Decision-Making under Uncertainty
Decision-Making under Uncertainty
Separate action from state
HarborMart must decide evening picker capacity before demand is known.
| Contribution after staffing cost | Normal demand, 60% | High demand, 40% |
|---|---|---|
| current staffing | £4,000 | £2,000 |
| add one picker | £3,700 | £3,600 |
| add two pickers | £3,200 | £4,200 |
Expected values are:
With these probabilities and a risk-neutral objective, one extra picker wins by £60 over two. That small margin should trigger sensitivity analysis, not a confident slogan.
Expected value of perfect information
With advance knowledge, HarborMart would use current staffing under normal demand and two extra pickers under high demand:
Therefore
£420 is an upper bound on what perfect demand information is worth for this decision. A forecast costing £1,000 per evening cannot be justified by this simplified payoff table.
Regret reveals fragility
Regret is the gap from the best action in each state:
| Regret | Normal | High | Maximum |
|---|---|---|---|
| current staffing | £0 | £2,200 | £2,200 |
| add one | £300 | £600 | £600 |
| add two | £800 | £0 | £800 |
The minimax-regret action is also one extra picker. Agreement with expected value strengthens the case here; it is not guaranteed in general.
Risk, ambiguity and model error
- risk: probabilities are treated as known;
- parameter uncertainty: probabilities/payoffs are estimated;
- model uncertainty: the listed states omit plausible mechanisms;
- ambiguity: no single probability distribution is credible.
Use scenarios, intervals, robust optimisation or explicit judgement according to the source of uncertainty. Adding decimal places does not remove ambiguity.
Recent decision theory explicitly studies models as approximations; see Cerreia-Vioglio et al., Making Decisions Under Model Misspecification. Its formal treatment is a postgraduate extension, not a reason to abandon transparent classroom scenarios.
Quick check
High-demand probability rises from 40% to 45%. Which action now has highest expected value?