monetary value Analysis (EMV).
Is a statistical concept that calculates the average outcome when the future includes scenarios that may not happen.
The EMV for opportunities will be expressed as positive values, while those of risks will be negative.
EMV is calculated by multiplying the value of each possible outcome by its probability of occurrence and adding them together.
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Expected Monetary value Analysis (EMV) Decision Tree Diagrams
When we have a series of decisions where
the outcomes for one stage is important to
the next stage, we use decision trees.
0.2
0.3
0.5
Probability Node Decision Node
Alternatives
Decision Trees
Used when decisions are sequential, that is, one decision leads to another, and so on. Thus, the decisions occur over a period of time that extends to the future.
The technique assumes the probabilities of events are known and future consequences can be reasonably estimated.
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Decision Tree Diagram
Strong Demand
Weak Demand
Strong Demand
Weak Demand
BUILD OR UPGRADE?
BUILD NEW PLANT
UPGRADING EXISTING
PLANT
EMV OF THE DECISION 99 – 50 =$49
EMV of the Prob. Node 0.65 (200) + 0.35 (90) = $ 161.5 M
Computed: (Payoffs minus costs) along path
Input: scenario probability, reward if it occur.
Output: Expected Monetary value (EMV)
Input: cost of each option
Output: Decision Made (TRUE, FALSE)
Decision to be made
Net Path Value Chance Node Decision Node Decision Definition
65%
$200
35%
$90
65%
$120
35%
$60
-$120
-$50
EMV OF THE DECISION 161.5 – 120 = $ 41.5 M
EMV of The Prob. Node 0.65 (120) + 0.35 (60) =$99
True
False
Expected Monetary Value (EMV)
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Expected Monetary Value (EMV)
Modeling & Simulation
Uses a model that translates the uncertainties specified at a detailed level of the project into their potential impact on project objectives.
Monte Carlo Technique is one of the most common used simulation.
In a simulation, the project model is computed many time (iterated), with the input values randomized from a probability distribution function chosen for each iteration. Then a probability distribution (e.g. total cost or completion date) is calculated.
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For a cost risk analysis, a simulation can use the
project WBS or cost breakdown structure as its model.
For a schedule risk analysis the precedence diagram
schedule is used.
Outputs:
Forecasts of potential project schedule and cost results, listing the possible completion dates or project duration and costs with their associated confidence level).
Prioritized list of quantified risks (includes those risks posing the greatest threats and those presenting the greatest opportunity to the project). The list also identifies the risks that requires the greatest cost contingency and those that are most likely influencing the critical path.
Trends in quantitative risk analysis results. (As analysis is repeated, a trend can be drawn that leads to conclusions affecting risk responses).
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5. Risk Response Planning
Developing options and determining actions to enhance opportunities and reduces threats to project objectives.
Addressing risks by their priority, inserting resources and activities into the budget, schedule and project management plan, as needed.
The process:
includes specific methods and techniques to deal with known risks;
identifies who is responsible for the risk (risk response owner);
provides an estimate of the cost and schedule associated with reducing the risk.
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Objectives:
Increase the opportunity of success by reducing the
probability and / or consequences of high probability
risks.
Identify and address the most critical risk categories
and cost / schedule elements; and
Provide a way – forward plan for mitigating risks that
includes actions items, responsibilities and dates.
Types of risk response:
Immediate change or alteration to the project which
results in elimination of the risk.
Contingency plan that will only be implemented if an
identified risk should materialize.
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Identified Risk
Avoidance
Reduction
Transference
Retained
Consid
er
each r
esponse /
mitig
ation
str
ate
gy
Remove the cause Consider alternative solutions
Abort the project
Consider alternative solutions Examine in detail and obtain more information
Take management or design action
Insurance Selection of contracts
Warranties or guarantees sharing
Contingency management
Tools & Techniques
Strategies for negative risks or threats
Avoid: by changing the project management plan to:
Eliminate the threat posed by an adverse risk.
Isolate the project objectives from the risk’s impact, or
Relax the objective that is in jeopardy (extending the
schedule, reducing scope,…
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Transfer: Risk transfer involves shifting the negative
impact of a threat, along with ownership of the response,
to a third party.
Transferring the risk does not eliminate it but simply gives
another party the responsibility of its management.
Examples: Use of insurance, Performance bonds, Warranties,
Guarantees, … etc.
Contracts can be used to transfer liability for a risk to another
party. (cost type contracts transfer cost risk to the buyer, fixed
price contracts transfer risk to the seller)
When portion of the risk is transferred, whilst some risk is
retained, this is known as risk sharing.
