project evaluation under risk and uncertainty

Risk Vs Uncertainty in Project Management

Fahad Usmani, PMP

January 11, 2024

risk vs uncertainty

The project-management environment is dynamic and complex, and often, a project manager must make decisions without having all the information. Risk and uncertainty play a key role in these situations.

In risk, you can guess probabilities and the event’s impact based on historical data, while uncertainties are unpredictable situations with no background information or data.

Understanding the difference between risk and uncertainty is essential, as it influences the decision-making approach in project management. According to a World Economic Forum (WEF) study , businesses that effectively manage risk and uncertainty tend to be more resilient. 

In today’s article, we will understand risk, uncertainty, and the difference between these terms.

A risk is the possibility of unexpected events or circumstances that can affect the project objectives . These uncertainties can arise from various sources, such as technological changes, market conditions, or external factors beyond the project team’s control. Risk management is vital to avoid setbacks and ensure project success.

Risk is when you can estimate the impact of the chance of occurring the event.

A Project Management Institute’s (PMI) 2021 Pulse of the Profession report shows the importance of risk management. The report reveals that 68% of organizations experience at least one project failure in 12 months, often due to avoidance of risk management practices. According to another Standish Group’s CHAOS Report, 40% of project failures are linked to inadequate risk management. 

This emphasizes the need to use risk management practices to manage project risks proactively.

By identifying risks early in the project, you can develop a risk-response plan to manage them proactively. This will increase the chances of meeting deadlines, staying within budget, and achieving project objectives. A proactive risk-management approach is crucial for project success.


Uncertainty is a lack of complete certainty. It is the presence of unknown factors that can impact the project, but you cannot predict or measure these events. Unlike risks, uncertainties are characterized by a lack of available data or historical information. Therefore, the project management team cannot assess and develop a response plan to manage these uncertainties.

Uncertainty occurs when you cannot calculate the probability of the event occurring or the strength of its impact due to the absence of historical data.

According to a survey conducted by the Project Management Institute (PMI) in their Pulse of the Profession report for 2021 , 50% of organizations reported uncertainty as a significant challenge in project management. These uncertainties can come from changes in regulatory environments, evolving market conditions, emerging technologies, etc.

Managing uncertainty is a key project management skill that allows a project manager to guide their teams through uncertain environments.

Making Decisions in Risky or Uncertain Situations

Making decisions under risk or uncertainty involves careful planning and a strategic approach.

When dealing with risks, you will assess them and develop risk-response plans. Effective risk-management planning significantly reduces the chance of project failure.

In uncertain situations, decision-making requires adaptability and flexibility. The ability to navigate uncertainty depends on flexible, agile planning and continuous monitoring. Create contingency plans, stay vigilant to changes, and be ready to adapt promptly.

Risk and uncertainty management involves effective communication with all stakeholders, including the project team, organization, project sponsor, etc. Open communication channels encourage collaboration and allow team members to share insights and adapt collectively. 

Regularly reassess the project performance and update strategies as needed. By integrating risk management practices and embracing adaptability, you can improve your decision-making under risks and uncertainties and increase the chance of achieving your project objectives with minimal hassle.

Key Differences Between Risks and Uncertainties

These are the differences between risks and uncertainties:

  • Risks can be predicted, while uncertainties cannot.
  • Risks can be managed, while uncertainties are uncontrollable.
  • Risks can be measured and quantified, while uncertainties cannot.
  • Risks can be assigned a probability, while uncertainties cannot.

Uncertainties Vs Unknown Risks

Uncertainty is not an unknown risk.

In uncertainty, you completely lack the background information of an event, even though it has been identified. In the case of unknown risks, you have the historical data, but you missed it during the risk identification process.

A Real-World Example of Risk and Uncertainty

Assume two famous teams will play a football match the next day.

Can you tell me exactly which team will win?

No, you can’t; however, you can make an educated guess by analyzing the past performances of both teams and the results of matches they played against each other.

Then you can produce the numbers (e.g., “There is a 30% chance of Team A or Team B winning the match,” or, “There is a 70% possibility of Team A or Team B losing the match.”).

Now, let’s view the same football match in a different scenario.

Again, two teams will play a game with new players.

In this situation, if somebody asked you which team would win, what would your response be?

You will be clueless because you don’t know the performance of the team and players, and you have no idea how the teams will perform.

Here, you don’t have any information on past performances and cannot predict the event’s outcome, even though the rules and the stadium are the same.

This situation is called uncertainty.

Managing risks is easier because you can identify them and develop a response plan based on your experience. However, managing uncertainty is difficult, as no historical records are available, and you cannot predict the outcome.

You must be cautious, proactive, and open-minded to manage risks and uncertainties so that you can complete your project successfully.

project evaluation under risk and uncertainty

I am Mohammad Fahad Usmani, B.E. PMP, PMI-RMP. I have been blogging on project management topics since 2011. To date, thousands of professionals have passed the PMP exam using my resources.

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by identifies risk and I must proactive to the uncertainty event by doing this my project will be successfully doing.

You should be proactive in risk management. It will surely help you complete your project successfully.

Mathematically Risk = an uncertain event if occurs can impact the outcome of event in a positive or negative direction So it has two parts Risk = Probability * impact Now under probability theory an event can occur in three ways 1) It will happen ( a certain event) prob = 1, impact you can input based on your findings to find Risk 2) It may occur ( a probable event, however small it could be, those who talk about unknown unknowns or uncertainties all fall here) the probability could be infinitesimal or we just ignore it as It’s not worth * impact = get the risk value . 3) It will not happen ( improbable event, with zero probability) * impact = no risk associated. There is nothing that falls outside it. Those uncertainties even we may may not think or imagine will also fall under it but only worry about the major probable events that may impact our project. Your life has millions of variables all uncertain, even lightening striking us may have a probability, but we don’t really consider it Day to Day risk, but those who are not so lucky and it get struck , despite infinitesimal probability they loose. Every single event whether known and unknown has a probability of occurrence and it sums up to 1. Now you choose what your sample space is?

Well said Vinod.

I’m sorry, I disagree with the basic definitions you are using. To begin with, uncertainty is an umbrella term to define any known or unknown event or series of events. It encompasses Allowances, Contingency and Risks. Allowances are “known-knowns” whose exact value is not known at the time but whose expenditure is certain to occur. Hence an amount is assigned to this particular cost, and later revisited when additional information becomes available. Contingencies are “known-unknowns,” within the defined project scope. It is a specific provision for unforeseeable elements of cost within the defined project scope, particularly important where previous experience relating estimates and actual costs has shown that unforeseeable events that increase costs are likely to occur (AACEI). Contingency event estimates are made based on experienced judgment from subject matter experts (SMEs)on that estimate. Risks are the “unknown-unknowns” whose probability of occurrence and cost impact is not certain. But even the unknown-unknowns can be estimated by SMEs, based on their experience using Monte Carlo computer models to estimate the probability of occurrence and an estimated value of the impact. The Risk Register is where the risks (or opportunities) are listed and discussed in a Risk Workshop of SMEs, and both qualitative and quantitative descriptions are assigned to each risk element. The risk elements are prioritized, and the SMEs then look for mitigation measures to reduce or eliminate each risk. The residual post-mitigation risks are then used as the basis for the Monte Carlo computer analysis. The analysis will return the calculation that there is a (say) 80% probability that the total cost of the risks will be less than $ X thousand, or other percentages and impact cost depending on the risk estimator’s (or management’s) risk appetite. This amount should be added to the Project Base Cost (which would include Allowances) and the Contingency, defined as the Project Baseline Cost, to arrive at the project funded (or budgeted) cost.

For a more complete treatise on Uncertainty which I co-authored, please read “Addressing Uncertainties in Cost Estimates for Decommissioning Nuclear Facilities,” © OECD 2017, NEA No. 7344.

These definitions are based on the PMBOK Guide fifth edition.

Err unless you guys have decided project management should have a different definition of uncertainty than other fields of human endeavour like Science, engineering and medicine I suggest reading some of the many books on the topic. Uncertainty certainly can be measured and is used in serious fields to assign a probability that an outcome will happen within a defined range.

Google uncertainty in science or uncertainty budget

I fear you may have got some of your info from the field of economics (which can make astrology and black magic look bad) ;)

Can you explain it little further:

Uncertainty certainly can be measured and is used in serious fields to assign a probability that an outcome will happen within a defined range.

Thanks for sharing the ideas about risk and uncertainty. What Angel says is not different from your right and simple idea to make it clear. The difference is only in the statement but you both have presented the same difference eithet it is quntifiable or not which clears the fundamental difference between them. Thanks for making me more clear on the subject matter.

In uncertainty you completely lack the historical and pas information. The construction of a house or painting a wall does not fall in this category. Here you can estimate the cost will a good accuracy. Most of the times these contracts are given under fixed price or cost reimbursable.

In risk, you can guess the outcome but in uncertainty you can’t.

Can someone tell me the relationship of risk and uncertainty

Risk can be said to be an uncertain event which chances of occurrence can be predicted and measured whereas, uncertainty can also be said to be an uncertain event which chances of occurrence cannot be predicted and measured. The difference is that the probability of a risk event happening can be predicted and measured while the probability of uncertainty cannot be predicted and measured.

FAHAD Can we say contingency plan dedicated for negative risk while management reserve dedicated for uncertain issues as we can’t guess their impacts?

This is a tricky question.

As per my understanding, since the uncertainty is a identified risk, you can passively accept the uncertainty and keep some contingency reserve based on educated guess.

I also request other visitors to share their thoughts on it.

Risk: We don’t know what is going to happen next, but we do know what the distribution looks like.

Uncertainty: We don’t know what is going to happen next, and we do not know what the possible distribution looks like.


In my view uncertainty is imperfect knowledge. Throughout a project we strive to improve definition (reduce uncertainty) to improve chances of success (reduce risk of failure.) There are key uncertainties in projects that you must understand well before making strategic decisions. Cost estimating is a good example to illustrate uncertainty.It is very difficult (if not impossible) to estimate the final cost of a complex project to the last cent. Do you remember what happened the last your did a remodelling job at your house? If you did not understand the uncertainty well, you may end up regretting the decision of remodeling the kitchen yourself. That is why you do the front end work: develop the scope, prepare the plans, get quotes, etc. it is to reduce uncertainty. Uncertainty analysis helps us understand the expected ranges of outcomes & test against project objectives to make informed decisions. For example, we can test whether a project is resilient to various cost grow scenarios and make an informed decision to sanction the project. We can then characterise the risk or opportunity.

Sorry to add confusion but I agree fundamentally with Angel. .

Lets suppose we have to paint a wall in our kitchen.

Initially (at the planning stage) we are uncertain of the amount of paint to be used but can estimate it as a random number We are uncertain of the time it will take to paint the wall . There is a risk that the plaster will fall apart in preparation. There is a risk that the paint will bubble after it has been applied.

Uncertainty is managed by research and by putting slack into a project Negative Risk is managed by process improvement and recovery strategies.

Incidently you can have uncertainty about the likelihood of a risk event occuring :)

Can you please help in providing details/difference of Perform Qualitative and Quantitative risk analysis?

Thanks, Naveen

In Qualitative risk analysis, you prioritize the risks by multiplying their probabilities and impact. And in Quantitative risk analysis, you numerically analyse the risks. Here, you find the cost of each risk (if it occurs individually) and then you add it up to get the overall effect on the project.

Thanks a lot !!!

Both risk and uncertainty are inevitable in today’s scenario of Project Management. one has to driven his path midway.

Yes, one has to chose the best path suitable to the project.

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PRINCE2 and Agile are two Project Management methodologies that offer timely review, evaluation and manage risks. These Project Management methodologies assist the project team in predicting risks and making new risks more predictable. They can pre-determine risks by logging previous risks and learning how to determine and resolve them.  

This blog highlights how a project is susceptible to uncertainty. We'll examine project risk management's definition, sources of uncertainty, and strategies for lowering the risk of uncertainty in project management.  

Table of Contents

1) Let’s discuss the term – Risk and Uncertainty in Project Management 

2) What is Project Risk Management? 

3) What are the Sources of Project Uncertainties? 

4) Manage Uncertainties in Project Management 

5) Conclusion 

Let’s discuss the term – Risk and Uncertainty in Project Management  

Risk - A risk is an unplanned event that can affect the success of your project or also alter the planned cost, schedule or even resources. The risk is considered positive if it has a good impact on your project and negative if it has a negative one. 

Uncertainty - As the word suggests, uncertainty is a lack of certainty. Because you lack any prior knowledge of the event, the outcome of any uncertain event cannot be measured or predicted. 

Even though an event has been identified, you are utterly unaware of i ts background in uncertainty. In risk management, it is sometimes considered that risks and uncertainty are the same things. Many professionals mistakenly believe that risk and uncertainty are the same, despite the fact that there is a significant distinction between the two. 

Learn more about Risk Management in PRINCE2. Check out our   PMI Risk Management Professional Course   today!   

What is Project Risk Management?

The risk management process deals with getting ready to deal with unforeseen issues. Every project has a certain amount of risk. Risks can occur at any point during the life cycle of a project and have an impact on its budget, schedule, and resources. By creating a thorough risk management plan, risks may be addressed. The project managers should be able to anticipate, evaluate, and risks proactively. 

Why should We Track Risk in Projects?  

The impact of a risk can affects the scope and complexity of the project. The project team and Project Managers are responsible for tracking and developing mitigation plans for reducing the negative impacts of the risks on the project.  

When the team follows for risks, they can also come across positive risks that are not harmful to the project but beneficial. A risk management plan will help you identify and take advantage of positive risks. The purpose of risk tracking is to enable the project team to respond quickly and make the needed modifications. They can also make sure that future projects can benefit from the lessons learned. A project's success or failure depends on its ability to manage risks effectively. Monitoring risks in advance will maximise a project's success.   

Interested to know more about how PRINCE2 works? Register for our PRINCE2® Foundation and Practitioner Training Course now!     

What are the Sources of Project Uncertainties?  

Let ’s say you want to establish a manufacturing unit in an already-constructed building. You will have to remodel that building and estimate all the required elements.  

Though you may have estimated everything, it may vary when practical because of undetermined uncertainties. Uncertainties come in many ways, like human errors, not considering a standard procedure while estimating or maybe neglecting essential aspects. They are simply called sources of uncertainties.  

1) Incomplete Understanding of Scope  

We might not have taken into account every necessity. Do the baseboards need to be replaced? If we didn't consider the baseboards, our idea of scope would be incomplete, and our estimate wouldn't account for the work necessary to replace them.  

2) Incomplete Understanding of Work per Scope  

Let's say baseboard replacement was included in the scope this time, but we figured it would just require a few nails to secure the new ones in place. Unfortunately, even though the scope was correct, the effort estimate will be too low because we failed to take into consideration the work involved in measuring and cutting the baseboards to the proper dimension.  

3) Imperfect Understanding of Known Work  

Even if we remembered to account for everything that needs to be done to install the baseboards, our estimates m ight still be inaccurate because some of the boards may split when nailed. To prevent splitting when we nail them, we shall either replace those baseboards or drill them. In either case, the workload will go beyond the initial estimation.  

4) Inability to Forecast the Unexpected

These external events are unpredictable and disrupt our scope or schedule, thereby affecting the entire plan. The same is the case with the project, which may affect its success.  

Get trained in Agile Project Management. Register for our  Agile Project Management Practitioner Course now!  

Manage Uncertainties in Project Management  

Until now, we learned about the uncertainty and risk in project management , and after finding the problem, we need to look at solutions to control and manage these risks.  

Follow these steps to manage uncertainties:  

1) Understand ing the Cause of the Issue :

Firstly, understand the cause of uncertainty before making the next move. As for some things, we tend to overestimate the problem, while it may be silly. But this can only be understood after thorough analysis first.  

Finding the true root of the problem is also a productive endeavour because it will provide a thorough understanding of the cause and possibly lead to the suggestion of a workable remedy. 

2) Try to find Issues Q uick ly :

Only the project manager s are qualified to respond to inquiries about uncertainty or risk. This means that in order to determine the amount of harm to the project, they should examine the issue or problem as soon as feasible. They should suggest a course of action so stakeholders can unwind and the project can proceed. 

