Mitigate Risks

Sensitivity Analysis

Stop the guesswork and start identifying factors that make the largest impact on your output with probabilistic sensitivity analysis. By combining sensitivity analysis with Monte Carlo simulation, you can analyze the impact of different variables in your model by ranking inputs in order of importance and easily communicate results with tornado charts and spider graphs – leading to more informed decisions.

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Prioritize Risks by Ranking their Impacts

Analyzing uncertainty, and specifically the key inputs that drive that uncertainty, is at the heart of risk analysis. Which variables actually impact your outputs the most? When you prioritize your key risks, you can efficiently and optimally assign controls and mitigations across your entire business.

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What is Sensitivity Analysis?

The Monte Carlo method is a computerized mathematical technique that allows people to quantitatively account for risk in forecasting and decision-making. At its core, the Monte Carlo method is a way to use random samples of parameters to explore the behavior of a complex system. A Monte Carlo simulation is used to handle an extensive range of problems in a variety of different fields to understand the impact of risk and uncertainty.

Rank Your Inputs in Order of Importance

Deterministic sensitivity analysis is a method of analyzing models that allows you to rank your inputs in order of importance. It’s an advanced yet accessible practice that helps you make informed decisions on topics such as effective allocation of your organization’s limited resources and risk mitigation. By itself, risk sensitivity analysis is critical information, but can be a complete game-changer when combined with Monte Carlo simulation to create probabilistic sensitivity analysis.

Communicate Results with Graphs

A sensitivity assessment model displays quantitative data based on the behavior of outputs in response to changing inputs. This data allows the creation of tornado diagrams and spider graphs, giving a visual representation of the inputs’ relative impact on your key outputs. Together, these graphs and data provide communication tools and hard numbers to validate your business and research decisions.

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Use cases are varied, and include:

Inventory management

Budgeting

Resource and production scheduling

Product and marketing mix

Supply chain planning

Market entry timing and more

Project, loan, and investment portfolio maximization

A Range of Outcomes (one col list)

Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows:

the extreme possibilities

the outcomes of going for broke and for the most conservative decision

along with all possible consequences for middle-of-the-road decisions

History of Monte Carlo Simulation

The technique was first used by scientists working on the atom bomb; it was named for Monte Carlo, the Monaco resort town renowned for its casinos. Since its introduction in World War II, Monte Carlo simulation has been used to model a variety of physical and conceptual systems.

How Does Sensitivity Analysis Work?

Sensitivity analysis operates directly on your preexisting model – modeling sensitivity analysis in the form of a tornado diagram. After the software will identifies all inputs affecting an output you specify (e.g., NPV, Total Project Cost, or Return), the inputs are stepped through a meaningful range of values (such as +/- 10%) – indicative of the uncertainty in each. For every one of these values, the entire model is recalculated and new data is recorded for all identified outputs. This data represents the direct impact that each input has on the calculated output value. The magnitude of this range is the metric by which the inputs are ranked and are conveniently displayed in tornado charts and spider graphs. A greater impact score on the sensitivity model means an input is more important, requiring mitigation or further investigation and modeling.

A tornado graph showing the results of a sensitivity analysis. Large bars on top have the most impact.

100% Microsoft Excel Integration

With PrecisionTree, you never leave your spreadsheet, allowing you to work in a familiar environment, and get up to speed quickly.

Full Statistics Reports and Graphs

See results in risk profile graphs, 2-way sensitivity, tornado graphs, spider graphs, policy suggestion reports, and strategy-region graphs.

Advanced Features

Set up your decision tree in Microsoft Excel exactly as you need it with logic nodes, reference nodes, linked trees, custom utility functions, and influence diagrams.

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Local and Global Sensitivity Analysis

In general, sensitivity analysis falls into one of two categories: local and global.

Local Sensitivity Analysis

This method is appropriate for simple models and involves adjusting input variables one at a time across a defined, but generally limited, range. For instance, you might vary all inputs +/- 10%, as noted earlier. As any one given input variable is adjusted, all others are fixed. Local sensitivity analysis is an excellent precursor for further analysis as it saves tremendous time and energy by helping to focus the project.

Global Sensitivity Analysis

Global sensitivity analysis adjusts all input variables at the same time. In addition, the ranges of values sampled for each variable is much broader and is meant to represent the entire range of possible values each variable could take. Effectively, global sensitivity analysis is performed using Monte Carlo simulation to measure input sensitivity probability.

FEATURES LIST (not always shown)

Feature	Benefit	Professional Edition	Industrial Edition
Optimization under uncertainty	Combines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems. Used for budgeting, allocation, scheduling, and more.
Efficient Frontier Analysis	Especially useful in financial analysis, Efficient Frontiers determine the optimal return that can be expected from a portfolio at a given level of risk
Ranges for adjustable cells and constraints	Streamlined model setup and editing
Genetic algorithms	Find the best global solution while avoiding getting caught in local, “hill-climbing” solutions
Six solving methods, including GAs and OptQuest	Always have the best method for different types of problems
RISKOptimizer Watcher and Convergence Monitoring	Monitor progress toward best solutions in real time
Overlay of Optimized vs Original Distribution	Compare original output to optimized result to visually see improvements
Original, Best, Last model updating	Instantly see the effects of three solutions on your entire model

Normal

Values are positively skewed, not symmetric like a normal distribution. It is used to represent values that don’t go below zero but have unlimited positive potential. Examples of variables described by lognormal distributions include real estate property values, stock prices, and oil reserves.