Mitigate : Risk mitigation implies a reduction in the probability and / or impact of adverse risk event to an acceptable threshold
Taking early action to reduce the probability and / or impact of risk occurring in the project is more effective than trying to repair the damage after it occurs.
Examples: using less complex process, conducting more tests or choosing more stable suppliers,...
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Strategies for positive risks or “Opportunities”:
Exploit: This strategy is used when the organization
wishes to ensure that the opportunity is realized.
It seeks to eliminate the uncertainty associated with a particular upside risk by making the opportunity definitely happen.
Examples: assigning more talented resources to the project to reduce time of completion, provide better quality than originally planned,…
Share: involves allocating ownership to a third party
who is best able to capture the opportunity for the
benefit of the project.
Example: forming risk sharing partnerships – joint
venture, teams,…
Enhance: modifies the size of an opportunity by
increasing probability and / or positive impact.
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Strategy for both Threats & Opportunities
Acceptance: (passive or active)
Passive acceptance requires no action, leaving the project team to deal with the threats or opportunities as they occur.
Active acceptance include: establishing a contingency reserve.
Outputs
Risk register (Updates)
Is developed and updated in earlier stages. In this stage, appropriate responses are chosen, agreed upon and included in the risk register.
Components of the risk register at this point can include:
Identified risks, their description, area (s) of the project affected, their causes and their effect on project objectives.
Risk owners and assigned responsibilities.
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Outputs from qualitative & quantitative risk analysis processes including prioritized lists of risks and probabilistic analysis.
Agreed upon response strategies.
Specific actions to implement the chosen response strategies.
Budget & schedule activities required to implement the chosen responses.
Contingency reserves of time & cost that are calculated based on the quantitative analysis of the project
Fall back plans for use as a reaction to a risk that has occurred and the primary response proves to be inadequate.
Project management plan (Updates)
The plan is updated as response activities are added
and integrated within the project.
Risk – related contractual agreements
Contractual agreements, such as agreements for
insurance, service and others.
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6. Risk Monitoring & Control
Identifying, analyzing and planning for newly arising risks,
Keeping track and reanalyzing of the identified and existing risks and those on the watch list,
Monitoring trigger conditions for contingency plans and reviewing the execution of risk responses while evaluating their effectiveness.
Choosing alternatives strategies, executing a contingency or fall back plan, taking corrective action and modifying the PM plan.
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Tools and Techniques
Variance & trend analysis, representation, assessment tools,…
Risk Reassessment
Risk monitoring and control often requires identification
of new risks and reassessment of risks, analysis of
planned responses and perform additional response
planning to control the risk, if necessary.
Risk Audits
Audits examine and document the effectiveness of
risk responses in dealing with identified risks and their
root causes as well as the effectiveness of the risk
management process.
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Variance and Trend Analysis
To be used for monitoring overall project performance.
Technical Performance Measurement
Compare technical accomplishment during project
execution against planned to forecast the degree of
success in achieving project’s scope.
Reserve Analysis
Compares the amount of contingency reserves
remaining throughout project execution with the
amount of risk remaining at any time in the project to
determine if the remaining reserve is adequate.
Status Meeting
Project risk management can be discussed at periodic
status meetings highlighting identified risks, their
priority and suggested response methods.
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Outputs
Risk Register (Updates)
Outcomes of risk assessment, risk audits and periodic risk
review which may affect probability of risk, its impact,
priority, response plans and so on.
Actual outcomes of project risks and risk response that
can be used for future projects.
Requested Changes
Approved change requests become inputs to the project
management execution process and risk monitoring and
control.
Recommended Corrective Actions
These include contingency plans and work around plans
that were not initially planned, but are required to deal with
emerging risks that were unidentified.
Recommended Preventive Actions
Actions used to prevent deviation from original project
management plan.
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Organizational Process Assets
Information from the six project risk management
processes are used by the organization for future
projects. Lessons learned should be captured and
included in the organization knowledge database.
Project Management Plan (Updates)
PM plan is to be revised and updated to reflect any approved changes.
Project Risk Management
1.Inputs
•Enterprise environmental factors. •Organizational process assets. •Project scope statement. •Project management plan.
2.Tools & techniques: •Planning meetings ad analysis.
3.Outputs: •Risk management plan.
Risk Management Planning
1.Inputs •Enterprise environmental factors. •Organizational process assets. •Project scope statement. •Risk management plan. •Project management plan. 2.Tools & techniques: •Documentation reviews. •Information gathering techniques. •Checklist analysis. •Assumption analysis. •Diagramming techniques 3.Outputs: •Risk register
Risk Identification
1.Inputs •Organizational process assets. •Project scope statement. •Risk management plan.