3) Keep the Team Updated on the Progress :   

Gaining trust and credibility requires maintaining s olid relationships, communication, a plan, and a routine.  Building trust, cooperation, and honesty among the project team members are crucial since a strong team will group and attempt to find a solution.   


4) Mark the Issue as Solved for Future Projects :  

Accounting the problem and its resol ution will help you avoid running into it again in upcoming projects. Once this uncertainty has been resolved, it can be recorded as a known project risk.

Learn how to determine risks and prepare mitigation plans. Register in Certified Risk Management Professional CRMP today!  


Uncertainty cannot be eliminated by any estimation methods. It arises partly because of imperfect knowledge of what to do and how long it should take and partly because of unpredictable events. Reducing scope helps to reduce uncertainty, but only to a point.  

In this blog , we have discussed everything about how risks are inherent in a project and how to determine them. You have to know that risks and uncertainties in a project are inevitable, but a good mitigation plan will make your project successful and clients satisfied.  

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Managing Project Uncertainty: From Variation to Chaos

Project managers can’t predict the future, but accurately gauging the degree of uncertainty inherent in their projects can help them quickly adapt to it.

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Uncertainty is an inevitable aspect of most projects, but even the most proficient managers have difficulty handling it. They use decision milestones to anticipate outcomes, risk management to prevent disasters and sequential iteration to make sure everyone is making the desired product, yet the project still ends up with an overrun schedule, overflowing budget and compromised specifications. Or it just dies.

To find out why, we studied 16 projects in areas including personal-computer development, telecommunications, Internet startups, pharmaceutical development, iron-ore processing, airship development and building construction. Interviews with team members and scrutiny of project documentation over five years showed managers consistently failing to recognize that there are different types of uncertainty, each of which requires a different management approach. The lack of awareness is understandable, given that the commonly accepted definition of a project (“a unique interrelated set of tasks with a beginning, an end and a well-defined outcome”) assumes that everyone can identify the tasks at the outset, provide contingency alternatives and keep to the same overall project vision throughout. 1 Those are fair assumptions for routine or well-understood projects, but not for novel or breakthrough initiatives, which require companies to rethink the traditional definition of a project — and the ways to manage it. (See “Beyond Risk Management.”)

Beyond Risk Management

A project risk is an uncertain factor — positive or negative — that can significantly affect achievable performance. * Risk management is the practice of identifying, evaluating and controlling those factors to avoid or mitigate potential negative effects. †

A power-plant contractor that executes projects in the Middle East might identify risks including natural events (a sand storm), technical events (a test failure), partner events (a supplier not delivering), financial events (a guarantee falling through) or political events (a local power broker’s resistance). Each identified risk would be assigned a probability, and then methods such as scenario evaluations, simulations or decision trees would be used to estimate potential impact and prioritize risks. Handling the risks could mean avoiding them, taking preventive action or simply accepting them as a nuisance. For significant risks, the team might draw up contingency plans at the project’s start, then monitor events and implement the contingent response when necessary.

Risk management is geared to identifying and controlling variation and foreseeable uncertainty. It acknowledges that unanticipated events may necessitate crisis management, but it also holds that “while crisis management may be necessary, few crises should come totally out of the blue.” ‡ But what about breakthrough projects or projects undertaken in rapidly changing environments where unforeseen uncertainty or chaos may be unavoidable and important? To deal with such extreme uncertainty, managers need to go beyond traditional risk management, adopting roles and techniques oriented less toward planning and more toward flexibility and learning.

* C. Chapman and S. Ward, “Project Risk Management” (Chichester, United Kingdom: Wiley, 1997), 7. † R.L. Kliem and I.S. Ludin, “Reducing Project Risk” (Hampshire, United Kingdom: Gower, 1997), 10–25. ‡ Chapman, “Project Risk Management,” 10, 241.

A more forward-thinking approach is uncertainty-based management, which derives planning, monitoring and management style from an uncertainty profile comprising four uncertainty types — variation, foreseen uncertainty, unforeseen uncertainty and chaos. From variation to chaos, managers move progressively from traditional approaches that are based on a fixed sequence of tasks to approaches that allow for the vision to change, even in the middle of the project.

What Uncertainty Looks Like

Some projects have few uncertainties — only the complexity of tasks and relationships is important — but most are characterized by several types of uncertainty. Accepted practice is to classify uncertain events by their source (technical issues, market, people, cost, schedule and quality) or by potential impact. 2 Our categories, however, emphasize uncertainty as it relates to project-management techniques. (See “Characterizing Uncertainty in Projects.”) Although each uncertainty type is distinct, a single project typically encounters some combination of all four.

Characterizing Uncertainty in Projects

project evaluation under risk and uncertainty

View Exhibit

project evaluation under risk and uncertainty

Variation comes from many small influences and yields a range of values on a particular activity — activity X may take between 32 and 34 weeks, for example. At the start of projects characterized by variation, managers know the sequence and nature of activities and have clearly defined objectives. The project plan is detailed and stable, but schedules and budgets vary from their projected values. A shifting schedule causes the critical path (the train of activities that determines overall project duration) to move, forcing project managers to monitor variations across the board, not just critical activities. In a construction project, for example, myriad events (worker sickness, weather, delayed parts delivery, unanticipated difficulty of tasks) influence budget, schedule and specifications. Such influences are too small to plan for and monitor individually, but the project team could plan for and monitor the resulting variations in expense and time.

Foreseen Uncertainty

Foreseen uncertainties are identifiable and understood influences that the team cannot be sure will occur. Unlike variation, which comes from combined small influences, foreseen uncertainty is distinct and may require full-blown risk management with several alternative plans. Pharmaceutical development typifies foreseen uncertainty. It is geared toward detecting and managing risks, primarily in the form of drug side effects. A developer of a new drug can anticipate possible side effects because they have appeared previously in related drugs. It then can outline contingency plans to change the prescribed dosage or restrict usage to certain indications or well-controlled circumstances. The side effect is the foreseen uncertainty. The contingency plan may never be used, but it is there if the side effect occurs.

Unforeseen Uncertainty

As its name suggests, unforeseen uncertainty can’t be identified during project planning. There is no Plan B. The team either is unaware of the event’s possibility or considers it unlikely and doesn’t bother creating contingencies. “Unknown unknowns,” or “unk-unks,” as they are sometimes called, make people uncomfortable because existing decision tools do not address them. Unforeseen uncertainty is not always caused by spectacular out-of-the-blue events, however. It also can arise from the unanticipated interaction of many events, each of which might, in principle, be foreseeable. Unforeseen uncertainty occurs in any project that pushes a technology envelope or enters a new or partially known market. Pfizer’s block-buster drug Viagra, for instance, began as a heart medication to improve blood flow by relaxing the arteries. When clinical studies found that it also increased sexual performance, the company ended up developing that unexpected side effect into a block-buster drug, implementing new clinical development and a new marketing approach midway through the original project.

Whereas projects subject to unforeseen uncertainty start out with reasonably stable assumptions and goals, projects subject to chaos do not. Even the basic structure of the project plan is uncertain, as is the case when technology is in upheaval or when research, not development, is the main goal. Often the project ends up with final results that are completely different from the project’s original intent. For example, in 1991, Sun Microsystems conceived of Java as software to drive a controlling device for household appliances. It wasn’t until 1995 that Java became hugely successful as a programming language for Web pages. Ironically, a decade after Java’s conception, we are finally seeing consumer-appliance applications for it.

Creating Uncertainty Profiles

In the rare projects that have little uncertainty, the project manager is primarily a coordinator and scheduler — planning tasks according to experience and using task-breakdown structures and critical-path methods. Relationship management consists of identifying conflicts, clarifying responsibilities and defining deliverables. Monitoring consists of comparing budget, schedule and deliverables against the project plan, coordinating stakeholders and suppliers and enforcing deliveries.

The greater the uncertainty inherent in a project, however, the more the team may have to redefine the tasks — or even the structure of the project plan — in midcourse. It is much easier to do that if everyone has begun the project with the same assumptions about how changes will be managed. The mechanism that ensures agreement is the uncertainty profile — a qualitative characterization of the degree to which each type of uncertainty may affect the project. For example, although the dominant uncertainty an Internet startup faces may be chaos (for example, the potential for fundamentally changed circumstances), it also may face variation (IT implementation taking longer than planned), foreseen uncertainty (market entry by a competitor) and unforeseen uncertainty (human-resource issues).

The uncertainty profile is the team’s subjective estimate and indicates which uncertainty types are potentially the most important. To help identify the dominant uncertainty types, teams may use hunches based on previous projects or may adopt more formal approaches, such as statistical analyses, technology and market forecasts, scenario planning or creativity-management techniques. Teams draw from many sources to create the profile. Its form is not as important as its purpose — to ensure that everyone understands the major uncertainty types faced and how each uncertainty type influences management style.

Once a profile is created, it can be used to build a project infrastructure to execute a plan (in the case of variation or foreseeable uncertainty) or to learn from events and adjust (unforeseeable uncertainty or chaos). 3 The project manager’s role and the planning and monitoring activities change as the uncertainty profile evolves. So flexibility — and the ability to communicate changes — is key.

Managing Variation

In projects subject primarily to variation, the project manager is first and foremost a troubleshooter who can identify deviations and push through solutions to get the project back on track. Radical changes to the plan are not the concern as much as how to control slippage in the budget, schedule and deliverables. If no one has planned for variation, the project manager must resort to firefighting to get the project back on track — a waste of resources and a drain on stakeholders. A better approach is to account for variation during project planning and build in buffers at strategic points in the project — for example, increased capacity or budget reserves. 4 Top management must respect those buffers and avoid treating them as bargaining chips to be negotiated away.

Once the critical path is established and appropriate buffers are defined, managers need procedures for monitoring progress and authorizing changes in the project plan, such as expediting certain tasks. 5 Formal methods such as statistical control charts let managers monitor variations without identifying the small, underlying causes. They can track performance variables —such as days ahead of or behind schedule, or differences between the budgeted and current project cost. As long as the variable stays within an acceptable range, no action is needed. But once it falls outside the range, managers must identify causes and take action. The project team must have the ability and authority to react, for example, by shifting suppliers’ and subcontractors’ intermediate delivery dates. Reacting to significant deviations is more effective than monitoring every small critical-path variation in an endless battle to stay the course.

The Mobile Systems Unit (MSU) of Taiwan computer maker Acer learned the importance of that principle in its development and manufacture of PC notebooks. 6 Notebook development happens under extreme time-to-market pressure, and in 1998, MSU development cycles had shrunk to eight months. Missing the market introduction window by only one month on a given model virtually eliminated the unit’s profit potential for that model.

MSU saw that missed introductions were due to significant schedule variations with multiple causes. Vendors would occasionally not deliver sufficient volumes of a promised new component on time. Major customers such as IBM would change their requirements. Design problems with the motherboard would cause an additional design loop. Negotiations among multiple parties might change internal specifications. Relentless pressure on the engineers and insufficiently documented procedures would lead to shortcuts in testing, causing major rework at a more costly stage.

Acer attacked the multiple causes on multiple fronts. First, MSU management created buffers in the form of slack capacity by killing two projects that were already delayed. That wasn’t easy, because one project was to be a top-of-the-line model and the decision to kill it was hotly contested. (The controversy ultimately prompted Acer to adopt a more focused market-segment strategy.) MSU then concentrated on improving the way it documented operating procedures so that it could increase testing coverage and facilitate training of young engineers. Those steps reduced the number of correction loops during product development and improved the quality of the company’s manufacturing ramp-up. Acer also concentrated the responsibility for product specifications in one group, reducing negotiation loops and internally caused specification changes. Over the next two years, MSU more than doubled its sales and gained significant market share.

Managing Foreseen Uncertainty

In projects with major sources of foreseen uncertainty, project managers must first identify events that could affect the project. The task could be as simple as making a list of risks or opportunities and identifying different courses of action to deal with events as they materialize. Although critical-path methods are still good for handling complexity, there also must be some way to represent the potential influence of foreseen uncertainties. The decision tree — a graphic that helps managers to consider and communicate the effects of early decisions on later uncertainties and thus on later decisions — is a useful approach. 7 Each branch of the tree represents a contingency plan for a major foreseen uncertainty.

To track projects featuring unforeseen uncertainty, teams must monitor not only which activities are complete, but also which branch of the decision tree has materialized. The manager shifts from master scheduler and troubleshooter to reactive consolidator of what the team has achieved so far. With unforeseen uncertainty, managers must ensure all parties know the contingencies and, from the project’s outset, buy into the alternative plans and outcomes. During the project, managers must constantly monitor all risks and communicate them to stakeholders.

It is dangerous to ignore foreseen uncertainty. Consider the case of the pharmaceutical company Alpex (not its real name), which launched Nopane in Germany in 1995. Nopane was an effective painkiller with blockbuster potential. 8 The company knew of several life-threatening potential side effects, which it carefully controlled and ultimately eliminated during clinical trials. One less dangerous side effect was low blood pressure to the point of dizziness and fainting. Patients could avoid that effect if they kept their pulse rate below 120 beats per minute for five days after taking Nopane. Unfortunately, many patients ignored the warning. After 700,000 packets of Nopane were sold in the first six months, 500 fainting cases — a few of them well publicized — occurred because patients exercised too soon after the drug had controlled their pain. The German health agency ended up restricting the drug to a small niche, and Alpex lost the chance to market a blockbuster.

Alpex could have used more-disciplined management in introducing Nopane. The company had seen signs of irresponsible patient behavior and fainting in the U.S. trials and also in China, where the drug was introduced in 1993, but certain stakeholders argued against the relevance of the U.S. and Chinese experiences to the German market. Alpex developed no formal contingency plans for the low-blood-pressure effect.

Also, Alpex marketed to doctors, which clouded its vision of the behavior of real customers — patients. Moreover, an organizational rift stunted effective oversight, and early warning systems broke down. High expectations and rigid managerial systems kept the company from fully responding to what should have been anticipated. When the German health agency discovered there had been signs of the side effect during clinical trials, it reacted strongly. That was the end of Nopane’s large-scale potential.

If stakeholders had agreed on a contingency plan for non-threatening side effects — perhaps testing the drug outside the hospital under more realistic conditions of patient behavior —the causal link between exercise and fainting would have been harder to ignore.

Managing Unforeseen Uncertainty

Unforeseen uncertainty makes contingency planning more difficult because the project team cannot anticipate everything. Because it is impossible to create a complete contingency plan, the plan must evolve as the project progresses. Teams must go beyond mere crisis management and continually scan for emerging influences — either threats or opportunities. When enough new information arises, they must be willing to learn and then formulate new solutions. To deal with unforeseen uncertainty, project managers must move from troubleshooting to opportunistic orchestrating and networking.

As the manager of the Ladera Ranch earth-moving project in California notes, “Fifty percent of my job is managing relationships with our subcontractors, regulatory agencies and landowners. Thirty percent is scanning the horizon more than three months out to identify potential problems while we can still do something about them. The final 20% is driving to the site and keeping track of what is really happening.” Tools such as Gantt charts — graphical representations of the exact timing of all project activities — are inadequate. As the team manager observes, “A Gantt chart is more a reflection of what happened last week, and what someone hopes will happen next week.”

The Ladera Ranch team moves millions of cubic yards of dirt for independent builders in Southern California needing house pads, streets, water runoff, landscaping and utilities. The major objective is to plan the cuts and fills in a way that moves dirt the shortest distances possible. Although geological studies exist, the moisture level and exact soil type are unpredictable. That’s a problem because moist earth requires more excavation and takes longer to settle before anyone can build on it. A project team might opt to dry the dirt rather than delay selling lots. Also, some soil types may require different slopes for stability and that can affect the amount of flat area available for houses and streets.

The Ladera Ranch team is forced to deal with unforeseen uncertainty. The number of scenarios proliferates with the number of locations considered. The team could, in theory, handle that problem as a series of foreseen uncertainties, building a contingency plan for each scenario. (“If soil is moist and type X at location Y, use Plan A. If it is dry and type Z, use Plan B.” And so on.) However, that rapidly becomes infeasible because of the interdependence of cuts and fills across locations. Sometimes, markedly unexpected events — such as the discovery of prehistoric Indian ruins or a rare animal or plant species — can alter the operation completely.

