How to use it
- 1. Edit the numbersPayoffs ($M) and probabilities are all editable. The tree folds back instantly.
- 2. Read right to leftChance nodes average (EMV); decision squares pick the best branch. The red path is the optimal plan.
- 3. Price the crystal ballEVPI = what a perfect demand forecast would be worth. Never pay a consultant more than this.
- 4. Slide P(High)The sensitivity chart shows where the best decision flips - the crossover probabilities.
Capacity decision under uncertainty
Demand probabilities
P(Low) = 0.25 (the remainder). If High + Medium exceed 1, Medium is trimmed.
Net payoffs ($M)
| High | Med | Low |
Payoffs are net of build cost. “Small” includes the option to expand later if demand turns out High.
Small plant’s embedded option
If you build small and demand is High, a second decision appears: stay small or expand. The tree prices that flexibility automatically.
Squares = decisions (take the max). Circles = chance (take the expectation). The red trail is the optimal policy; grey branches are pruned.
EMV of each first-stage action as P(High) sweeps 0→1 (Medium:Low ratio held). Vertical line = your current P(High); dots mark decision flips.
Try these experiments
- At the defaults, Large wins (15.9 against 13.1 for Small). Raise the expand-later payoff to 30 and watch Small + option take over - flexibility only wins if exercising it pays enough.
- Slide P(High) to 0.7: Large dominates and EVPI shrinks - information is worth most when you are genuinely unsure.
- Make Low brutal (Large = −10): the maximin choice diverges from the EMV choice. Expected value is not the whole story when ruin is on the table.
About this tool
The concept
Decision analysis separates what you control (decision nodes) from what you don’t (chance nodes), then folds the tree back from the leaves: expectation at circles, maximum at squares.
How it works
EMV = Σ p·payoff at each chance node. EVPI = E[best payoff per state] − best EMV. The embedded expand decision is a real option priced by backward induction.
Winning strategy
Buy information only below EVPI. Prefer flexible small commitments when uncertainty is high - the option value shown is exactly what that flexibility is worth.