•Risk register. 2.Tools & techniques: •Risk probability and assessment. •Probability and impact matrix. •Risk data quality assessment. •Risk categorization. •Risk urgency assessment. 3.Outputs: •Risk register (updates).
Qualitative Risk Analysis
1.Inputs •Organizational process assets. •Project scope statement. •Risk management plan. •Risk register. •Project management plan - project schedule management plan - project cost management plan. 2.Tools & techniques: •Data gathering and representation techniques. •Quantities risk analysis and modeling techniques. 3.Outputs: •Risk register (updates).
Quantitative Risk Analysis
1.Inputs •Risk management plan. •Risk register. 2.Tools & techniques: •Strategies for negative risks or threats. •Strategies for positive risks or opportunities. • contingent response strategy. 3.Outputs: •Risk register (updates). •Project management plan (updates) •Risk related contractual agreements.
Risk Response Planning
1.Inputs •Risk management plan. •Risk register. •Approved change requests. •Performance information. •Performance reports 2.Tools & techniques: •Risk reassessment. •Risk audits. •Variance & trend analysis. •Technical performance measurement . •Reserve analysis. •Status meetings. 3.Outputs: •Risk register (Updates). •Requested changes. •Recommended corrective actions. •Organizational process assets updates. •Project management plan (updates).
Risk Monitoring & Control
Overview
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Risk Management Techniques
PERT
Monte Carlo Simulation
Decision Analysis (Decision Trees)
The PERT Approach for Project Risk Assessment
The program evaluation and review technique (PERT) was developed
by the late 1950’s. The objective was to evaluate the risk in meeting
the time goals of the execution of projects whose activities had some
uncertainty in their duration estimates. To represent the uncertainty
in duration estimates, the PERT technique recognizes the
probabilistic, rather than deterministic, nature of the operations
involved in high-risk activities. Accordingly, the PERT technique
incorporates three durations for each activity into its methodology.
The 3 estimates are:
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The PERT Approach
Optimistic duration (a): estimated time (comparatively short) of
executing the activity under very favorable working conditions. The
probability of attaining this duration is about 0.01;
Pessimistic duration (b): estimated time (comparatively long) of
executing the activity under very unfavorable working conditions. The
probability of attaining this duration is also about 0.01; and
Most Likely duration (m): estimated time of executing the activity that
is closest to the actual duration. This estimates lies in between the above
two extremes.
The PERT Approach
In PERT, the given estimates of times and the likelihood of occurrence are represented by a beta curve, as shown below. However, with the three estimates of time for each activity, we cannot perform traditional CPM analysis to determine project duration. Therefore, we need to get a single weighted average duration for each activity. The formulas for the expected duration, called expected elapsed time (te) are as follows:
Beta-Distribution Curve
a
m
b
0.5
Activity
Duration te
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Expected time for the activity (te) =
Standard deviation for activity ơ =
To +4Tm +Tp
6
Tp - To
6
The PERT Approach
Analysis Steps:
Step 1: Individual Activity Durations
a = Optimistic duration = Minimum duration
m = Most Frequent duration (most likely)
b = Pessimistic duration = Maximum duration
te = activity expected duration = (a + 4 m + b) / 6
te2 = activity duration variance = [(b - a) / 6]2
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The PERT Approach
Step 2: CPM Calculations
Using the activities’ te durations, CPM calculations are performed following the forward and backward passes to determine the project duration (TE). Activity floats and also calculated and critical activities identified.
Step 3: Distribution of Project Duration
Since the probability is 0.5 that each activity will finish at its te durations, there is a probability of 0.5 for the entire project being finished at time TE. However, the expected project duration does not follow a beta curve as did the activities comprising the project. Assuming that the project is executed a large number of times, the resulting population of project durations may be assumed normally distributed.