The Ladera Ranch project-management team is run on principles its project leader saw firsthand in the U.S. Marine Corps: “Every play we run,” he says, “is an option play. I want my people to be able to make decisions in the field without having to report back to me every time something comes up.” The team meets weekly to discuss whether the project or target path will change and, if so, how. The approach ensures that team members view unforeseen uncertainties as incrementally solvable problems, not roadblocks or rationales for underperformance.

With unforeseeable uncertainty, a lot of time and effort must go into managing relationships with stakeholders and getting them to accept unplanned changes. Stakeholders often dig in, so much of the manager’s job is to anticipate and soften resistance by creating flexible contracts and keeping stakeholders well informed. Top-management support, negotiation techniques, team-building exercises and the project manager’s charisma can help resolve conflicting interests.

The project management team at Ladera Ranch has worked hard to share subcontractors’ risk, recognizing that taking advantage of a supplier today limits flexibility tomorrow. The relationship is characterized by trust and relieves both the management team and the subcontractors of having to anticipate every little event. Without such trust, no subcontractor would cooperate until the project team had drawn up a formal contract — a barrier to handling unforeseen events. A high degree of flexibility is difficult to obtain and often is received unenthusiastically. That’s understandable given that most top managers have been more concerned with hitting established targets than in doing the best overall job possible. But flexibility is key to moving projects beyond the vague assumptions characteristic of unforeseen uncertainty.

Managing Chaos

Even greater flexibility is required in managing projects subject to chaos. The management team must work with conceptual models that may be redefined repeatedly as feedback spurs learning. Contingency plans are insufficient because learning may cause a fundamental change in the project structure, which in turn requires redefining the entire project. To keep the chances of success high enough, teams must be willing to try fundamentally different approaches, either in series or in parallel. Tracking is less focused on the current status of the project relative to its target and more on the current status of learning about basic project assumptions.

The need for flexibility and iteration obliges project managers to cope with constant change. They become entrepreneurs — developing and maintaining close but loose contacts with customers and opinion leaders. In projects characterized by chaos, team managers must have a high degree of autonomy. They must continually verify the original project idea, quickly run experiments to collect feedback on new ideas and consolidate what they learn. Rapid prototyping is one way to support such an experimental approach. 6

However, autonomy must be in balance with organizational discipline. Companies must be ruthless in cutting projects when the chance of success becomes too small. Changing the project’s basic concept requires the involvement of the organization’s leaders and may force them to make major decisions about what resources to commit and how to set targets., a German Internet company launched in 1999, wanted to use the Priceline reverse-auction business model (which cannot be patented in Europe). Despite numerous changes in the selling process to accommodate the preferences of the German consumer, the company could see by mid-2000 that the consumer-auction boom was faltering. Knowing that it could not survive on customer-driven pricing alone, it developed software services for industrial customers and an Internet-based ticket search engine for travel agents. By summer 2001, the search engine, which dynamically optimizes offers from multiple airline-reservation systems, had become the most promising of the company’s offerings. successfully navigated chaotic uncertainty, but there were painful points along the way. One investor commented, “How can they change the business model this much? It’s like we gave them money to develop a sausage factory, and now they tell us they have moved into building fighter planes.” Fortunately, the project managers knew that to survive they would have to do more than control a few identifiable risks or bring a schedule into line. Had the company not recognized the chaotic market and taken the steps to deal with it, its evolution would have floundered.

That much discipline will strain even the most trusting relationships. Tying in partners through contracts or dedicated assets may backfire if a radical change nullifies partners’ participation. For projects in chaotic environments, painful redefinitions are inevitable. Successful partners typically are those that share a long-term vision of the project’s mission. 10

The Circored project — a collaboration of U.S. ore provider Cleveland-Cliffs and Lurgi Metallurgy GmbH — provides an object lesson. 11 Cleveland-Cliffs wanted to develop a new market, delivering directly to steel plants rather than to dealers, and Lurgi had technology that though unproven appeared to be a breakthrough. The Circored project started in 1995 with Cleveland-Cliffs, Lurgi and a third partner making plans to build a plant in Trinidad. It soon became clear that Lurgi’s new technology would not meet expectations and would have to be fundamentally changed. As market prices for the product collapsed, the third partner pulled out. Cleveland-Cliffs and Lurgi wavered. They agreed to continue only after an elaborate trust- and team-building effort. Lurgi’s efforts to rethink the technology finally bore fruit in March 2001. The plant began to produce volume and now has business potential, although world market prices are still down.

One manager reflected, “Why did we all agree to go through this pain? Only because we all underestimated what was ahead of us. The risks we thought we were facing turned out to be irrelevant; the problems that did hit us were unexpected; and the outcome was different from the original idea.”

Striking a New Balance

How management style varies with uncertainty profile.

project evaluation under risk and uncertainty

Knowing your project’s uncertainty profile — ranging from simple variation to outright chaos — will help you choose the right management strategy.

project evaluation under risk and uncertainty

Though many projects are characterized by one dominant type of uncertainty, they often will display a blend of types. Managers must be flexible enough to adopt the right approaches at the right time. The challenge in managing uncertainty, to whatever degree, is to find the balance between planning and learning. Planning provides discipline and a concrete set of activities and contingencies that can be codified, communicated and monitored. 12 Learning permits adapting to unforeseen or chaotic events. The two require different management styles and project infrastructure. Projects in which variation and foreseen uncertainty dominate allow more planning, whereas projects with high levels of unforeseen uncertainty and chaos require a greater emphasis on learning. (See “How Management Style Varies With Uncertainty Profile.”) Openness to learning is new to many companies. But it’s obvious from the many spectacular project failures that the time has come to rethink some of the traditions in project management. In an era of rapid change, uncertainty is a rule, not an exception. Companies that understand that have the greatest chance to produce spectacular project successes.

About the Authors

Arnoud De Meyer is dean and professor of technology management at INSEAD Singapore, where Christoph H. Loch is professor of technology management and Michael T. Pich is assistant professor of technology management. Contact the authors at [email protected], [email protected] and [email protected].

1. J.R. Meredith and S.J. Mantel, “Project Management — A Managerial Approach” (New York: John Wiley & Sons, 1995); C. Chapman and S. Ward, “Project Risk Management” (Chichester, United Kingdom:

Wiley, 1997), 7; and R.L. Kliem and I.S. Ludin, “Reducing Project Risk” (Hampshire, United Kingdom: Gower, 1997), 10–25.

2. C.B. Chapman, “A Risk Engineering Approach to Project Risk Management,” International Journal of Project Management 8 (1990): 5–16.

3. For more examples of projects with variation, see A. De Meyer and C.H. Chua, “Banyan Tree Resorts and Hotels: Building the Physical Product,” INSEAD case no. 4943 (Singapore: INSEAD, 2001);

A. De Meyer, “Product Development for Line Transmission Systems Within Alcatel NV,” INSEAD case no. 9991 (Fontainebleau, France: INSEAD, 1992); and C.H. Loch, A. De Meyer and S. Kavadias, “Dragonfly,” INSEAD case no. 4885, (Fontainebleau, France: INSEAD, 2000). For more examples of projects with foreseen uncertainty, see C.H. Loch, “Crossair: The Introduction of DGPS,” INSEAD case no. 4751 (Fontainebleau, France: INSEAD, 1998); and P. Verdin and A. De Meyer, “Alcatel Access Systems,” INSEAD case no. 4873 (Singapore: INSEAD, 2000).

For more examples of projects with unforeseen uncertainty, see M.T. Pich and C. H. Loch, “Delta Electronics,” INSEAD case no. 4874 (Singapore: INSEAD, 2000); C.H. Loch and A. Huchzermeier, “Cargolifter,” INSEAD case no. 4866 (Fontainebleau, France: INSEAD, 1999); and C.H. Loch and K. Bode-Greuel, “Evaluating Growth Options as Sources of Value for Pharmaceutical Research Projects,” R&D Management 31 (2001): 231–248.

4. These techniques were first proposed by A.A.B. Pritsker, “GERT: Graphical Evaluation and Review Technique,” memorandum RM-4973-NASA (Santa Monica, California: The Rand Corp., 2000). For more on network planning and scheduling, see “Project Management — A Managerial Approach.” Buffers have been proposed by E.M. Goldratt, “Critical Chain” (New York: North River Press, 1997), 151–160. Such buffers are applied routinely in software projects, as described in M.A. Cusumano and M.W. Selby, “Microsoft Secrets” (New York: Free Press, 1995), 190–207.

5. C. Terwiesch and C.H. Loch, “Managing the Process of Engineering Change Orders,” Journal of Product Innovation Management 16 (1999): 160–172.

6. C.H. Loch, “Acer Mobile Systems Unit (A and B),” INSEAD case no. 4825 (Fontainebleau, France: INSEAD Euro Asia Center, 1999).

7. Another formal approach is scenario planning. But rather than formal approaches, many companies use risk lists with a contingency plan appended to each risk, implicitly treating each uncertain event as independent.

8. C.H. Loch and C. Terwiesch, “The Development of Nopane,” INSEAD case no. 4661 (Fontainebleau, France: INSEAD, 1997).

9. M. Iansiti and A. MacCormack, “Developing Products on Internet Time,” Harvard Business Review 75 (September–October 1997): 108–117.

10. B.M. Bensaou, “Collaboration Support Technologies in Interorganizational Relationships: An Empirical Investigation in Buyer-Supplier Joint Design Activities,” working paper 99/78/TM/ABA, INSEAD, Fontainebleau, France, 1999.

11. Based on discussions with management; see also R. von Bitter et al., “Circored: Experiences With Two New Fine Ore Reduction Processes” (presentation at the METEC Congress, Düsseldorf, Germany, June 13–15, 1999). Lurgi’s ( metallurgy business was sold to the Finnish company Outokumpu in July 2001.

12. R.P. Smith and S.D. Eppinger, “A Predictive Model of Sequential Iteration in Engineering Design,” Management Science 43 (1997): 1,104–1,120; and J. Mihm, C.H. Loch and A. Huchzermeier, “Modelling the Problem Solving Dynamics in Complex Engineering Projects,” working paper 2001/48-TN, INSEAD, Fontainebleau, France, 2001.

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Qualitative and quantitative project risk assessment using a hybrid PMBOK model developed under uncertainty conditions

This study presented a qualitative and quantitative project risk assessment using a hybrid PMBOK model developed under uncertainty conditions. Accordingly, an exploratory and applied research design was employed in this study. The research sample included 15 experienced staff working in main and related positions in Neyr Perse Company. After reviewing the literature and the Project Management Body of Knowledge (PMBOK), 32 risk factors were identified and their number reduced to 17 risks using the expert opinions via the fuzzy Delphi technique run through three stages. The results of the confirmatory factor analysis showed that all risks were confirmed by the members of the research sample. Then the identified risks were structured and ranked using fuzzy DEMATEL and fuzzy ANP techniques. The final results of the study showed that the political and economic sanctions had the highest weight followed by foreign investors' attraction and the lack of regional infrastructure.

Project risks; Project management body of knowledge (PMBOK); Uncertainty; Mixed qualitative and quantitative risk assessment approach; Mathematics; Probability theory; Engineering; Industrial engineering; Business

1. Introduction

It can be stated with certainty that uncertainty exists in all projects, and appropriate methods should be employed to deal with this uncertainty and reduce its impact on managers' decision making [1] . One way to reduce uncertainty and counteract it is to use the fuzzy set theory, which can reflect somehow the ambiguity inherent in the problem under analysis, and present results that are closer to reality [2] . There are many risks in oil projects which can cause many problems if there is no required control and planning [3] . Considering the great importance of such projects and the vital impact of oil on various aspects of the life of Iranian people, it is necessary to conduct extensive studies to increase the reliability of planning. Risk management as one of the most important branches of management science, especially project management, aims to increase reliability. Accordingly, several methods have been devised and proposed. Fuzzy set theory and fuzzy logic as modern concepts will be able to play a major role in risk management f they are combined with management science. Construction projects constitute the greatest and most important projects in the oil industry, and they naturally are replete with small and big risks that can be dealt with through accurate planning [4] .

The oil and gas industry is the most important industry in terms of financial turnover and employment. Given the degree of development in the industry which depends on oil and its derivatives, new projects are initiated every day. Therefore, the number of projects in the oil and gas sector is very high. Considering the financial tunover of oil projects, the management of these projects is very important [4] . On the other hand, these projects are also at high risk which can be attributed to the high risky nature of gas and oil and the flammability and hazardous nature of their derivatives, which are often the cause of accidents in exploration and exploitation projects. For this reason, reducing the risks associated with oil projects, especially in exploration and exploitation projects, is very important [5] . Gas and oil projects are associated with a variety of risks in the present era. Therefore, the management of project risks is critical to the survival of these projects. Risk management is one of the phases of project management and project risk ranking is a key part of the risk assessment phase in the process of project risk management. Also, according to experts and practitioners of oil industry projects, the probable impact of risks affect project objectives such as cost, time, scope and quality of the project [3] . The PMBOK standard identifies risk management at various steps and provides control programs to reduce the severity of risks. These steps are stated as follows:

  • 1. Risk management planning
  • 2. Risk identification
  • 3. Quantitative risk analysis
  • 4. Qualitative risk analysis
  • 5. Risk response planning
  • 6. Risk monitoring and control [2]

An important point in risk assessment and assessment is uncertainty. Uncertainty in estimating the time and cost of industrial projects is considered as a major challenge in project management science. Accordingly, one of the most effective solutions to solve this problem is risk analysis. In fact, risk management is the systematic use of management policies, procedures, and processes related to risk analysis, assessment, and control activities. Therefore, prior to initiating the project, the project risks must be identified and quantified, and ultimately an appropriate strategy taken to prevent their occurrence or mitigate their effects [6] . Two issues are critical in implementing the risk management process. First, the critical risks that have a great impact on the time and cost of the project are identified, because the analysis of all risks in a project is time-consuming and not effective. Second, after identifying critical risks and analyzing them, responding to the risks is essential, because the risk management is effective only in cases where the effects of risk are eliminated or mitigated with precise and predetermined planning as soon as the risk occurs. To this end, the use of a method that can perform quantitative analysis at a higher speed and reduce uncertainty in the decision-making context can be effective. Therefore, the present study focuses on the use of statistical and multi-criteria decision making methods and fuzzy techniques which are used to structure and prioritize the risks of oil projects in the exploration and exploitation phases. The risks inherent in oil projects due to the great number of these projects can have a negative impact on the project quality, time, and cost, and their management can greatly hinder the occurrence of risk-associated accidents. Thus, given the presence of European countries such as France for collaborating on oil projects after the Joint Comprehensive Plan of Action (JCPOA), it seems that focusing on risk management and mitigating their effects is one of the requirements that contracting companies need to pursue engineering, procurement, and construction (EPC) projects. This kind of risk mitigation will also lead to the increased trust of foreign companies and lower their costs. The review of databases showed that, despite the importance of risk assessment and analysis in oil exploration projects, mixed methods have not been employed for risk analysis and evaluation. Therefore, the present study seeks to use mixed methods including fuzzy Delphi, factor analysis, and DEMATEL, and Fuzzy ANP techniques to propose an executive and operational framework for risk analysis that minimizes the risks of exploration projects. Thus, the main questions addressed in this study are stated as follows:

  • 1. What risks exist in oil exploration and exploitation phase projects based on the PMBOK classification?
  • 2. How do these risks affect and how they are affected?
  • 3. What is the significance of each project risk?

2. Literature review

2.1. concepts and theories, 2.1.1. definition of the project and the importance of its management.

Considering the rapid development of industries in the country and the gradual increase of new industrial, construction, and development projects, correct project planning, and management is essential in these industrial sectors. Overall, a project can be defined as a series of complex, non-repetitive, and interrelated operations that are implemented by the management or an administrative organization to meet certain goals within a predetermined schedule and budget framework: Project management is a process in which the project will achieve the desired outcome during its lifetime through the easiest and most cost-effective way. The project management process consists of three main components: planning, implementation, and supervision [4] .

