Decision Lab: AHP, TOPSIS, EMV Trees & Monte Carlo

Decision Lab is a five-panel workbench for choosing between alternatives and pricing uncertainty. One scorecard of alternatives × criteria can be read as a weighted-sum ranking, as AHP weights from pairwise judgements, or as a TOPSIS closeness ranking; a risk decision becomes a decision tree that rolls back to an expected monetary value (EMV); and a business case can be swept by seeded Monte Carlo for quantiles and the probability of falling below a threshold. Everything runs locally.

Updated 2026-10-01Reviewed by CalcX Editorial Team5 sources4 min read

How to run a panel

Open a panelfrom the tabs on /finance/decision, or directly: /finance/decision/matrix, /finance/decision/ahp, /finance/decision/topsis, /finance/decision/tree, /finance/decision/montecarlo.
Fill a score matrix— weighted scoring and TOPSIS share one grid: one row per alternative, one column per criterion with a name, weight and direction; weights are rescaled to sum to 1 and cost criteria reverse automatically.
Compare in pairs (AHP)— edit only the upper triangle on the Saaty 1–9 scale. Read the weights plus λmax, CI, CR and RI; CR above 0.1 means the judgements contradict each other and should be revisited. Alternatives add a second layer and a global ranking.
Draw a tree (EMV)— decision □, chance ○ and terminal ◁ nodes; branches may carry a cash flow (negative = cost). The rollback returns the root EMV and the optimal choice at every reachable decision node.
Simulate a scenario— set each variable's distribution (normal, triangular, uniform), then trials, seed and the threshold for P(Y < t) to read quantiles and downside probability.

Worked readouts

Every figure comes from the panel defaults, which the demo buttons restore.

Panel	Input	Readout
Weighted scoring	4 laptops × 4 criteria, weights 35/30/20/15%; scores performance 72/85/95/60, price 5,499/6,999/8,999/4,999 (cost), portability 90/70/45/95, support 80/85/75/70	Min–max totals: Ultrabook A 0.663, All-rounder B 0.65, 2-in-1 D 0.5, Gaming C 0.4
AHP	price/location/area compared at 1/3, 5 and 7	Weights 27.9% / 64.9% / 7.2%; λmax 3.065, CI 0.032, CR 0.056 against RI 0.58
TOPSIS	the same four-laptop grid	Ultrabook A Ci 0.656 (D⁺ 0.053, D⁻ 0.101); 2-in-1 D 0.581; All-rounder B 0.573; Gaming C 0.414
Decision tree	drill at −500, then 25% × 2,400 oil vs 75% dry, against no drill	EMV 100; optimal choice "drill"
Scenario MC	(price − cost) × qty; price tri(80, 120, 100), cost normal(70, 5), qty normal(1000, 100); 20,000 trials, seed 20250101, threshold 0	Mean 30,030.862, sd 10,042.528, median 29,780.447, P(Y < 0) 0.02%; 5th percentile 14,060.865, 95th 47,082.577

The tree readout is 0.25 × 2,400 − 500 = 100, the chance node (600) net of the sunk cost. In the scenario, four of the 20,000 draws fall below zero; a threshold of 20,000 reads 16.44%, and seed 20250101 replays identically.

What the five methods assume

Weighted scoring normalises each criterion and adds weighted contributions — fully compensatory: a strong score can cover a weak one. AHP takes the principal eigenvector of the pairwise matrix and checks the judgements' consistency. TOPSIS ranks by Euclidean distance to best and worst ideals, punishing a single very poor criterion. Tree rollback is backward induction under risk neutrality; Monte Carlo reads the outcome distribution instead of a point estimate.

Assumptions and limits

Numbers inherit the inputs.: Criterion weights and pairwise judgements are opinions, not measurements; a passing CR only says the comparisons do not contradict each other past Saaty's 0.1 threshold. Monte Carlo answers carry sampling error and converge as 1/√M.
What it does not do:: it does not estimate probabilities, effects or costs from data, and it does not model risk appetite — EMV is risk-neutral, right for repeatable, affordable bets but misleading for one-shot large stakes. For raw-sample tests use Statistics; for a measurement uncertainty budget use Uncertainty; for study design use Applied Statistics.

Why the winner moves when nothing changes

The signature trap is the normalisation switch. On the default scorecard, min–max puts Ultrabook A first at 0.663 against B's 0.65; switch to max-ratio and 2-in-1 D climbs to 0.845 between A's 0.869 and B's 0.825; choose raw scores and the 5,000-scale price swamps the rest — D wins at −1,449.2, A at −1,594.5. TOPSIS keeps A on top but swaps the runner-up: D 0.581 ahead of B 0.573. Record the normalisation with the ranking.

Where it fits

Choosing a purchase, vendor or hire

Load the four-laptop demo and switch between weighted scoring and TOPSIS: A wins both, but the composition bars show different criteria carrying the front-runners. A table sent from another tool opens an intake card, so measured scores need not be retyped.

A go/no-go with a real downside

The drill tree prices a 25% success chance against a sunk cost: EMV 100 says drill, and the strategy table names every choice. Lower the success probability enough and the optimal branch flips to staying out.

Budgeting under uncertainty

The profit model turns a threshold into a risk statement: P(Y < 0) = 0.02%, but P(Y < 20,000) = 16.44%; quantiles give a range to plan around.

References

Saaty, T.L., A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology 15(3), 234–281, 1977, doi.org （访问日期：2026-10-01）— the 1–9 scale, priority vectors and consistency.
Hwang, C.-L. & Yoon, K., Multiple Attribute Decision Making: Methods and Applications, Springer, 1981, link.springer.com （访问日期：2026-10-01）— TOPSIS and relative closeness.
Wikipedia, Analytic hierarchy process, en.wikipedia.org （访问日期：2026-10-01）— random index and the CR ≤ 0.1 rule.
Wikipedia, Decision analysis, en.wikipedia.org （访问日期：2026-10-01）— decision trees, expected value, risk attitude.
Wikipedia, Monte Carlo method, en.wikipedia.org （访问日期：2026-10-01）— sampling and convergence.