11.3 Sensitivity analysis and risk assessment

Sensitivity analysis techniques help decision-makers understand how changes in variables affect outcomes. From one-way analysis to Monte Carlo simulations, these methods reveal which factors matter most. Tornado diagrams visually rank variables by impact, guiding where to focus efforts.

Risk assessment tools aid in evaluating decision alternatives under uncertainty. Expected value of perfect information quantifies the worth of reducing uncertainty. Various risk measurement techniques and decision criteria help managers navigate complex choices while considering their risk preferences.

Sensitivity Analysis Techniques

Sensitivity analysis for decision impact

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• One-way sensitivity analysis varies one variable at a time observing changes in optimal decision (interest rates)
• Two-way sensitivity analysis varies two variables simultaneously creating 2D graph visualizing decision regions (price vs demand)
• Threshold analysis identifies point where optimal decision changes (break-even point)
• Scenario analysis evaluates best-case, worst-case, and most likely scenarios (economic boom, recession, steady growth)
• Monte Carlo simulation generates random values for uncertain variables running multiple iterations to assess overall impact (stock market fluctuations)

Critical variables in tornado diagrams

• Tornado diagram construction lists variables on vertical axis showing impact range on horizontal axis
• Variable ranking orders variables from most to least impactful
• Interpretation of tornado diagrams wider bars indicate higher sensitivity narrower bars suggest lower sensitivity
• Steps to create a tornado diagram:

1. Identify key variables
2. Determine reasonable range for each variable
3. Calculate outcome for each variable's high and low values
4. Sort variables by impact magnitude

• Applications in decision-making focus on high-impact variables for further analysis allocate resources to reduce uncertainty in critical variables (market demand, production costs)

Risk Assessment and Decision-Making

Expected value of perfect information

• EVPI maximum amount decision-maker would pay for perfect information
• Calculation of EVPI $EVPI = EV_{PI} - EV_{max}$ where $EV_{PI}$ is expected value with perfect information and $EV_{max}$ is expected value of best alternative without perfect information
• Decision tree analysis for EVPI constructs decision trees with and without perfect information comparing expected values
• Applications of EVPI determine value of additional research or data collection assess whether to invest in reducing uncertainty (market research, geological surveys)
• Limitations of EVPI assumes risk-neutral decision-maker may overestimate value of information in practice

Risk assessment in decision alternatives

• Risk measurement techniques include standard deviation of outcomes variance of outcomes coefficient of variation
• Probability distributions for risk assessment normal distribution triangular distribution uniform distribution
• Risk attitudes risk-averse risk-neutral risk-seeking
• Utility theory uses utility functions to represent risk preferences expected utility for decision-making
• Risk-adjusted decision criteria risk-adjusted net present value (RANPV) certainty equivalent
• Portfolio theory concepts diversification to reduce risk efficient frontier
• Decision-making under uncertainty:
  • Maximin criterion (pessimistic approach)
  • Maximax criterion (optimistic approach)
  • Hurwicz criterion (weighted approach)
  • Minimax regret criterion