2.1.2. Project planning and control system

The success of major industrial and construction projects is dependent on a systematic approach to planning and controlling the way activities are carried out in terms of the execution time and cost. The main function of the project planning and control system is preparing, compiling, recording, and keeping the information related to different stages of the project lifecycle and also processing, classifying, and analyzing the information, and preparing the necessary reports for the project manager. The purpose of this system is to direct the project according to the determined schedule and budget, and to provide the final objectives and products of the project and to store the resulting information for use in future projects. This system should assist the project manager in optimizing the three factors of time, cost, and quality in project implementation. A good project planning and control system should have the following capabilities and features [7] :

  • 1. Determining the completion date of the project at the planning and initial scheduling stage
  • 2. Determining the work breakdown structure (WBS) for proper implementation and non-interference of activities and their resources
  • 3. Providing cost-effective solutions to compensate for delays in executing some project activities at the execution time
  • 4. Delivering cost-effective solutions to expedite project implementation in case of changes in the economic and social conditions of the country or the project-generating organization and changes in the project priorities and the need for its faster implementation
  • 5. Scheduling and planning for the use of human resources, machinery and equipment, and, in general, reusing the resources for optimum use of them and avoiding possible bottlenecks and limitations
  • 6. Determining the distribution of materials and, in general, non-reuse resources between projects and their various activities
  • 7. Scheduling purchase orders for materials, materials, machines, and equipment to reduce storage and waste costs as well as losses caused by stagnant project finance.
  • 8. Determine the amount of the project's liquidity per time unit for timely payment of bills and prepayments
  • 9. Recording and analyzing the results when necessary to change the project planning and maintenance for use in future projects and prevent similar problems [7] ).

2.1.3. Project planning and control stages

1. Planning stage Project planning includes tasks that are done to identify project activities and their interrelationships, and estimate the time, resources, and cost of implementing them based on criteria in the project-generating organization. The various project planning stages can be divided into the following categories: Step 1: Project analysis, understanding activities and their interrelationships, preparing the work breakdown structure (WBS)

  • 1. Determining the project implementation phase based on the implantation organization of its activities and determining the major activities of each project phase, i.e. dividing the project to its sub-projects
  • 2. Breaking down each sub-project into its components and determining all project activities based on how they are implemented
  • 3. Designing the work breakdown structure (WBS) using a systematic and top-down approach, which according to the type, organization, and scope of the project can affect the project implementation phases, major project activities, final product, and its components, units contributing to the implementation of the project or a combination of them
  • 4. Determining all project milestones to facilitate subsequent controls and emphasize the completion of some vital activities at a given time
  • 5. Identifying and defining the order of activities in an accurate and realistic way [8] .

Step 2: Estimating the time, resources, and cost of implementing each project activity

  • 1. Estimating the duration of implementation of any of the activities identified in the first step according to the opinions of executive experts and prior experience in the implementation of similar projects
  • 2. Plotting the project network using the critical path method (CRM) and utilizing professional software programs for project planning and control
  • 3. Estimating human resources, equipment, and machinery required for implementing each project activity
  • 4. Estimating the materials needed to implement the project
  • 5. Identifying existing and available resources and their applicability
  • 6. Estimating the cost of each activity with respect to their fixed and variable costs
  • 7. Analyzing the project costs and comparison of the results with the budget determined for project implementation by the project-generating organization [8] .

Step 3: Project scheduling, resource planning, cost-time trade-off analysis, and reviewing possible problems

  • 1. Analyzing the network time, determining the critical path, and identifying activities that are less floating (critical activities)
  • 2. Allocating available resources to project activities based on the existing resource constraints
  • 3. Analyzing the project resources and changing the initial scheduling due to existing resource constraints
  • 4. Leveling resources if necessary and changing the initial scheduling according to the leveled resources
  • 5. Analyzing cost-time trade-off and project scheduling with minimal cost using the existing and new methods presented in this field
  • 6. Reviewing inappropriate atmospheric conditions and other predictable problems affecting the implementation and timing of project activities [8] .

2.1.4. Risk management

Chapman and Ward have proposed a general project risk management process consisting of nine phases: 1) Identifying key aspects of the project; 2) Focusing on a strategic approach to risk management; 3) Identifying the time of occurrence of risks; 4) Estimating risks and the interrelationship; 5) Allocating ownership of risks and providing appropriate responses; 6) Estimating uncertainty; 7) Estimating the importance of the relationship between different risks; 8) Designing responses and monitoring the risk situation; and 9) Controlling the implementation stages [4] .

In order to achieve tangible development, developing countries are forced to increase investment in infrastructure, which, apart from meeting basic needs, has a positive impact on accelerating economic development [9] [10] . Although developing countries such as Iran faces some limitations and uncertainties when moving toward this goal, they have to engage in domestic and foreign private sectors in projects or infrastructural services in order to overcome or reduce such uncertainties. Growing development in a country like Iran requires a large amount of investment in the infrastructural sector [11] . Therefore, due to the uncertain nature of projects and the need for the optimal utilization of resources, each project faces uncertainties. The belief that projects are fraught with uncertainties, such as technical skills or management quality reinforces the fact that many projects fail in terms of their goals, benefits, costs, and the expected time. The existence of risk and uncertainty in the project reduces the accuracy in the proper estimation of the goals and reduces the efficiency of the projects. Therefore, the need for project risk identification and management is essential [12] . Considering the importance of the science of project management in recent years, various standards have proposed in this regard. These standards include the basic principles and requirements that are considered necessary for the successful management of a project or the implementation of a project management system. Some of the famous standard project management standards are presented in Table 1 .

Famous project management standards [4] .

The most famous and extensive standard among the above standards is the Project Management Body of Knowledge (PMBOK). This standard covers nine areas of knowledge for successful project management. Of these areas, project scope management, project time management, project cost management, and project quality management are considered as the main areas. One of the most important support areas is risk management [8] . Risk management is the process of identifying, analyzing, evaluating, and responding to the risks in the project [13] . The Project Management Body of Knowledge is a set of words, guidelines, and instructions for project management developed and proposed the Project Management Institute. This body of knowledge has evolved over time in the form of a book entitled “A Guide to the Project Management Body of Knowledge”. The fifth edition of this guide was released in 2013. The Project Management Body of Knowledge (PMBOK) also overlaps with the concept of management in its overall sense because both involve concepts such as planning, organizing, human resources, implementing, and controlling organizational operations. The Project Management Body of Knowledge (PMBOK) has similarity and overlap in other management disciplines, such as financial predictions, organizational behavior, management science, budgeting, and other planning approaches [2] .

The purpose of project risk management is to identify and analyze risks in a manner that the risks are understood easier and managed more effectively [14] . A systematic risk management process is usually divided into three categories:

  • 1. Risk identification and classification
  • 2. Risk analysis
  • 3. Risk mitigation [14] .

2.1.5. Project risk management

Project risk management is one of the main project issues [20] and is considered a key factor in most of the organizations involving in the project [21] . Risk management is the systematic process of identifying, analyzing, and responding to project management, which involves maximizing the probability of occurrence of positive events and their outcomes and minimizing the risk of adverse events and their outcomes [22] . He proposed a two-stage process for project risk management as follows:

  • 1. Risk assessment including risk identification, analysis, and prioritization
  • 2. Risk management including risk management planning, risk precautions, follow-up, and corrective actions

Risk assessment is the process of estimating the likelihood of the occurrence of an event (desirable or undesirable) and its impact [23] . This step can help to select less risky projects and eliminate the residual risk [22] . In the first step, using one of the risk identification tools, major threats and opportunities that can affect the project processes and outcomes are identified. After identifying the main risks, the second step involves the accurate assessment of the frequency of the occurrence and the results of each risk and then ranking the various risks based on the assessment results. In this way, identified risks can be compared with each other, and in the next phases of the risk management process, an appropriate risk response method can be decided.

2.2. Previous studies

2.2.1. domestic studies.

See Table 2 .

Summarizes the studies conducted in Iran.

2.2.2. Foreign studies

See Table 3 .

Summarizes the studies conducted abroad.

2.3. Identified factors

The risks of exploration and exploitation projects are considered as variables and units of analysis and are initially classified using the PMBOK standard based on the following model (see Fig. 1 ).

Figure 1

Risks classified based on the PMBOK standard [4] ).

Also, based on studies in the literature, the following risks were identified for oil projects in the exploration and exploitation phase (see Table 4 ). Thus, various risks were identified based on the studies in the literature.

Risks identified in oil projects in the exploration and exploitation phase.

As mentioned above, there are notable researches addressing Risk Assessment. However, to the best of our knowledge, none of them considered an Fuzzy Dematel and Fuzzy ANP techniques in the risk assessment problems in oil and gas companies. This has been a motivation of the current work. More specifically, the main contributions of this paper can be described as follows:

  • 1. Qualitative and Quantitative Project Risk Assessment Using a Hybrid PMBOK Model is developed Under Uncertainty for oil and gas company.
  • 2. 32 risk factors were identified using Literature and their number reduced to 17 risks using the expert opinions via the fuzzy Delphi technique run through three stages.
  • 3. The identified risks were structured and ranked using fuzzy DEMATEL and fuzzy ANP techniques
  • 4. The performance of the developed solution approaches are evaluated by running the mentioned techniques

The rest of this paper is structured as follows. Section 3 is devoted to the Methodology. Section 4 represents the results and comprehensive experimental analysis comprehensive experimental analysis. Finally, conclusion of this paper is provided in Section 5 .

3. Methodology

The present study is an exploratory research in terms of its objectives as it seeks to identify and evaluate the risks of exploration and exploitation projects. In addition, this study employs descriptive and analytical design as the researcher does not manipulate the variables and only describes the variables in their normal states and analyzes the collected data. This study is also a survey because it collected expert data and opinions using various questionnaires. First, this study presented a review of the literature and addressed the risks under analysis. Then, using the PMBOK standard, other risks were identified. The fuzzy Delphi method was used to confirm the related risks based on expert opinions. The results identified the relevant risks, which ones are relevant. Afterward, the fuzzy DEMATEL technique was employed to structure and investigate the network relationships among the risks. Finally, based on the fuzzy DEMATEL results, the interrelationship between risks was identified using the fuzzy ANP questionnaire. Besides, the fuzzy rank and weight of each risk were estimated using the fuzzy ANP technique (see Fig. 2 ).

Figure 2

The research procedure.

3.1. Expert panel

In order to identify and evaluate the project risks, the opinions of experts and specialists in managing oil exploration and exploitation projects in Neyr-Perse Company were used. Regarding Cochran sampling method 60 experts were asked to fill the questionnaire. In order to complete the Delphi, DEMATEL, and ANP questionnaires, 15 experienced experts who held the main and related positions in the company were surveyed. The experts were selected based on their expertise and availability.

3.2. Instruments and data collection procedure

The data were collected through library and field techniques. The secondary data were collected via the library technique and the initial data were collected using the field technique, i.e. by distributing questionnaires among the respondents in the research sample. In this study, three fuzzy Delphi, fuzzy DEMATEL and fuzzy ANP questionnaires were used. To determine the validity of the questionnaire, expert opinion was used. That is, all three questionnaires have a stereotypical structure and the indices are first extracted from the research literature and entered into the Delphi questionnaire. Then the confirmed risks are entered into the DEMTEL and paired ANP comparison questionnaire. Therefore, the professors as well as the experts in the first stage of the research confirm the risks.

3.3. Data analysis

The data collected in this study were analyzed in three stages. First confirmation of the identified risks using fuzzy Delphi analysis, second construction of the validated factors using fuzzy DEMATEL and then prioritization of the final indicators using fuzzy ANP. The following is a description of each method:

3.3.1. Fuzzy set theory

Decision-making in the area of risk analysis cannot be made in a purely definitive space. In classical multi-criteria decision making, the weight of the criteria is well known, but due to the ambiguity and uncertainty in the decision-maker statements, expressing the data definitively is inappropriate [24] . In this study, verbal expressions were used instead of definite numbers to determine the weight of the indexes and to rank the options. In this study, Table 5 proposed by [25] to determine the effectiveness of risks and their weights and Table 6 presented by [26] to form the decision matrix were used.

Correspondence of verbal expressions with triangular fuzzy numbers.

Verbal variables associated with indicators.

In this study, triangular fuzzy numbers are used to prevent ambiguity from decision making at all stages. A fuzzy triangle number denoted by à = (l, m, u). The parameters l, m, and u respectively represent the lowest possible value, the most probable value, and the highest possible value of a fuzzy event [24] . To assess the experts' views on the severity of the impact of the risks in pairwise comparisons, the five preferred linguistic variables “equal”, “low”, “high”, “very high” and “very high” were used.

It should be noted that triangular fuzzy numbers is used in Fuzzy DEMATEL and Fuzzy ANP methods and trapezoidal Fuzzy numbers is used in Fuzzy Delphi Method. The description of both method is as follows.

3.3.2. Fuzzy Delphi technique

The fuzzy Delphi technique is, in fact, a combination of the Delphi method and the analysis of the collected data using the definitions of the theory of fuzzy sets as follows:

  • 1. Selecting experts and explaining the research problem to them
  • 2. Preparing the questionnaire and sending it to experts

In Eq. (1) A i indicates the opinion of expert i and in Eq. (2) , A a v e represents the average of the expert opinions. Also, a 1 , a 2 , a 3 , and a 4 represent trapezoidal fuzzy numbers.

  • 4. In this step, the previous opinion of each expert and its difference with the average opinions of others along with the next round of questionnaires will be sent back to the experts.

If the difference at this step exceeds the threshold, step 4 should be repeated.

  • 6. However, if the difference between the two steps is smaller than the threshold, the fuzzy Delphi process is stopped.

3.3.3. Fuzzy DEMATEL technique

Given that expert opinions are required to use the DEMATEL method and include both verbal and ambiguous expressions, it is advisable to convert them to fuzzy numbers in order to integrate them. To solve this problem, Lin and Wu developed a model using the dimensional method in the fuzzy environment [28] . The procedure is described below [25]

Step 1: Obtaining the expert opinions and averaging them

Suppose p experts have expressed their opinions about the relationship between risks is using the verbal expressions in Table 5 . Therefore, there are p matrixes x ˜ 1 , x ˜ 2 , …, and x ˜ p , each representing the opinions of one expert, and the matrix components are identified with the corresponding fuzzy numbers. Eq (4) is used to estimate the average matrix of opinions

Matrix Z is called the initial fuzzy direct relation matrix.

Step 2: Calculation of the normalized direct relation matrix

Equations (5) and (6) are used to normalize the obtained matrix:

The steps for performing the fuzzy DEMATEL technique are described below:

Step 3: Calculating the total T relation fuzzy matrix

The total relation fuzzy matrix is calculated via equations (7) through (9) :

Where each component is expressed as t ˜ i j = ( I i j t , m i j t , u i j t ) and is calculated as follows:

Where I is the identity matrix, and H I , H m , and H u are each an n ⁎ n matrix whose components constitute the lower, middle, and upper numbers of the triangular fuzzy numbers of matrix H [29] .

Step 4: Calculating the sum of the rows and columns of the matrix T 4

The sum of rows and columns is obtained according to equations (11) and (12) :

Where, D ˜ and R ˜ are n ⁎ 1 and n ⁎ 1 matrixes, respectively.

Step 5: Determining the weight of indexes D ˜ + R ˜ and the relationship between the criteria D ˜ − R ˜

If, D ˜ − R ˜ > 0 the related criterion will be effective and if D ˜ − R ˜ < 0 the related criterion will be affected.

Step 6: Defuzzification of fuzzy numbers D ˜ + R ˜ and D ˜ − R ˜ calculated in the previous step

The fuzzy numbers D ˜ + R ˜ and D ˜ − R ˜ calculated in the previous step are defuzzificated using center of Gravity method Eq. (13) – (16) :

Where Z ⁎ is the defuzzificated value of A ˜ = ( a 1 , a 2 , a 3 ) .

Step 7: Calculating weight and impact factors:

The relative importance of the criteria will be estimated through the following equation [30] [31]

Step 8: Normalization of the weights of the criteria

Where, W ˜ j is the final weight of the decision-making criteria.