The PERT Approach
The normal distribution of project duration is defined by its mean () and standard deviation () values, determined as follows:
TE = TE = te of critical activities;
TE = te2 of critical activities
Step 4: Analysis of Project Completion Probabilities
Using the project normal distribution, it is possible now to find the
probability values associated with specific project duration. By scaling the
project distribution to the standard normal distribution, we can obtain
probabilities from standard probability tables and make conclusions, as
follows: Z = Desired Completion Date - TE
TE
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34.1% 34.1%
13.6% 13.6% 2.1% 2.1%
-3ơ -2ơ -ơ ơ 2ơ 3ơ
Te ơ = 68.2% of the area under the curve + -
Te 2ơ = 95.4% of the area under the curve + -
Te 3ơ = 99.7% of the area under the curve + -
V (activity variance)= ơ2 activity
Ơ Total = (Ơ)2A + (Ơ)2
B + (Ơ)2C + ……
(for the critical path) (activities in the critical path)
Example
Consider a project whose critical path
consists of 4 activities A,B,C,D. Each
activity has three time estimates as shown:
A
2 6 8
B
3 9 12
C
2 8 10
D
4 6 9
50
Solution
The Expected Time and Standard Deviation
for each critical Activity
6.16
7.33
8.5
5.66
Te
0.83 5 9 6 4 D
1.33 8 10 8 2 C
1.5 9 12 9 3 B
1 6 8 6 2 A
Activity standard deviation
(Tp – To) / 6
Tp - To Tp Tm To Activity
Expected time for the project =
5.66 + 8.5 +7.33 + 6.16 = 27.65
Ơ Total = (1)2 + (1.5)2
+ (1.33)2 + (0.83)2
= 2.39
51
To calculate the probability of finishing
within any given time, you calculate Z
where:
Where T is the time required
And from the normal curve table we find the
probability
T - Te
Ơ T
Z =
The PERT Approach (Example)
Pessimistic Time (b)
Most Prob. Time (m)
Optimistic Time (a)
Predecessors Activity
8 5 2 ------- A
12 9 6 A B
8 7 6 A C
7 4 1 B,C D
8 8 8 A E
17 14 5 D,E F
21 12 3 C G
9 6 3 F,G H
11 8 5 H I
52
Variance
[(b-a)/6]2
Standard Deviation
[(b-a)/6]
Expected time
Te =
Activity
1 1 5 A
1 1 9 B
1/9 1/3 7 C
1 1 4 D
0 0 8 E
4 2 13 F
9 3 12 G
1 1 6 H
1 1 8 I
a + 4m + b 6
The PERT Approach (Example)
0 5
0 5 5
A
5 14
5 9 14
B
5 12
7 7 14
C
5 13
10 8 18
E
14 18
14 4 18
D
12 24
19 12 31
G
18 31
18 13 31
F
31 37
31 6 37
H
37 45
37 8 45
I
Ơ Total = Ơ2A + Ơ2
B + Ơ2D + Ơ2
F + Ơ2H + Ơ2
I
Ơ Total = (1)2 + (1)2
+ (1)2 + (2)2
+ (1)2 + (1)2
= 9 = 3
53
What is the probability of completing the project in 50
days? And what is the probability of completing the
project in 4 days less than the expected duration.
Prob. (T ≤ 50) = Prob. (Z1 ≤ 1.67)
From table Prob. (T ≤ 50) = 0.9525 = 95.25%
T - Te
Ơ T
Z1 = 50 _ 45
3
=
= 1.67
The PERT Approach (Example)
Prob. (T ≤ 41) = Prob. (Z2 ≤ -1.33)
From table Prob. (T ≤ 41) = 0.0918 = 9.18%
T - Te
Ơ T
Z2 = 41 _ 45
3
=
= - 1.33
The PERT Approach (Example)
54
What will be the total duration if you want to be 97.5% confident that the project will not exceed it?
From table Z = 1.96
duration = 1.96 (ơ) + 45 = 51 days
you are adding 6 days (contingency) to be 97.5% confident that the project will not exceed the duration.
The PERT Approach (Example)
Range Estimating
Range Estimating is similar to the PERT approach, where the estimators are asked to supply three estimates for each activity: lowest (L), highest (H) and most likely (M).
55
E = Expected Value =
= Standard Deviation =
For each individual activity
Standard deviation for the project
Where n is the total number of activities in the project
L + 4M +H
6 H - L
6
= (1)2
+ (2)2
+ (3)2
+ ...+ (n)2
Range Estimating
Example
Standard deviation
Expected Value
Highest Most Likely
Lowest Description Act. No.
1,350 8,120 10,402 9,005 2,300 Mobilization 10
309 2,980 3,654 3,106 1,800 Influent Control Structure
20
619 10,308 13,200 9,796 9,485 Raw Sewage Pumping
30
642 5,234 6,450 5,589 2,600 Grit / Screen Handling
40
2,760 22,500 27,761 24,009 11,200 Primary Sediment
50
2,108 20,515 25,746 21,061 13,100 Effluent Pumping
60
4,350 44,875 54,201 46,738 28,100 Aeration Tanks 70
56
Expected value of the project = $114,532
Range Estimate = $114,532 5804.9
(we are 84.1% confident that the project will not exceed $120,336.9)
+ -
Project = ()210 + ()2
20 + ……+ ()270
= $5804.9
Example
How much should we add as a contingency to be 98% confident that the project will not exceed the estimated value.