Lognormal

Uniform

All values have an equal chance of occurring, and the user simply defines the minimum and maximum because they have no knowledge of which values are more likely than others. Examples of variables that could be uniformly distributed include manufacturing costs or future sales revenues for a new product.

Triangular

The user defines the minimum, most likely, and maximum values. Values around the most likely are more likely to occur. Variables that could be described by a triangular distribution include past sales history per unit of time and inventory levels.

PERT

The user defines the minimum, most likely, and maximum values, just like the triangular distribution. Values around the most likely are more likely to occur. However values between the most likely and extremes are more likely to occur than the triangular; that is, the extremes are not as emphasized. An example of the use of a PERT distribution is to describe the duration of a task in a project management model.

Discrete

FEATURES LIST (not always shown)

Feature	Benefit	Professional Edition	Industrial Edition
Optimization under uncertainty	Combines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems. Used for budgeting, allocation, scheduling, and more.
Efficient Frontier Analysis	Especially useful in financial analysis, Efficient Frontiers determine the optimal return that can be expected from a portfolio at a given level of risk
Ranges for adjustable cells and constraints	Streamlined model setup and editing
Genetic algorithms	Find the best global solution while avoiding getting caught in local, “hill-climbing” solutions
Six solving methods, including GAs and OptQuest	Always have the best method for different types of problems
RISKOptimizer Watcher and Convergence Monitoring	Monitor progress toward best solutions in real time
Overlay of Optimized vs Original Distribution	Compare original output to optimized result to visually see improvements
Original, Best, Last model updating	Instantly see the effects of three solutions on your entire model

Random Sampling Versus Best Guess

During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is called an iteration, and the resulting outcome from that sample is recorded. Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes. In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.

Monte Carlo simulation provides a number of advantages over deterministic, or “single-point estimate” analysis:

Probabilistic Results. Results show not only what could happen, but how likely each outcome is.

Graphical Results. Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence. This is important for communicating findings to other stakeholders.

Sensitivity Analysis. Deterministic analysis makes it difficult to see which variables impact the outcome the most. In Monte Carlo simulation, it’s easy to see which inputs had the biggest effect on bottom-line results. This allows you to identify and mitigate factors which cause the most risk.

Scenario Analysis: In deterministic models, it’s very difficult to model different combinations of values for different inputs to see the effects of truly different scenarios. Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred. This is invaluable for pursuing further analysis.

Correlation of Inputs. In Monte Carlo simulation, it’s possible to model interdependent relationships between input variables. It’s important for accuracy to represent how, in reality, when some factors go up or down, others go up or down accordingly.

An enhancement to Monte Carlo simulation is the use of Latin Hypercube sampling, which samples more accurately from the full range of values within distribution functions and produces results more quickly.

How PrecisionTree Is Used

PrecisionTree has a multitude of applications, including:

Oil, Gas, & Mineral Reserves: Map out sequential, probabilistic exploration plans of prospective sites containing oil, natural gas, or other minerals. Estimate uncertain reserves to make wise drilling decisions.

Litigation & Bidding Strategy: Plan step-by-step strategies in complex legal or business negotiations, or when bidding on contracts. Map what could happen at each stage and your response to, along with probabilistic chance events.

Real Options Valution: Quantify the value of real options, or the right to undertake an investment or not, in the face of uncertainty future outcomes.

Supply Chain Management: Develop multi-stage plans for complex supply chains, incorporating probabilities of failures and other chance events.

Medical Treatment Planning: Establish sequential, multi-stage treatment plans for complex medical conditions given uncertain outcomes at each stage.

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Enterprise Licensing
Better Research, Insights, and Outcomes for All

Whether your organization’s focus is qualitative, quantitative, or mixed methods data analysis, we can help your whole team work better together — collaborating to aggregate, organize, analyze, and present your findings. Lumivero’s enterprise licensing options offer volume pricing for teams and organizations needing nine (9) or more licenses.

Enterprise licenses allow the flexibility to install Lumivero software and solutions on multiple computers (up to the maximum number of licenses that your site has purchased) with a centralized management solution.

Lumivero’s team-based solutions allow you to:

Stay up-to-date with free upgrades to the latest releases

Reduce IT costs with one platform deployed across your organization

Reassign licenses to different users as teams evolve

Centralize license and subscription management in one place

Streamline budget allocation, especially for smaller groups and consultancy firms

Enjoy a Dedicated Customer Success Manager and pro-rated rates for new users

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