3.3.4. The fuzzy analysis network process (FANP)

The analysis network process (ANP) is generally the analytic hierarchy process (AHP) and a method for supporting multi-criteria decision-making for breaking down complex issues, with hierarchical relations among its components. The ANP also uses clockwise paired comparisons. The compatibility indicator is also used to indicate the convergence of the expert opinions. Each network component is denoted with symbols such as C h and h = 1 , . . . , m , with n h elements. We show these elements with e h 1 , e h 2 , and e h n h . The effect of a dataset of elements in a component in the system is represented by a priority vector derived from the paired comparisons. The purpose of grouping and sorting these data is to transform the structure into a matrix. This matrix is used to represent the effect of an element of a component on itself, or of a component with an arrow from it to another component. Sometimes, like hierarchical mode, effects are run only from the beginning of the arrow to the end of the arrow. The effects of elements on other elements of the network can be shown via the supermatrix displayed in Fig. 3 (a).

Figure 3


Each W i j in the supermatrix is called a block as shown in Fig. 3 (b). Each W i j column is an eigenvector of the effect (significance) of elements in the network component i on an element in the network component j . Some data may be zero for the lack of impact. Therefore, we do not need to use all the elements of a component in pairwise comparisons to obtain an eigenvector and only non-zero effects are sufficient. In the last step, we take the limit of the supermatrix W using the Markov process as follows, in order to obtain the ultimate priority: [32]

After completing the comparison matrix, the priority or weight of each criterion and alternative are calculated. In the analysis process, two types of weight should be calculated: relative weight and final weight.

The relative weight is obtained from the pairwise comparison matrix. The elements of each level are compared in terms of their respective element at the higher level in even pairs and their weights are calculated. These weights are called relative weights, while the final weight is the final rank of each option calculated from the combination of relative weights. Any pairwise comparison matrix may be compatible or incompatible. If this value is less than 0.1 it is accepted but in case of inconsistency, pairwise comparisons need to be repeated to obtain a consistent pairwise comparison matrix. Because a good decision model requires ambiguity, fuzzy set theory is used to solve the usual ANP, commonly known as fuzzy ANP or FANP. The following steps are taken to do so:

  • 1. Breaking down the project risk analysis into a network. The overall goal is to select the risks with the highest importance.
  • 2. A questionnaire is prepared on the basis of the mentioned network and experts are asked to complete it. The questionnaire is developed based on pairwise comparisons and a nine-point clock scale. The compatibility index and compatibility ratio are calculated for each matrix to test the consistency of the opinions of each expert. If the compatibility test is not accepted, the main values in the comparative pairwise matrix must be reviewed by the expert.

Conversion of expressive variables to fuzzy numbers.

A fuzzy positive two-way matrix can be defined as follows:

Where A ˜ k is the positive two-way matrix of the decision maker k and a ˜ i j is the related importance between the decision elements i and j :

If k represents expert p 1 to p k , each of the pairwise comparisons between the two criteria will have a k-positive fuzzy two-way triangular value. The geometric averaging method is used to integrate the multiple answers of experts. Accordingly, the integrated fuzzy positive two-way matrix is as follows:

  • 4. Using the center of Gravity method (explained in Fuzzy DEMATEL technique section), the generated triangular fuzzy numbers are converted to ordinary numbers.
  • 5. The pairwise comparison matrix is computed using non-fuzzy values and the priority vector for each pairwise comparison matrix is calculated.

Figure 4

The supermatrix used in this study.

  • 7. The limit supermatrix is calculated by raising it to the power of the weighed supermatrix until the supermatrix converges to a stable supermatrix. Risk priority weights are obtained from the limit supermatrixes by using the Fuzzy ANP Solver software.

After the necessary information and data have been collected, extracted and categorized, the model and the information will be solved and analyzed respectively. This chapter uses the fuzzy Delphi method to specify identified risks in oil exploration and exploitation phases, and a novel fuzzy DEMATEL structuring method, as well as a fuzzy ANP ranking method for analyzing the collected data and structuring and rating of these factors. Following are the identified risks from the research sources, the results of the fuzzy Delphi method, the data analysis using the fuzzy DEMATEL method and finally the results of the fuzzy ANP technique.

4.1. Identified risks

This section presents the 32 identified risks from previous literature and studies and their categorization using the PMBOK classification (see Table 8 ).

Identified risks.

By identifying these risks, given that these risks are taken from standard authorities, some of them may not be applicable in the Iranian field of operation or there may be other risks in the process of exploration and exploitation in Iran that should be addressed and only experts can comment on this. Therefore, fuzzy Delphi technique was used to gather expert opinion and reach consensus on identified risks. The reason for using fuzzy Delphi is to accept the uncertainty and ambiguity of the expert opinion as described below.

4.2. Fuzzy Delphi results

After distributing the questionnaire in two rounds and the averaging of the opinions, the results of the difference in averages and the final results of the consensus of the experts on the risks are presented in the following table.

4.2.1. Definition of linguistic variables

Qualitative variables are defined as trapezoidal fuzzy numbers: low (0,0,2,4), medium (3,4,6,7), high (6,8,10,10). Although trapezoidal fuzzy numbers have more complex computational process than triangular fuzzy numbers, they can Carry out more ambiguity in the verbal and qualitative variables in range from b to c defined for trapezoidal fuzzy numbers that the use of trapezoidal numbers for the Delphi section may reveal more ambiguity in expert opinion [33] .

4.2.2. Risk analysis

Based on the suggested options and definition of linguistic variables, the questionnaire was designed. The results of the survey responses to the questionnaire are presented in Table 9 .

First questionnaire results.

We also convert fuzzy numbers to definite numbers by using the Minkowski formula. Minkowski formula was used because with regards to the data in this paper in comparison with another defuzzification methods had better answer and was easier to use.

According to Tables ​ Tables9 9 and ​ and10, 10 , each expert's disagreement can be calculated according to Eq. (3) [27] . In fact, based on this relationship, each expert can measure his opinion with average comments and adjust his previous opinions if desired. The result of this step is given in Tables ​ Tables11 11 and ​ and12 12 .

Average opinions of experts from the first questionnaire.

Second questionnaire results.

Average opinions of experts from the second questionnaire.

Following is a review of the results of the mean differences and the final conclusions of the experts on the risks.

As it can be seen, the experts did not agree on 6 cases. They also agreed to omit 10 risks and they confirmed 16 risks. Thus, to determine the assignment of the remaining six indices, the third Delphi questionnaire was redistributed and asked to re-evaluate their opinion (see Table 13 ).

Differences in the experts' opinions in the first and second questionnaires.

As it is shown in Table 14 , it appears that the experts agreed with the remaining 6 items in the third stage. They omitted 5 risks and confirmed only 1 risk (No. 23). Thus, in total, 17 risks were confirmed by the experts and 15 were not confirmed due to climatic conditions of exploration and exploitation activities(see Table 15 ). Table 16 presents the list of the confirmed risks.

Differences in the experts' opinions in the second and third questionnaires.

The identified risks.

One expert's opinion on the pairwise comparison of indicators in terms of effectiveness.

4.3. Fuzzy DEMATEL results

At first, the DEMATEL questionnaire was distributed among the experts and they were asked to compare the extent to which the indexes under analysis are effective or being affected by each other using verbal descriptions. In the next step, the questionnaires were collected and the verbal descriptions were converted to the corresponding fuzzy numbers (see Table 17 ).

Corresponding fuzzy numbers for pairwise comparisons.

In the next step, the matrix of the expert opinions was formed in the form of fuzzy numbers for each expert, and the opinions were accumulated using the mean arithmetic method. The matrix of accumulated expert opinions is obtained as a fuzzy set [34]

This matrix is called the initial direct-relation fuzzy matrix, in which Z ˜ i j = ( l i j ′ , m i j ′ , u i j ) is a triangular fuzzy number and Z ˜ i i ( i = 1 , 2 , … , n ) is considered a triangular fuzzy number ( 0 , 0.0 ) .

Then, by normalizing the initial direct-relation fuzzy matrix, the normalized direct-relation fuzzy matrix X ˜ is obtained as follows:

Where r is defined as follows:

Table 18 shows the normalized accumulated expert opinion matrix.

The normalized accumulated expert opinion matrix.

In the next stage, high, middle, and lower fuzzy triangular numbers were separated from each other and entered into the DEMATEL Solver software as three separate matrices. Then the results were combined. That is, R and J values for all three parts were combined and the three matrices formed a single fuzzy matrix. Then the R+J and R-J were calculated using fuzzy equations (see Table 19 ).

The result of the DEMTEL technique for the bottom section of triangular fuzzy.

The results showed that the risk of political and economic sanctions, lack of attraction of foreign investors in project implementation, sanctioning of specialized consultations by foreign companies, and lack of necessary infrastructure in the region for the implementation of industrial projects in the first priority up to Fourth is in the analysis of bottom numbers of triangular fuzzy (see Table 20 ).

The result of the DEMTEL technique for the middle section of triangular fuzzy.

The results showed that the risk of political and economic sanctions, lack of attraction of foreign investors in project implementation, sanctioning of specialized consultations by foreign companies, and lack of necessary infrastructure in the region for the implementation of industrial projects in the first priority up to Fourth is in the analysis of middle numbers of triangular fuzzy (see Table 21 ).

The result of the DEMTEL technique for the above section of triangular fuzzy.

The results showed that the risk of political and economic sanctions, lack of attraction of foreign investors in project implementation, sanctioning of specialized consultations by foreign companies, and lack of necessary infrastructure in the region for the implementation of industrial projects in the first priority up to Fourth is in the analysis of above numbers of triangular fuzzy.

In order to determine the final ranks and design the impact model Table 22 is deffuzzified as follows [35] , [36]

Fuzzy R+J and R-J relations.

As is clear from the calculations, R 17 has the greatest impact. This means that it also affects a large number of risks and has the greatest impact. Fig. 5 shows the impact of the final risks in the exploration and exploitation phase (see Table 23 ).

Figure 5

The impact of final risks in the exploration and exploitation phase.

Final defuzzificated results.

As it can be seen in the figure above, each factor at the highest point of the model (RJ) can affect the highest number of factors, and each factor on the right side of the model (R + J) can have the greatest impact on other factors. The results also indicated that the political and economic sanction is at the top of the model. Therefore, it affects the greatest number of factors. The non-attraction of foreign investors in the implementation of the projects and Banning professional consultation by foreign companies occupy the other positions in terms of their effects on other factors. In addition, political and economic sanction is located at the rightmost point the model, occupying the first place in terms of intensity. Also, the non-attraction of foreign investors in the implementation of the projects and the failure of contractors and consultants to consider minus requirements in tenders and their failure to consider the project final cost and estimate profit and loss occupy the next positions.

4.4. Fuzzy ANP results

To better understand the effect of the indexes, the threshold value must be specified so that the low-effect relationships are filtered out and removed from the model. In other words, only the effects are displayed that their value in the matrix T exceeds the threshold. According to the experts, the threshold covers the effects that are below the lower limit. To determine the threshold, the fuzzy matrix was defuzzificated and a DEMATEL analysis was performed for it. Then the defuzzificated threshold was estimated to be 0.05. In other words, the relations whose impact was higher than 0.05 were determined in the total impact matrix as shown in Table 24 . [35] , [36] :

The effects higher than the threshold in the total impact matrix.

As it can be seen, only the factors whose interrelationship exceeds 0.05 are entered into the ANP questionnaire, and other relationships are considered to be zero due to their low importance. The initial relation matrix based on the above results is presented in Table 25 .

The impact matrix (0, 1).

Table 26 displays the normalized matrix.

The normalized matrix.

Accordingly, the normalized weights of the risk impact matrix were determined. Then, in order to determine the weight of each risk, the risks were initially classified based on PMBOK standard into seven categories including time and cost, human resources, quality, contract, score, communication, and others, and the final risks of each index were determined in Fig. 6

Figure 6

Risk-relation matrix based on DEMATEL results in fuzzy ANP software.

Once the model has been identified, the main categories should be compared and weighted first. Each group of risks is then compared and weighted. Categories with single risks are weighted 1. The three categories of quality, range and other risks have only one risk. In addition, two categories of human resources and contract have two risks, the weight of which was determined by experts in the questionnaire. In order to achieve the purpose of the research, paired comparisons questionnaires were designed and distributed among experts. According to the fuzzy approach in this study, the verbal expressions and fuzzy numbers in Table 27 were used.

Fuzzy spectrum and corresponding verbal expressions.

In this section, according to Fig. 7 , pairwise comparisons are made and using the modified method of [37] , [38] [39] , [35] the component weights were obtained and prioritized accordingly. In this software Gogus and Butcher method was used to calculate compatibility. The following tables show the geometric mean of expert opinions. In the last column of these tables, the special vector is shown. The following example tables for explaining how to calculate the eigen vector and the geometric mean.

Figure 7

The final weight matrix for criteria in terms of oil exploration and exploitation risks.

The following figures and tables (see Fig. 8 and Tables ​ Tables28, 28 , ​ ,29, 29 , ​ ,30, 30 , ​ ,31, 31 , ​ ,32, 32 , ​ ,33, 33 , ​ ,34 34 and ​ and35) 35 ) show the final weights for each risk category:

Figure 8

The final weight matrix for sub-criteria in terms of oil exploration and exploitation risks.

Mean paired comparisons to the risk of oil exploration and exploitation.

Mean paired comparisons to Time and Cost.

Mean paired comparisons to R l .

The result of mean paired comparisons to each risk and consistency/inconsistency of expert's opinions.

As it can be seen, cost and time have the highest weight followed by quality risks and other major risks.

As it is shown, economic and political sanctions have the highest weight followed by the attraction of foreign investors and the lack of the regional infrastructure which occupied the second and third positions.

5. Conclusions

Neyr Perse Company is one of the most important companies in the field of exploration and exploitation of oil projects whose operations are always exposed to risks. Considering the importance and necessity of risk management in the company's projects, this study proposed a hybrid model of risks presented in the Project Management Body of Knowledge (PMBOK) in order to structure and rank these risks using the expert opinions. The results showed the weight factor (importance) of the risks under analysis. Accordingly, economic and political sanctions were found to have the highest weight followed by the attraction of foreign investors and the lack of the regional infrastructure which occupied the second and third positions. Based on the results and the qualitative and quantitative approach taken in this study, a couple of suggestions are provided to the officials of Neyr Perse Company:

  • 1. Managers of the company are recommended to plan and counteract the risks by continuously recognizing and assessing the company's risks. Without the use of scientific methods, the decisions made by the manager may deviate a lot from reality and compensating for themistakes made in the decision may be costly.
  • 2. Managers of the company can take decisions based on a combination of approaches derived from theories and previous studies, documentation, and global and national standards, risk management instructions such as PMBOK, as well as the opinions of the experts and managers of the company that are the result of their expertise and experience, and thus contribute to promoting the position of the company and the achievement of its goals.
  • 3. The structuring of identified risks helps managers analyze the extent to which the risks can affect and be affected and recognize that the degree to which the improvement in each of the risks can be effective in improving other risks. In this way, managers can identify the domino effect of risks and focus their attention on those risks whose improvement can change the entire model.
  • 4. There is no possibility of changing some of the risks for managers, and some of the risks have features that managers should pay attention to when making decisions. The use of multi-criteria decision-making techniques helps them to prioritize risks.
  • 5. Given the uncertainty in the risk management environment and the importance of using fuzzy logic to control ambiguity and complexity in this environment, a combination of techniques used with the fuzzy approach can help the company's manager to reduce the ambiguity and complexity inherent in decision making and get better and more realistic results by using verbal descriptions.
  • 6. Mixed approaches allow managers and decision makers to have a set of tools that can both take into account the collective opinions of experts and construct a structuring and ranking model using structuring and multi-criteria decision-making approaches in order to improve their decisions.


Author contribution statement.

B. Barghi: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

S. Shadrokh: Conceived and designed the experiments; Performed the experiments; Contributed reagents, materials, analysis tools or data.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Competing interest statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.

Project Risk, Uncertainty and Decision Analysis - An Introduction

Disciplines: Management | Projects, Facilities, and Construction

Course Description

This course provides an introduction to the application of systematic risk analysis to identify, quantify, and manage the risks and uncertainties involved with modern petroleum field development.

