Dealing with risk and uncertainty in decision-making

Welcome to Decision-Making Under Pressure!

In your studies so far, we’ve often assumed we know exactly what will happen in the future—like exactly how many units we will sell or exactly what the price will be. But in the real world, managers are not psychics! They face risk and uncertainty every day.

This chapter is all about the tools you can use to make the best possible decisions when you aren't 100% sure what the future holds. Don't worry if this seems a bit "maths-heavy" at first; we will break it down step-by-step using simple logic.

1. Risk vs. Uncertainty: What’s the Difference?

Students often use these words interchangeably, but in Performance Management, they have very specific meanings:

Risk: This is when there are several possible outcomes, and we know the mathematical probability of each one happening (e.g., there is a 60% chance of rain). Think of it like a game of dice—you don't know the result, but you know the odds.

Uncertainty: This is when we have several possible outcomes, but we cannot assign a probability to them (e.g., a brand new competitor enters the market, and we have no idea how customers will react). It’s like being in a fog where you can’t see the path ahead.

Quick Review:

Risk = Probabilities are known.
Uncertainty = Probabilities are NOT known.

2. Sensitivity Analysis

Imagine you are planning a concert. You think you’ll make a profit, but you’re worried about what happens if ticket sales are lower than expected. Sensitivity Analysis asks: "By how much can a variable change before our decision becomes a bad one?"

Usually, we want to know how much a variable (like sales volume or material cost) can change before the project's profit hits zero (breakeven).

The Formula:
\( \text{Sensitivity (\%)} = \left( \frac{\text{Net Profit}}{\text{Total value of the variable being tested}} \right) \times 100 \)

Example: If your project profit is $10,000 and your total sales revenue is $100,000, the sensitivity to sales revenue is \( (10,000 / 100,000) \times 100 = 10\% \). This means if your sales drop by more than 10%, you will start making a loss.

Key Rule:

The lower the percentage, the more sensitive (and therefore riskier) that variable is. If a 1% change in price ruins your profit, that's a very risky project!

Common Mistake to Avoid:

Sensitivity analysis only changes one variable at a time. In reality, multiple things often change at once (like price and volume), but this model is too simple to show that.

3. Expected Values (EV)

When we face Risk (where we have probabilities), we use Expected Values to find the "long-term average" outcome.

The Formula:
\( EV = \sum px \)
(This just means: Multiply each possible Outcome (x) by its Probability (p) and add them all up.)

Analogy: If a friend offers you $100 if a coin lands on heads (50% chance) and you lose $20 if it lands on tails (50% chance):
\( EV = (0.50 \times \$100) + (0.50 \times -\$20) = \$50 - \$10 = \$40 \).
\nTechnically, you will never actually receive $40 (you'll get either $100 or -$20), but $40 is the mathematical average.

Pros and Cons of Expected Values:

Pros: It gives a single, clear figure for making decisions and is great for repetitive decisions (like daily production runs).
\nCons: It is less useful for "one-off" projects because the EV might not be one of the actual possible outcomes. It also ignores the attitude to risk (a huge loss might bankrupt you even if the EV is positive!).

4. Decision Rules: Attitudes to Risk

In the exam, you'll meet three types of managers. How they choose a project depends on their "personality":

A. The Optimist (Maximax)

The Maximax rule looks for the best possible outcome for each option and chooses the highest one. It’s the "Go Big or Go Home" approach. To use it:
\n1. Find the Maximum profit for each choice.
\n2. Pick the Maximum of those maximums.

B. The Pessimist (Maximin)

The Maximin rule is for managers who hate losing. They look at the worst-case scenario for every option and choose the one that is "the least bad." To use it:
\n1. Find the Minimum profit for each choice.
\n2. Pick the Maximum of those minimums (The "Best of the Worst").

C. The Opportunist (Minimax Regret)

This manager hates "missing out." They want to minimize their Regret (the profit they missed out on by making the wrong choice). This requires a Regret Table.

Step-by-Step Regret Table:
\n1. For each possible "future scenario" (e.g., High Demand), identify the best possible profit.
\n2. Subtract all other profits in that scenario from that best profit. (This shows your "Regret").
\n3. For each decision, find the Maximum Regret.
\n4. Choose the decision with the Minimum Maximum Regret.

Memory Aid:

Maximax: Best of the Best (Optimist)
\nMaximin: Best of the Worst (Pessimist)
\nMinimax Regret: Least Regret (Fear of FOMO)

5. Decision Trees

A decision tree is just a map of a complex decision. It uses squares for decision points (where the manager chooses) and circles for outcome points (where "fate" or probability takes over).

How to solve them:
\n1. Draw left to right: Map out the choices and possible outcomes.
\n2. Calculate right to left ("Rollback"): Calculate the Expected Value at each circle. At each square, pick the best option and "cut off" the others.

Important Tip:

Remember to subtract any costs of the decision (like the cost of a survey) from the final outcome at the end of the branches!

6. The Value of Information

Sometimes, we can pay for a market research report to tell us exactly what will happen in the future. How much should we pay for it?

Value of Perfect Information (VOPI):
\n1. Calculate the EV of the decision with perfect information (as if you knew the future every time).
\n2. Calculate the EV without the information (your standard EV calculation).
\n3. VOPI = (EV With Info) - (EV Without Info).

Analogy: If a crystal ball helps you make $1,000 extra profit, you should be willing to pay up to $1,000 for it, but not a penny more!

Summary Takeaway

In Section C of your PM exam, remember:
- Use Sensitivity Analysis for "What if" questions.
- Use Expected Values when you have probabilities.
- Use Maximax/Maximin/Minimax Regret when probabilities are unknown (Uncertainty).
- Always be logical: If a manager is risk-averse, they will prefer Maximin over Maximax!

Don't worry if this seems tricky at first! The more you practice building Regret Tables and rolling back Decision Trees, the more natural it will become. You've got this!