CVEN9892 Chap.8 Decision Trees and Multicriteria Analysis
Decision Trees and Multicriteria Analysis
This chapter structures choices with uncertain branches and several consequence criteria. Decision trees separate alternatives, chance events, probabilities and terminal outcomes. Multicriteria decision analysis defines feasible alternatives, non-overlapping criteria, preference direction, normalisation, weights and aggregation.
Sensitivity analysis reveals whether a ranking is robust or depends on a narrow data or preference assumption. Use a decision tree when choices lead to ordered chance events and terminal consequences. Draw the decision node first, then chance nodes and complete paths. Probabilities leaving a chance node should sum to one, and each terminal value should include every consequence incurred along that route.
Roll expected values back from right to left only after the structure is correct. A control cost paid regardless of success belongs on every controlled path or outside the chance calculation, not only on the failure branch. Expected value is one summary and may not represent tolerability, distribution or a catastrophic constraint.
Multi-criteria decision analysis is appropriate when alternatives must be compared across environmental, health, reliability, cost or social consequences that do not share a natural unit. Define the goal and feasible alternatives before building the matrix. Each criterion needs a precise measure, boundary and preference direction.
Check overlap: capital cost may already be included in life-cycle cost, and energy use may overlap with a climate indicator. Duplicated criteria give one concern extra influence. Preserve the raw value and unit before normalisation. For a benefit criterion, higher performance should produce a higher normalised score; for a cost or burden criterion, lower performance should score higher.
Declare the formula and handle equal maxima and minima deliberately. Simple additive weighting multiplies each normalised value by its criterion weight and sums across criteria. Check that weights share one scale and sum to one. A table of weighted contributions reveals which criterion drives the total and makes arithmetic reconstructable.
Weights express priorities rather than measured physical facts, so record how and by whom they were chosen. Data uncertainty and preference sensitivity should be examined separately. First vary uncertain performance with weights fixed, then test defensible weight sets with data fixed. Find the value or weight at which two options tie.
A switch point inside a plausible range means the preference is conditional, even if displayed scores contain several decimal places. Compare central ranking, nearest competitor, important adverse branch and feasibility constraints. When a result is fragile, improved evidence, stakeholder discussion or an adaptive option may be more valuable than declaring a winner.
The final recommendation should identify the decision method, dominant contribution, rank-switch condition and remaining consequence that the aggregate score could conceal.
What this chapter covers
- 01
Decision nodes
- 02
Chance branches
- 03
Criterion design
- 04
Normalisation
- 05
Simple additive weighting
- 06
Rank sensitivity
Worked example · free
Calculate simple additive scores
- +1Check the weights sum to 1.00.
- +1Calculate A = 0.635.
- +1Calculate B = 0.680.
- +1Report B's narrow lead and test sensitivity.
Key terms
- Decision node
- A point in a tree where the decision maker selects an alternative.
- Chance node
- A point where uncertain outcomes branch according to probabilities.
- Criterion
- A measurable consequence or attribute used to compare alternatives.
- Simple additive weighting
- An MCDA method that sums weighted normalised criterion scores.
- Rank switch
- A point where changing a weight or performance value reverses the preferred order of two alternatives.
Decision Trees and Multicriteria Analysis FAQ
Why normalise MCDA data?
Criteria may use incompatible units and ranges. Normalisation maps them onto a comparable scale, but the chosen formula and whether higher or lower is desirable must be declared.
What do MCDA weights represent?
Weights express relative importance within the chosen decision model. They are preferences or policy inputs, not physical properties, so stakeholder ownership and sensitivity should be reported.
How can double-counting occur?
Closely related criteria can reward or penalise the same consequence repeatedly. Review causal overlap, redefine criteria and test whether the preferred option depends on the duplicated concern.
Exam move
Draw one complete decision tree and practise rolling it back from terminal outcomes. For MCDA, retain raw data, direction, normalised values, weights and weighted contributions in separate columns. Change one weight or uncertain datum at a time, then locate any rank switch and explain what value judgement or evidence controls it.
Before scoring, screen infeasible alternatives and define every criterion with its unit, boundary and preference direction. Check pairs of criteria for overlapping consequences. Recalculate benefit and cost normalisation from raw values and verify the endpoints. Sum weights and weighted contributions independently.
Run a data range with weights fixed, then a preference range with data fixed, so the cause of a rank change remains visible. Report the central winner, nearest competitor, dominant contribution and plausible switch point. Add a worst-consequence check so an aggregate score does not hide an unacceptable branch.