  • Understanding probability and statistics as the language of uncertainty. This includes different types of distributions and when to use what, the central limit theorem, dependencies, and their impact
  • Decision analysis with a focus on the value of information
  • The application of Bayes’ theorem.
  • Geologic, non-geologic, and commercial chance of success plus multi-zone analysis
  • Exercises focused on developing better estimating skills with an emphasis on estimating in ranges, rather than single values

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1 or 2 days

You’ll learn tools and techniques for identifying which variables have the greatest impact on overall project value.

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Petroleum engineers, geologists, geophysicists, managers and others involved in the design or implementation of risk analysis systems.

0.8 CEUs (Continuing Education Units) are awarded for this 1-day course.

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James (Jim) Gouveia,  BaSc, Chemical Engineering, University of Toronto Mr. Gouveia is a registered Professional Engineer with a diverse technical, business and operations background in the petroleum industry. He joined Rose & Associates in March, 2002 after 21 years with Amoco and BP Energy.  Mr. Gouveia has worked in a variety of technical and managerial assignments in exploration, production and reservoir engineering, strategic planning, and risk management.  Prior to BP's acquisition of Amoco in 1999, Mr. Gouveia was a Director of Risk Management for the Amoco Energy Group of North America.  In this role he was accountable for assurance of consistent project evaluation of major capital projects.  In his last roles Mr. Gouveia led BP's strategic initiative into unconventional gas resources in Western Canada. With BP, he was a member of several task forces including a world-wide task force focused on growth initiatives in mature basins and developing a portfolio management process for BP's North American unconventional gas assets. Mr. Gouveia is a key author in the development of Rose & Associates course on the assessment of Unconventional resource plays.  He has consulted with firms in North America, South America, the Middle East, S.E. Asia and Australia on the resource, reserve and economic evaluation of their Unconventional assets.  Mr. Gouveia has co-authored and presented papers, most recently as a contributing author to the SPEE’s 2011 Monograph 3, “Guidelines for the practical evaluation of undeveloped reserves in Resource plays”, and SPE 185077, 175527, 175888 & 121525.  Mr. Gouveia is a member of APEGA, SPE, SPEE and AAPG.  Mr. Gouveia is a partner in Rose & Associates.

project evaluation under risk and uncertainty

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MBA Notes

Project Evaluation Under Risk and Uncertainty

Table of Contents

In the realm of business and finance, decision-makers often face a complex landscape characterized by risk and uncertainty. Project evaluation under these conditions requires specialized tools and methodologies to assess potential outcomes. In this blog, we will explore the concept of project evaluation under risk and uncertainty, the challenges it presents, and the strategies used to make informed decisions in uncertain environments.

Certainty, Risk, and Uncertainty

Before diving into project evaluation, it’s essential to understand the distinctions between certainty, risk, and uncertainty:

  • Certainty : In situations of certainty, outcomes are known with absolute confidence. There is no ambiguity or doubt about future events.
  • Risk : Risk involves situations where multiple potential outcomes exist, each with a known probability. While the exact outcome is uncertain, probabilities can be assigned to various scenarios.
  • Uncertainty : Uncertainty, on the other hand, arises when future outcomes are not only unknown but also inherently unpredictable. It involves scenarios where the range of possible outcomes is vast, and probabilities cannot be reliably assigned.

Challenges of Project Evaluation Under Risk and Uncertainty

Project evaluation under risk and uncertainty poses several challenges:

  • Lack of Data : Uncertain situations often lack historical data or precedents to inform decision-making.
  • Complexity : Uncertainty can lead to complex, interrelated factors that are challenging to model and analyze.
  • Subjectivity : Assigning probabilities to uncertain outcomes can be subjective and influenced by personal biases.
  • Dynamic Environment : Market conditions and external factors can change rapidly, further complicating decision-making.

Approaches to Project Evaluation Under Risk and Uncertainty

Several approaches and techniques are used to evaluate projects in uncertain environments:

1. Sensitivity Analysis

Sensitivity analysis involves testing how variations in key variables affect the project’s outcomes. It helps identify which factors have the most significant impact on project viability.

2. Scenario Analysis

Scenario analysis constructs multiple plausible scenarios representing different future states. Each scenario considers a unique combination of variables and their potential outcomes. This approach provides a range of possible project outcomes.

3. Monte Carlo Simulation

Monte Carlo simulation is a sophisticated method that uses random sampling to model uncertainty. It generates thousands of simulations, each with different input values, and calculates the probability distribution of project outcomes.

4. Decision Trees

Decision trees visualize decision-making processes under uncertainty. They incorporate decision nodes, chance nodes, and branches representing different options and their probabilities. Decision tree analysis aids in identifying optimal choices.

5. Real Options Analysis

Real options analysis extends financial options concepts to evaluate project investments. It allows decision-makers to consider the flexibility to adapt and change course as new information becomes available.

6. Expected Value Analysis

Expected value analysis calculates the weighted average of all possible outcomes, considering their associated probabilities. It provides a single value that represents the project’s expected return.

Importance of Expert Judgment

In situations of high uncertainty, expert judgment plays a critical role. Experts with domain-specific knowledge can provide insights into potential risks and opportunities that may not be evident in data or models.

Project evaluation under risk and uncertainty is a complex but necessary task in the world of business and finance. While it presents challenges related to data, complexity, and subjectivity, various approaches and techniques empower decision-makers to navigate uncertainty effectively. By employing sensitivity analysis, scenario analysis, Monte Carlo simulation, decision trees, real options analysis, and expected value analysis, and complementing these methods with expert judgment, organizations can make informed decisions that maximize value and mitigate risks in uncertain environments.

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Capital Investment and Financing Decisions

1 Nature of Long Term Financial Decisions

  • Nature of Financial Decisions
  • Wealth Maximisation Objective
  • Cardinal principles of Financial Decision
  • Time value of Money
  • Determination of Implied interest Rates, Implied Principal Amount and Annuities
  • Basic Factors Influencing Long term financial Decisions

2 Cost of Capital

  • Concept of Cost of Capital
  • Computing Cost of Capital of Individual Components
  • Weighted Cost of Capital
  • Significance of Cost of Capital
  • Misconceptions about the Cost of Capital

3 Capital Structure Decisions

  • Conceptual Framework
  • Characteristics of Important long term sources of Funds
  • Criteria for determining pattern of Capital Structure
  • Risk and Capital Structure
  • Theories of Capital Structure Decision
  • Factors Influencing Pattern of Capital Structure
  • Relevance of Debt-equity ratio in Public enterprises

4 Project Planning and Formulation

  • Nature of a Project
  • Classification of Projects
  • The Project Life Cycle
  • Project Management Defined
  • Planning Project Work

5 Investment Appraisal-Evaluation Criteria

  • Nature of Capital Budgeting
  • Utility of Capital Budgeting
  • Investment Proposals and Administrative Aspects
  • Choosing among Alternative Proposals
  • Estimating cash flows from Capital Budgeting
  • Evaluating Investment Proposals
  • Capital Budgeting Methods in Practice

6 Project Implementation and Control

  • Designing of the Monitoring System
  • How to Collect Data
  • Information needs and the Reporting Process
  • Report Types
  • Project Control
  • Types of Control Processes
  • Design of Control System
  • Control of creative Activities
  • Progress Review
  • Personnel Reassignment
  • Control of Input Resources

7 Social Cost Benefit Analysis (SCBA)

  • Concept of Market Efficiency
  • Market Failures
  • Types of SCBA
  • Basic Steps of SCBA
  • Conceptual Foundation of SCBA
  • Valuation Methods

8 Investment Decisions-Risk and Uncertainity

  • Capital Asset Pricing Model
  • Measuring Betas and Capital Asset
  • Stability of Betas over Time
  • Business and Financial Risk
  • What determines Asset Betas
  • Discounted Cash Flow Approach

9 Project Evaluation Under Risk and Uncertainty

  • Concept of Certainty, Risk and Uncertainty
  • Measurement of Project Risk:
  • Game Theory
  • Expected Utility Approach
  • The Expected Utility Model

10 Financing through Domestic Capital Markets

  • Introduction to Domestic Markets
  • Methods of Procuring Financ

11 Financing through Global Capital Markets

  • Deregulation in Financial Markets
  • Developments in the Banking Sector
  • Developments in the Foreign Exchange Markets
  • Special Financial Institutions
  • Global Sources of Financing
  • Raising of Foreign Capital In India
  • External Commercial Borrowings
  • Foreign Direct Investment and Portfolio Investment

12 Other Modes of Financing

  • Non-Traditional Sources of Long-term Financing
  • Non Traditional Services of Short-term Financing

13 Capital Restructuring

  • Corporate Restructuring
  • Financial Restructuring
  • Assessing Merger as a Source of a Value Addition
  • Formulating Merger and Acquisition Strategy
  • Regulation of Mergers and Takeovers in India
  • Takeover Strategies – Indian Experience
  • Divestitures
  • Characteristics of and Pre-requisites to Leveraged Buyout Success
  • Leveraged Recapitalization
  • Reorganization of Capital
  • Financial Reconstruction

14 Financial Engineering

  • Factors Contributing to Financial Engineering
  • Financial Engineering Process
  • Financial Engineering in Fixed Income Securities
  • Financial Engineering in Equity Products
  • Financial Engineering in Derivatives

15 Investors Relations

  • Corporate form of Business Organization
  • Demand for Information
  • Transparency and Disclosure
  • Corporate Governance
  • Investor Service

Project Net Present Value estimation under uncertainty

  • Original Paper
  • Open access
  • Published: 02 November 2017
  • Volume 27 , pages 179–197, ( 2019 )

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  • Helena Gaspars-Wieloch   ORCID: 1  

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The paper contains a description of a possible modification of the original Net Present Value which allows one to evaluate projects under uncertainty with unknown probabilities (understood mainly as frequencies). Cash flows are usually uncertain since both incomes and expenditure related to the project concern the future. Additionally, probabilities of particular scenarios may be unknown due to many factors (e.g. the diversity of definitions for probability, lack of historical data, lack of sufficient knowledge about possible states of nature). The novel approach is based on a hybrid of Hurwicz and Bayes decision rules and is supported by a sensitivity analysis. The new method applies scenario planning and takes into account the decision maker’s attitude towards a given decision problem (measured by coefficients of pessimism and optimism). The procedure can be used even in the case of asymmetric distributions of net cash flows at particular periods since it considers the frequency of each value. The modification of the Net Present Value may support any uncertain multi-period economic decision.

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1 Introduction

Projects may be evaluated and compared according to many statistic and dynamic methods of investment profitability assessment. One of them is the Net Present Value (NPV), which was formalized and popularized by Fisher ( 1907 ). This measure is computed on the basis of all foreseen and discounted revenues and costs over the lifetime of the project. The traditional version of NPV treats future cash flows as certain (deterministic) values. Nevertheless, many contributions devoted to the NPV estimation are based on the assumption that those data are uncertain, which is totally justifiable since both incomes and expenditure related to the project concern the future (except for the cash flow at moment 0). There are several different methods designed for taking uncertainty in such calculations into account, for instance: (1) to increase the discount rate, (2) to apply sensitivity analysis, (3) to compare pessimistic and optimistic cash flows or, (4) to estimate the expected cash flows by means of scenario planning and the probability distribution.

Note that the last procedure may be applied on condition that the decision maker knows or is able to estimate the likelihood of particular scenarios (states of nature, events). Meanwhile, it is sometimes quite complicated to compute probabilities due to the existence of many discrepant definitions of probability (Carnap 1950 ; Frechet 1938 ; Hau et al. 2009 ; Knight 1921 ; Kolmogorov 1933 ; Piegat 2010 ; Popper 1959 ; van Lambalgen 1996 ; von Mises 1949 , 1957 ), the lack of historical data in the case of totally new decisions and events (Guo 2011 ; Guo and Ma 2014 ; Gaspars-Wieloch 2015c , d , 2016a , b , 2017a , b ), the lack of sufficient knowledge about particular states or the fact that the set of possible scenarios forecasted by experts in the scenario planning stage does not satisfy the probability axioms—the sum of state probabilities should be equal to 1, the whole sample space must be precisely defined (see, Kolmogorov 1933 ). Furthermore, Finetti ( 1975 ) argues that objective probabilities do not exist: “No matter how much information you have, there is no scientific method to assign a probability to an event”, there are only subjective probabilities—different for particular decision makers. However, according to Caplan ( 2001 ), people may be even unable to declare subjective probabilities—they just implicitly set probabilities when acting. Additionally, according to von Mises ( 1949 ), the theory of probability can never lead to a definite statement concerning a single event—the probability of a single event cannot be presented numerically. Roszkowska and Wachowicz ( 2015 ) also point out that people prefer ordinal measures to cardinal ones.

Despite the fact that the probability, in some circumstances, may be difficult to estimate, supporters of the theory of economics stress that some probability-like quantities can be often estimated and applied. Hence, in many cases, except for the aleatory uncertainty which is not reducible due to its random nature (Tannert et al. 2007 ; Zio and Pedroni 2013 ), uncertainty may be measured and quantified somehow (Piasecki 2016 ). Therefore, we would like to propose a new approach which can be used for project Net Present Value estimation under uncertainty with unknown objective probabilities. The procedure described in the paper will allow the decision maker (DM) to use scenario planning and to take into account his or her risk aversion measured by coefficients of optimism and pessimism. We assume that the novel procedure is designed for the selection of projects performed only once (see one-shot decisions, Gaspars-Wieloch 2015a , 2016a , b , 2017a , b , c ; Kofler and Zweifel 1993 ), since the choice of a project from the same set of potential projects in the future requires re-scenario planning and a new declaration of the level of optimism.

The paper is organized as follows. Section  2 deals with the main features of the traditionally understood NPV method. Section  3 concerns the NPV technique with uncertain parameters. Section  4 describes the problem in the context of uncertainty with unknown frequencies. Section  5 presents a decision rule that may be used as a tool in evaluating NPV under uncertainty. Section  6 provides a case study. Conclusions are gathered in the last part.

2 Net Present Value

The Net Present Value or Net Present Worth (Lin and Nagalingam 2000 ; Berk et al. 2015 ) is defined as the sum of the present values of incoming (benefits) and outgoing (costs) cash flows over a period of time. NPV can be described as the difference between the sums of discounted cash inflows and cash outflows. According to the investment profitability assessment method based on NPV, a cash flow today is more valuable than an identical cash flow in the future because a present flow can be invested immediately and begin earning returns, while a future flow cannot (Berk et al. 2015 ).

NPV is a useful tool to determine whether a project will result in a net profit (NPV is positive, hence the investment would add value to the firm and the project may be accepted) or a loss (NPV is negative, hence the investment would subtract value from the firm and the project should be rejected). In the financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected ( ). NPV plays a central role in discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects ( ). It is widely applied throughout economics, finance and accounting (Balen et al. 1988 ; Naim et al. 2007 ). The NPV of a sequence of cash flows takes the cash flows and a discount rate as input, and outputs a price. Footnote 1 NPV may be calculated by means of one of the following time-discrete equations:

where n —number of periods; \(NCF_{t}\) —net cash flow at moment t ; r —discount rate (the rate of return that could be earned from an investment in the financial markets with similar risk); \(CI_{t}\) —cash inflow at moment t ; \(CO_{t}\) —cash outflow at moment t .

Equation ( 1 ) allows one to compute the sum of the discounted net cash flows. Equation ( 2 ) enables one to set the difference between the present value of benefits and the present value of costs. Formula ( 3 ) is a simplified version of Eq. ( 2 ) and it may be applied to situations with only one expense at the beginning of the project. The construction of NPV is based on a simplifying assumption that the net cash received or paid occurs in a single transaction on the last day of each period ( ).

NPV can also be written in a continuous variation (Buser 1986 ; Grubbström 1967 ), but in this paper we investigate only the discrete case. The original version of NPV applies a constant discount rate, which is suitable for short-term projects. The use of a variable discount rate is desirable when appreciating long-term investments (Fabozzi and Fong 1994 ; Piasecki and Ronka-Chmielowiec 2011 ). Here, we focus on constant discount rates. Due to the fact that the decision maker can reinvest particular cash flows, the true NPV may be higher. Therefore, the Modified Net Present Value has been proposed (Chandra 2009 ; Filho et al. 2012 ; McClure and Girma 2004 ). In this contribution we concentrate on NPV, but the reinvestment factor can be easily introduced.