From the table
P (98%) Z = 2.06 = (C – Ce)/
Total value = 2.06 * 5,804.9 + 114,532
= $ 126,490
contingency added = $11,958
Example
57
The PERT Approach (Critique)
Criticisms to PERT Technique
Requires three estimated durations for each activity.
Assumes continuous not discrete distribution for durations.
Beta distribution is debatable.
It focuses on a single critical path and ignores close-to-critical paths.
It assumes independent activity durations.
It ignores the risk that occurs at path convergence points.
Simulation
Simulation is an analytical method meant to imitate a real – life problem / system especially when other analyses are too mathematically complex or too difficult to reproduce.
Monte Carlo simulation is a form of simulation that
randomly generates values for uncertain variables over and over to simulate a model.
Spread sheet risk analysis uses both a model and
simulation to automatically analyze the effect of varying input on outputs of the modeled system / problem.
58
Simulation is a 4 step process
1. Identify the uncertain cells in the model.
2. Implement appropriate random number generators (RNGs) for each uncertain cell.
3. Replicate the model n times, and record the value of the bottom – line performance measures.
4. Analyze the sample values collected on the performance measure.
Monte Carlo Simulation
Step-By-Step
1. Determine the duration (or cost, …) distribution of each activity. It is possible to use discrete values or to use the simplified assumption of a triangular distribution;
Triangular Distribution
a
m
b Activity
Duration Activity
Duration
Discrete Distribution
59
Monte Carlo Simulation
2. Generate one project scenario by randomly generating one possible
duration (or cost) for each activity in the project (based on its
distribution). Perform CPM calculations (or cost) for this scenario and
determine the project duration (or cost);
3. Repeat step 2 for the number of desired simulations (scenarios) and
then tabulate the results;
4. Project Duration Distribution: Calculate the mean () and () values
for the resulting project durations (total cost); and
5. Using the () and () values, determine the probability of the project
being completed on or before any given date, or within any estimated
total cost.
Risk and Uncertainty in Construction
Tutorial 3
Risk Modeling using Excel Risk Analysis using Crystal Ball
60
Simulation Models
Assumptions
Variables e.g., activities’
durations
Predictions
Follow distributions
Target e.g., Total
Project duration
Assumptions Distributions
10 12 8
0.5 Duration for A, out of 1000 randomly selected values, 500 will be 10, 250 will be 9 and 250 will be 11.
8 9
0.4
0.6 Duration for A, out of 1000 randomly selected values, 600 will be 9, 400 will be 8.
61
Once you built the model, change the assumptions randomly according to their distributions and record the target value (the total project duration)
Repeat the process 100s of times and perform statistical analysis for the results
Crystal Ball
Crystal Ball is an add-in software for MS
Excel, similar to SOLVER.
Crystal Ball will facilitate the simulation
process, the definition of the probability
distribution, and the statistical analysis,
but will not create the original model.
62
63
Problem
Activity Predecessors Duration Cost/day ($)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
-
-
-
A
B
B
B
D, C
D, C
E
E
F,E
G, J
H
K
L, M, N, O, I
(4)
ND (6, 2)
Custom(2,2,2,3,3)
ND(8,1)
Triangle(7,10,12)
Triangle(14,16,18)
ND(8,3)
Uniform(5,7)
Triangle(5,6,7)
Uniform(4,8)
Custom(10,10,11,12)
ND (6,1)
Custom (6,7,8)
Custom (2(60%), 5 (40%)
1
---
2,500
3,000
1,250
4,000
5,500
3,000
500
1,750
800
800
1,000
550
600
2000
1650
---
The following table shows the activities of a small project
Perform a risk analysis study and show:
the impact of activities’ duration on both “Total Project Duration” and “Cost”, considering indirect cost /day =$500.
the distribution of the duration and cost for the whole project, and determine probable contingencies for both of them corresponding to 50%, 80% & 90% confidence levels.
64
Hint
Establish a link between, assumptions (activities’ durations) and prediction 1 (Total project duration) and between assumptions and prediction 2 (Total cost).
Activities’ durations Total Project Duration
CPM analysis
Activities’ Cost Total Project cost
Simple summation
A
ST B
C
D
F
G
J
K
H
E
I
FN