3 Net Present Value under uncertainty

Owing to the fact that, in most of cases, cash flows cannot be estimated in a very precise way since they are related to future periods, the exploration of NPV computations under uncertainty is justifiable. Due to the necessity to solve decision problems with uncertain parameters, a variety of theories have been developed, e.g. the probability theory (Kolmogorov 1933 ), the imprecise (interval) probability (Walley 1991 ), the evidence theory (Shafer 1976 ; Sentz and Ferson 2002 ), the possibility theory (Zadeh 1978 ; Dubois and Prade 2001 ) and the uncertainty theory (Liu 2007 , 2009 ). It is worth emphasizing that there is no unanimity in defining the notion of uncertainty (Gaspars-Wieloch 2017a ). According to the theory of decision the DM may choose the appropriate alternative (decision, strategy, variant):

under certainty (DMC) where parameters are deterministic,

under risk (DMR) where possible scenarios and their likelihood are known,

with partial information (DMPI) where possible states of nature are known, but their probability is known incompletely: the DM only knows the order of scenarios or the intervals with possible probabilities for each scenario,

under complete uncertainty (DMCU) where the scenarios are known, but the probability of their occurrence is not, or

under total ignorance (DMTI) where the DM is not able to define possible events.

Note that DMCU may also occur when the DM does not want to make use of the estimated probability distribution (Trzaskalik 2008 ). Comments concerning particular decision making circumstances can be found, for instance, in Chronopoulos et al. ( 2011 ), Groenewald and Pretorius ( 2011 ), Guo ( 2011 ), Kaplan and Barish ( 1967 ), Knight ( 1921 ), Perez et al. ( 2015 ), Render et al. ( 2006 ), Sikora ( 2008 ), Waters ( 2011 ) and Weber ( 1997 ). Uncertainty and risk were formally integrated in the economic theory by von Neumann and Morgenstern ( 1994 ). Supporters of the theory of economics state that uncertainty involves all the situations with non-deterministic parameters (known, unknown or incompletely known probability distribution, lack of information about possible scenarios), while risk is related to the possibility that some bad or other than predicted circumstances will happen (Aven 2016 ; Dominiak 2009 ; Dubois and Prade 2012 ; Fishburn 1984 ; Gaspars-Wieloch 2016b ; Guney and Newell 2015 ; Ogryczak and Sliwinski 2009 ; Waters 2011 ). Nevertheless, as it was mentioned in the introduction, within the theory of economics, even if the probability is not known, some probability-like quantities can be often estimated and applied. Apart from the two approaches described above, The Austrian Economic School is worth mentioning. It treats uncertainty as decision theorists do, i.e. as a situation where the likelihood is not known. Additionally, it is assumed that the mathematical probability of the occurrence of a given scenario is not known since probabilities concern only repetitive events, meanwhile in the majority of real problems the DM deals with non-repetitive events. According to von Mises ( 1949 ), the theory of probability can never lead to a definite statement concerning a single event—the probability of a single event cannot be presented numerically. The Austrian Economists state that uncertainty is not caused by the randomness of events, as main-stream economists think, but by many factors and only some of them are known in the DM process (Gaspars-Wieloch 2017a ). Note that scientists distinguish two main types of uncertainty: the epistemic/epistemological (reducible) uncertainty—due to the lack of knowledge (it can be reduced or eliminated after collecting information), and the aleatory/aleatoric (random) uncertainty—due to the inherent variability in a physical phenomenon (it cannot be reduced even after conducting n experiments) (Zio and Pedroni 2013 ).

In this paper we consider both the epistemic and aleatory uncertainty, which leads us to a conclusion that the likelihood of the occurrence of particular states of nature cannot be estimated in an accurate way. Additionally, owing to the fact that the contribution concerns one-shot decisions only (the selected project is performed only once, i.e. only one state of nature has the chance to occur within a given period), we refer in a sense to the Austrian approach where the probability understood as frequency cannot be computed for a single event. The theory of economics is also partially applied in this research since unknown probabilities are going to be replaced by some probability-like quantities.

Uncertainty in NPV has been already taken into account in many ways. For instance, one can increase the discount rate (Method I). Nevertheless, some researchers state that it is not a reasonable approximation since the increased discount rate reduces the impact of potential losses below their true financial cost. Actually, the increased discount rate reduces the impact of potential losses, but the use of a higher discount rate signifies that the DM intends to earn more and that he/she is more willing to risk (lose) his/her money—usually more profitable investments are riskier. On the other hand, if the DM applies a lower discount rate, that means that he/she intends to earn less and that he/she does not accept the possibility of the occurrence of significant losses—usually less profitable investments are less risky. Thus, in our opinion, the level of the discount rate reflects the DM’s nature (risk-prone behavior, risk-averse behavior), not the degree of uncertainty.

Another way consists in compounding the risk premium with the risk free rate (Method II). However, as a result, future cash flows are discounted by both rates, which entails an extremely low NPV.

The sensitivity analysis may be also applied to NPV (Method III), which enables one to check how NPV varies depending on the level of particular cash flows. Furthermore, it gives the possibility to set the interval for a cash flow at a given moment, within which NPV remains positive or higher than the NPV of another project.

When the DM knows possible scenarios at particular moments, it is recommended to refer to scenario planning (Pomerol 2001 ; Van der Heijden 1996 ). One can, for example, compare pessimistic and optimistic cash flows (Method IV), and, if the likelihood of each state of nature is estimated, the expected NPV may be calculated. The latter method (r-NPV: risk-adjusted Net Present Value) consists of the following steps: (1) computing the expected net cash flow \(E({ NCF}_{t})\) and standard deviations \(({ SD}_{t})\) at particular moments, (2) calculating the expected NPV, i.e. \(E({ NPV})\) , and the mean standard deviation ( MSD ) for the project, (3) computing the coefficient of variation CV (the quotient of MSD and E ( NPV ))—the lower CV is, the less risky the project is (Method V).

When probabilities are not known, but the mean net cash flows \((MNCF_{t})\) , standard deviations \((SD_{t})\) and correlations between sequences of cash flows from different periods ( \(\rho _{t,s}\) ) are given, \(MNCF_{t}\) values are treated as \(E(NCF_{t})\) and the whole standard deviation is computed on the basis of the partial standard deviations and the aforementioned correlations (Method VI).

The NPV estimation under uncertainty may be also supported by fuzzy numbers and interval arithmetic (Chiu and Park 1994 ; Gutiérrez 1989 ; Filho et al. 2012 ) (Method VII).

The above list of procedures designed for NPV calculation under uncertainty is not exhaustive, but allows one to be aware of the impressive variety of the existing approaches. In Sect.  4 we will concentrate on NPV in the context of scenario planning, risk aversion and uncertainty with unknown frequencies.

4 Scenario planning, risk aversion and NPV under uncertainty

Now, let us analyze the case of NPV estimation when the DM knows possible scenarios at particular moments and net cash flows connected with them, but the likelihood, mainly understood as frequency, is not known. Additionally, we assume that the DM is not able to define particular subjective probabilities exactly since his knowledge about future scenarios is not sufficient—the assessed projects are new. The result of the choice made under uncertainty depends on two factors: which decision (project, investment) is selected (internal factor) and which scenarios will occur in the future (external factor).

The NPV estimation under uncertainty with unknown probabilities may be presented with the aid of a cash flow matrix (Table  1 ) where n is the number of projects ( \(I_{1}, I_{2},{\ldots },I_{j},{\ldots },I_{n})\) , T denotes the number of future periods \((1,2,{\ldots },t,{\ldots },T)\) and m ( t ,  j ) signifies the number of mutually exclusive scenarios (let us denote them by \(S^{1}_{(t,j)}, S^{2}_{(t,j)}, {\ldots }, S^{k(t,j)}_{(t,j)}, {\ldots }, S^{m(t,j)}_{(t,j)})\) connected with period t and investment \(I_{j}\) . Symbol \(NCF^{k(t,j)}_{t,j}\) stands for the net cash flow related to period t , investment \(I_{j}\) and scenario \(S^{k(t,j)}_{(t,j)}\) . Note that the number of states of nature for particular periods and investments may vary—the sets of states of nature are independent! Of course, if there is no cash flow at a given moment t in the case of one of the considered projects, parameters \(NCF^{k(t,j)}_{t,j}\) for that investment are equal to zero. The cash flow matrix may be generated by the decision maker (the first case) or by experts (the second case). In the second case, parameters are more objective, which is an advantage. In Table  1 , scenario planning is applied only to future periods: \(1,{\ldots },t,{\ldots },T\) since one can assume that the first cash flow ( \(t=0\) ) constitutes a deterministic parameter.

Given such data, one could calculate the expected NPV on the basis of Method VI (see Sect.  3 ). Nevertheless, this time, we assume that the number of scenarios for a given period may be different for particular investments. Additionally, we will attempt to take into account the DM’s nature measured by the coefficients of pessimism ( \(\alpha \) ) and optimism ( \(\beta \) ). These parameters belong to interval [0, 1] and satisfy the condition \(\alpha +\beta =1\) . \(\alpha \) ( \(\beta \) ) tends to 0 (1) for extreme optimists (risk-prone behavior) and is close to 1 (0) for extreme pessimists (risk-averse behavior). Coefficients of pessimism and optimism have been already used in the decision making process, for instance in Hurwicz ( 1952 ) and Perez et al. ( 2015 ). In this contribution they will allow us to generate some probability-like quantities. Note that those quantities will not be directly estimated by the decision makers, but will be calculated on the basis of their level of optimism/pessimism. Hence, coefficients \(\alpha \) and \(\beta \) are the initial parameters and probability-like quantities constitute the secondary parameters.

There are numerous decision rules devoted to decision making under uncertainty (see, for example, Basili 2006 ; Basili et al. 2008 ; Basili and Chateauneuf 2011 ; Beauchene 2015 ; Chassein and Goerigk 2016 ; Ellsberg 2001 ; Etner et al. 2012 ; Gaspars-Wieloch 2012 , 2013 , 2014a , b , c , d , 2015a , b , c , d , e , 2016a , b , 2017a , b , c , d ; Ghirardato et al. 2004 ; Gilboa 2009 ; Gilboa and Schmeidler 1989 ; Halpern and Leung 2014 ; Hayashi 2008 ; Hurwicz 1952 ; Ioan and Ioan 2011 ; Marinacci 2002 ; Nakamura1996; Perez et al. 2015 ; Piasecki 1990 ; Savage 1961 ; Schmeidler 1986 ; Tversky and Kahneman 1992 ; Wald 1950 ), but some of them are based on the probability calculus or do notconsider the DM’s nature—thus, they cannot be applied to the aforementioned problem.

In Sect.  5 we are going to present the H+B decision rule for NPVU (Net Present Value under uncertainty). The original version of that procedure, i.e. the H+B rule (a hybrid of Hurwicz and Bayes rules), is described in Gaspars-Wieloch ( 2014a , 2015b , c , 2016b ). It is designed for decision making under uncertainty with unknown probabilities. Thanks to parameters \(\alpha \) and \(\beta \) , the H+B rule enables one to take into consideration the DM’s attitude towards a given problem The procedure is devoted to searching optimal pure (not mixed) strategy and to solving one-shot decision problems (Guo 2011 ). A pure strategy, as opposed to a mixed strategy, allows the DM to select and perform only one accessible alternative (Gaspars-Wieloch 2015e ). One-shot decision problems are connected with decisions performed only once.

Of course, one should wonder why we do not intend to apply the original Hurwicz decision rule, which also uses \(\alpha \) and \(\beta \) and usually leads to sensible results. The disadvantage of that approach is related to the following factor. In some cases the Hurwicz rule provides answers which are contradictory to the logic and do not reflect the decision maker’s preferences. Such a phenomenon stems from the fact that the Hurwicz criterion takes extreme payoffs into consideration only—transitional values connected with a given decision are ignored. Additionally, the above rule does not examine the frequency of relatively high and low payoffs belonging to the set of all profits assigned to particular alternatives (see, Gaspars-Wieloch 2012 , 2014a , c , 2016b ). In the H+B rule, in contrast to the Hurwicz approach, all outcomes have an influence (though not the same) on the value of the final measure. Hence, the H+B approach recommends logic rankings for both symmetric and asymmetric distributions of payoffs. And that is why it may be useful in the evaluation (choice) of investment projects on the basis of NPV under uncertainty. Note that the original H+B decision rule needs to be adjusted to that goal (i.e. NPV estimation) since, this time, payoffs connected with particular projects come from different periods.

5 The H+B decision rule for NPV under uncertainty (NPVU)

The suggested H+B rule for NPVU may consist of the following steps:

Define n (the number of projects) and generate the cash flow matrix for the whole set of projects, see Table  1 .

Determine \(\alpha \) and \(\beta \) for a given problem. If \({\alpha \in [0,0.5)}\) , then \({\alpha =\alpha _o ,\beta =\beta _o}\) ( \(\alpha _{o}\) and \(\beta _{o}\) are the optimist’s coefficients). If \({\alpha \in (0.5,1]}\) , then \({\alpha =\alpha _p ,\beta =\beta _p}\) ( \(\alpha _{p}\) and \(\beta _{p}\) are the pessimist’s coefficients).

Find a non-increasing sequence of net cash flows \(Sq_{t,j}^ =(a_{t,j}^1 ,...,a_{t,j}^s ,...,a_{t,j}^{m(t,j)} )\) for each project \(I_{j}\) and for each period \(t=1,{\ldots },T\) , where \(a_{t,j}^s \ge a_{t,j}^{s+1} \) ( \(s=1,{\ldots },m(t,j)-1\) ), m ( t ,  j )—number of terms in the sequence, s —number of the term in the sequence.

Calculate, for each project and each period, index \(hb_{{t,j}} (hb_{{t,j}}^p \) , \(hb_{{t,j}}^o \) or \(hb_{{t,j}}^{0.5} \) depending on parameter \(\alpha \) ). If \({\alpha \in (0.5,1]}\) , calculate \(hb_{{t,j}}^p \) (index for pessimists) according to Eq. ( 4 ). If \({\alpha \in [0,0.5)}\) , compute \(hb_{{t,j}}^o \) (index for optimists) following formula ( 5 ). If \(\alpha \) = 0.5, calculate \(hb_{{t,j}}^{05} \) using Eq. ( 6 ), where \(b_{t,j }\) denotes the Bayes criterion, i.e. the average of all net cash flows at a given period.

The denominators in Eqs. ( 4 )–( 5 ) are introduced so that the final value of particular indices belongs to interval \([a_{{t,j}}^{m(t,j)} ,a_{t,j}^1 ]\) . If, for a given project, there is no net cash flow at period t , then \(hb_{{t,j}}=0\) . In the case of period \(t= 0\) , \(hb_{0,j}=NCF_{0,j}\) .

Compute, for each project, \({\alpha NPV_{j}}\) (i.e. the Net Present Value considering the DM’s nature) on the basis of formula ( 7 ).

where r still denotes the discount rate, i.e. the rate of return that could be earned from an investment in the financial markets with similar risk.

Find project \(I^{*}_{j}\) fulfilling condition ( 8 ). If only one project satisfies Eq. ( 8 ) and its \({\alpha { NPV}_{j}}\) value is positive, select that project. Otherwise, go to step 7.

If one or more projects satisfy Eq. ( 8 ) and its (their) \({\alpha NPV_{j}}\) value is not positive, reject all projects or decrease the level of the discount rate, if it is justifiable, and go to step 5. Otherwise, go to step 8.

If more than one project satisfies Eq. ( 8 ) and their \({\alpha NPV_{j}}\) value is positive, calculate the mean standard deviation ( nMSD ) only for projects \(I^{*}_{j}\) following condition ( 9 ). Pessimists should choose the project with the lowest mean standard deviation. Moderate DMs and optimists may select a project \(I^{*}_{j }\) with more diffused cash flows (i.e. with a higher MSD ).

In the last part of Sect.  5 we would like to explain equations given in step 4 of the algorithm presented above in detail.

The assignment of such parameters ( \(\alpha \) and \(\beta \) ) to particular elements of non-increasing sequences in Eqs. ( 4 )–( 5 ), depending on the level of pessimism/optimism, is substantiated in Gaspars-Wieloch ( 2014a , 2015b , c , 2016b ) where the author concludes that, as opposed to the Hurwicz rule, the index value should depend on all payoffs, not only on the extreme ones. Hence, parameters \(\alpha \) and \(\beta \) have to be assigned to all of them, not only to the best and to the worst ones, and such a feature is typical of Bayes rule. Owing to the fact that an extreme optimist rather focuses on the highest payoff, an extreme pessimist focuses rather on the lowest payoff and a moderate DM mainly analyzes intermediate profits, the assignment of coefficients is supposed to be different, depending on the DM’s nature. Therefore, in the author’s opinion, in the case of optimists, the high coefficient of optimism should be assigned to \(a_{j,max}\) and the small coefficient of pessimism should be assigned to the remaining gains since optimists expect the occurrence of the best scenario, so it should have the biggest weight. In the case of pessimists, the high \(\alpha \) ought to be multiplied by \(a_{j,min}\) and the small \(\beta \) ought to be multiplied by the other profits. In the case of moderate DMs with parameters \(\alpha =\beta =0.5\) , it does not matter which equation ( 4 or 5 ) will be applied, since the use of both of them boils down to equal weights for each gain. The approach described above allows one to take into consideration the frequency of extreme, or nearly extreme, values. Of course, we may ask why parameters \(\alpha \) and \(\beta \) should be assigned to particular payoffs in that way. The answer is that if we assign them in an inverse way, i.e. for optimists the low \(\alpha \) to \(a_{j,min}\) and the high \(\beta \) to the other profits, and for pessimists the low \(\beta \) to \(a_{j,max}\) and the high \(\alpha \) to the remaining gains, we will assume that the pessimist expects, apart from the lowest profit, the occurrence of quite high ones (without the highest one) and that the optimist, apart from the highest profit, expects the occurrence of quite low ones (without the lowest one), which is illogical. The idea of the hybrid presented in Gaspars-Wieloch ( 2014a ) is to recommend for a strong pessimist an alternative with a relatively high payoff \(a_{j,min }\) or with quite frequent payoffs (almost) equal to \(a_{j,max}\) . On the other hand, that rule suggests for a strong optimist an alternative with the highest, or almost the highest, payoff \(a_{j,max}\) , but its highest payoffs do not have to be frequent. Thus, the H+B rule for NPVU recommends for a pessimist a project with relatively high net cash flows \(a^{m(t,j)}_{t,j}\) or with many net cash flows close to \(a^{1}_{t,j}\) . For an optimist, this procedure suggests an investment with the highest net cash flows \(a^{1}_{t,j}\) , but its highest flows do not have to be frequent (Gaspars-Wieloch 2016b ). When analyzing the levels of the aforementioned coefficients assigned to particular net cash flows, we may also question the use of merely two values instead of gradually increasing/decreasing parameters for consecutive payoffs connected with a given project and a given period. Let’s discuss the optimist’s case (the conclusions for the pessimist’s case are drawn by analogy). Why, for instance, is \({\beta _{o}}\) assigned only to \(a_{j,max}?\) An optimist might expect that higher cash flows are more likely to occur, but not necessarily think that only the single highest cash flow has much higher chance to occur compared to the rest. The explanation is as follows. If one is an extreme optimist, he or she counts only on the highest payoff and then \({\beta _{o}=1}\) (for the highest cash flow) and \({\alpha _{o}=0}\) (for other cash flows), just like in the case of the Hurwicz rule. If one becomes a moderate optimist, one is not so sure whether the highest payoff will occur. Hence, \(\beta _{o}\) decreases and \(\alpha _{o}\) increases: \(0.5<\beta _{o}<1\) (for the highest cash flow) and \(0<\alpha _{o}<0.5\) (for other cash flows). The less optimistic one is, the less likely the best payoff is and the more likely other payoffs are. Gradually increasing or decreasing parameters would be possible, but note that if so, the sequences of weights would not be the same for each investment in a given period. They would be different for particular projects since they would depend on the level of all intermediate payoffs. The idea of using diverse sequences of weights for each project would be perhaps more comprehensible. Nevertheless, there are three reasons for which the author applies two values only: \(\beta _{o}\) for the best cash flow and \(\alpha _{o}\) for the remaining ones. Firstly, the use of \(\alpha _{o }\) for intermediate payoffs provides the opportunity to take them into consideration and to include information about the frequency of extreme values in the final index (as opposed to the Hurwicz rule). Secondly, the use of increasing/decreasing parameters would not be appropriate for extreme decision makers with the coefficient of optimism equal to 1 since payoffs approximating the highest one would have too great importance: if the DM is an extreme optimist, only the best cash flow is vital for him—others are unimportant. Thirdly, the use of various parameters would entail additional, redundant computations as the change of weights for intermediate cash flows does not affect the rankings significantly.

It is worth emphasizing that in the procedure proposed in Gaspars-Wieloch ( 2014a ) the index value depends on the number of states of nature, which is not the case of Hurwicz rule. For pessimists, when the number of scenarios increases, the importance of payoff \(a_{j,min }\) in the index decreases and the significance of the remaining profits increases. On the other hand, for optimists, the importance of payoff \(a_{j,max }\) decreases and the significance of the remaining profits increases. Hence, again, we can observe the impact of Bayes rule in the analyzed hybrid, because the chance of the occurrence of a given event decreases along with the growth in the number of states of nature (Gaspars-Wieloch 2016b ).

Note that the sensitivity analysis may effectively support the H+B rule for NPVU. If possible, it is recommended to generate project rankings for different values of the discount rate and the coefficient of optimism. Given such a specification, the decision maker can make his or her final decision more consciously (see Method III in Sect.  3 ).

As it can be noticed, the H+B rule for NPVU contains an additional step (in comparison to the original H+B), i.e. the computation of the mean standard deviation. That element is characteristic of Method V (Sect.  3 ), but this time, we apply that measure only to the multiple solutions case.

In the described algorithm (H+B for NPVU) coefficients of pessimism/optimism are supposed to be constant, i.e. the same for each period. However, the DM may state that each period could be influenced by different factors, negative and positive, and that the level of those parameters should vary. The procedure may be easily extended and provides an opportunity to declare different values for \(\alpha \) and \(\beta \) , i.e. \(\alpha _{1}\) , \(\alpha _{2}\) , ..., \(\alpha _{t}\) , ..., \(\alpha _{T }\) and \(\beta _{1}\) , \(\beta _{ 2}\) , ..., \(\beta _{ t}\) , ..., \(\beta _{ T }\) (step 2) and to apply different formulas (Eqs.  4 , 5 or 6 , step 4) for each period depending on the level of the aforementioned coefficients. Note that all coefficients must be given before the choice of the project.

6 Case study

In this section we are going to solve a simple example presented in Table  2 by means of the H+B rule for NPVU.

We assume that the DM is a pessimist:

\(n=3\) , the cash flow matrix is given in Table  2 .

\({\alpha =\alpha _{p}=0.7}\) , \({\beta =\beta _{p}=0.3}\) (here the DM declares constant parameters for each period).

The non-increasing sequences are as follows:

for \(\hbox {I}_{1}\) : \(Sq_{1,1} =(0,-20,-30,-40)\) , \(Sq_{2,1} =(150,140,130,100)\) , \(Sq_{3,1} =(200,50,0)\) ,

for \(\hbox {I}_{2}\) : \(Sq_{2,2} =(200,170,160,80)\) , \(Sq_{3,2} =(150,70,50,0)\) ,

for \(\hbox {I}_{3}\) : \(Sq_{1,3} =(-50,-60,-80)\) , \(Sq_{3,3} =(500,300,250)\) .

Indices \(hb_{t,j}^p \) are computed in the following way (all the indices are presented in Table  3 ):

We assume that \(r=9\%\) . Measure \({\alpha NPV_{j}}\) is computed below for each project. Table  4 presents the values of that measure for \(r\in [0.05,0.15]\) .

\(I^{*}_{j}=I_{3}\) . The DM can select project \(I_{3}({\alpha NPV_{3}}>0)\) .

According to the H+B rule for NPVU the DM should choose investment \(I_{3}\) and steps 7–8 are not necessary. Nevertheless, thanks to the results gathered in Table  4 , it can be observed that for r equal to at least 10%, investment \(I_{1}\) becomes the best. That is why, the DM ought to reconsider the level of the discount rate in order to make the final decision. A similar analysis for the coefficient of pessimism/optimism can be made. The data presented in Table  5 signify that for \({\alpha <0.67}\) investment \(I_{1}\) becomes the best. Hence, before choosing project \(I_{3}\) , the DM should be really convinced that parameters r and \(\alpha \) have been estimated properly. We see that the sensitivity analysis may be an additional useful tool in the decision making process. It enables one to demonstrate how rankings change depending on the level of the discount rate, the coefficient of pessimism/optimism or the predicted future net cash flows.

7 Conclusions

In this contribution we have described a possible modification of the original NPV in order to evaluate projects, and choose the best one, under uncertainty with unknown probabilities (probabilities are not treated as initial parameters of the decision problem). The proposed method allows one to apply scenario planning and to take into account the decision maker’s attitude towards a given problem (measured by coefficients of pessimism and optimism). The new procedure can be used even in the case of asymmetric distributions of net cash flows at particular periods. The novel method does not require the estimation of probabilities, which is extremely desirable especially in the case of totally new decisions (projects) and for passive decision makers who do not intend to analyze each scenario, period and value very meticulously. Coefficients of optimism and pessimism are used to generate some probability-like quantities, which coincides with the theory of economics, according to which for the majority of uncertain problems, unknown objective or subjective probabilities may be replaced by other measures in order to quantify uncertainty. The approach presented in the paper has been called H+B rule for NPVU since it is partially based on the original version of H+B rule, which constitutes a hybrid of the Hurwicz and Bayes decision rules and which is designed for one-period decision problems. The modified version of H+B rule enables one to consider multi-period scenario-based decision problems.

We are aware of the fact that the suggested method may lead only to partially rational decisions since, due to some unknown factors concerning the future, decision makers possess only “bounded rationality” and have to make decisions by “satisficing” or choosing what might not be optimal, but will make them happy enough (Frish and Baron 2006 ; Simon 1957 , 1991 ).

It is worth stressing that the H+B rule for NPVU may be applied rather on the assumption that the cash flow matrix is estimated by experts instead of the decision maker, since the values are objective Footnote 2 and DM’s attitude towards a given problem is considered by means of coefficients of pessimism/optimism. If the aforementioned matrix is estimated by the DM, there is a risk that his/her attitude will be considered twice: in the cash flow matrix and in the coefficients of pessimism/optimism, which may distort real DM’s preferences (Gaspars-Wieloch 2015d ).

Note that, as in the case of the Hurwicz rule, the suggested decision rule is a subjective procedure since the coefficient of optimism/pessimism is estimated subjectively.

As part of the concluding remarks, we ought to discuss the problem of group (collaborative) decision making because investment decisions are usually made collectively. Thus, particularly in corporate reality, the procedure described in the contribution cannot be directly used in the decision making process. Nevertheless, it can hold a consultative (advisory) function as the final collective decision may constitute, for instance, the most frequent response from among the results obtained separately for each decision maker on the basis of that decision rule. Additionally, using the H+B rule for NPVU by particular members of a group facilitates the final collective choice of the best project since the original set of potential projects has the chance to be significantly reduced.

Another aspect, which needs to be mentioned in the paper, is related to the multi-stage character of the decision making process in the case of project selection. On the face of it, we could state that the H+B rule for NPVU is designed only for one-stage decisions. However, it can be easily used in multi-stage group decisions and combined with the Delphi method, where it is believed that during consecutive rounds the range of the answers will decrease and the group will converge towards the “correct” answer. In the case of multi-stage individual decisions the use of the H+B rule for NPVU could be also advantageous. First stages can, for example, concern situations where the investor is not able to determine a precise degree of optimism and, instead, he/she declares this parameter as an interval. Further stages concern a less “uncertain” uncertainty. Hence, the parameter can be estimated more precisely.

Owing to the fact that the project selection is a task requiring high responsibility, entailing expenditure and time-consuming execution, we would like to emphasize that the H+B rule for NPVU cannot be applied rashly. We strongly recommend that decision makers support the procedure with the sensitivity analysis. Thus, before making the final decision, it is desirable to check how the NPVs and the project rankings change after a slight modification of the level of the optimism coefficient.

The H+B rule for NPVU can be easily adjusted to further non-deterministic applications in areas such as the estimation of NPV with variable discount rates (for long-term investments), the NPV estimation with reinvested cash flows (Chandra 2009 ) and NPV assessment for make-to-order and make-to-stock manufacturing systems (Naim et al. 2007 ).

The converse process in DCF analysis consists in taking a sequence of cash flows and a price as input and inferring a discount rate as output, see Internal Rate Return (IRR). IRR or other efficiency measures are used as a complement to NPV because the latter tool does not provide an overall picture of the gain or loss of executing a certain project. Meanwhile IRR allows one to see a percentage gain relative to the investments in the project ( , ).

The more objective nature of scenario planning in the case of experts results from the fact that experts are better prepared to perform particular steps of that process. They are able (thanks to various methods such as brainstorming, 80:20 rule, Important Uncertainties Matrix) to determine the most important factors (variables) that will decide the nature of the future environment. They have sufficient skill to assess the impact of a given factor on the remaining ones. And finally, they can define the set of possible scenarios.

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This research is financed by the National Science Center in Poland (Project Registration Number: 2014/15/D/HS4/00771).

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Helena Gaspars-Wieloch

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Gaspars-Wieloch, H. Project Net Present Value estimation under uncertainty. Cent Eur J Oper Res 27 , 179–197 (2019).

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Published : 02 November 2017

Issue Date : 07 March 2019


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Measuring Risk and Uncertainty in Different Projects

project evaluation under risk and uncertainty

The following points highlight the four popular techniques for measuring risk and uncertainty in different projects. The techniques are: 1. Risk Adjusted Discount Rate Method 2. The Certainty Equivalent Method 3. Sensitivity Analysis 4. Probability Method.

Technique # 1. Risk Adjusted Discount Rate Method:

This method calls for adjusting the discount rate to reflect the degree of the risk and uncertainty of the project. The risk adjusted discount rate is based on the assumption that investors expect a higher rate of return on risky projects as compared to less risky projects.

The rate requires determination of:

(i) Risk free rate, and


(ii) Risk premium rate.

Risk-free rate is the rate at which the future cash inflows should be discounted. It is the borrowing rate of the investor. Risk premium rate is the extra return expected by the investor over the normal rate. The adjusted discount rate is a composite discount rate.

It takes into account both time and risk factors. In this technique, the discount rate is raised by adding a risk margin in it while calculating the NPV of a project. For example, if the rate of discount is 10% for the project, it may be raised to 11% by adding 1% to take account of risks and uncertainties.

The increased discount rate will reduce the discount factor, thereby lowering the NPV. Thus the project would be judged as undesirable. This method is used for ranking of risky projects. But the problem with this method is that there is no ‘specified margin’ which should be added to the free risk rate.

Technique # 2. The Certainty Equivalent Method :

According to this method, the estimated cash flows are reduced to a conservative level by applying a correction factor termed as certainty equivalent coefficient. The correction factor is the ratio of riskless cash flow to risky cash flow.

The certainty equivalent coefficient which reflects the management’s attitude towards risk is

Certainty Equivalent Coefficient = Riskless Cash Flow/Risky Cash Flow.

If a project is expected to generate a cash of Rs. 40,000, the project is risky. But the management feels that it will get at least a cash flow of Rs. 24,000. It means that the certainty equivalent coefficient is 0.6.

Under the certainty equivalent method, the net present value is calculated as:

project evaluation under risk and uncertainty

E v (NPV) = P 1 (NPV 1 ) + P 2 (NPV 2 ) + P 3 (NPV 3 ).

This method is conceptually sound. But it lacks objectivity as it is not possible to find out the probabilities of different outcomes.

Related Articles:

  • Methods for Taking Investment Decisions under Risk
  • Measuring Risk: Probability of an Outcome (explained with diagram)
  • Business Risk: Types, Measurement and Measures for Reducing It
  • Decision Making under Risk when Investment Projects

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