Decision Science

Analytic Hierarchy Process

Design a pairwise-comparison questionnaire, collect expert judgements on the Saaty scale, and rank alternatives using transparent AHP calculations.

Browser-based calculation Questionnaire JSON workflow Consistency ratio check

Why use this tool?

Decision Supported

Use this tool when a decision has several criteria, optional sub-criteria, and several alternatives that need structured judgement and measured evidence.

What It Tells You

It estimates criterion weights, sub-criteria weights where used, alternative scores under each evaluable criterion, overall ranking, and consistency ratios.

Example Input

Define criteria such as cost, quality, risk, and implementation time; add sub-criteria when a criterion needs a clearer breakdown.

Sample Output Interpretation

The top-ranked alternative has the highest weighted score. High consistency ratios suggest the comparisons should be reviewed before acting.

1 Design Define the goal, criteria, sub-criteria, and alternatives
2 Expert Survey Record pairwise judgements
3 Analysis Calculate weights and ranking

1. Questionnaire Design

Create the AHP decision structure before sending it to experts.

Sample template

Questionnaire design is created locally in your browser. Export the JSON file before sharing it with experts.

Project title Number of criteria Number of alternatives

2. Expert Survey

Import a questionnaire JSON, complete the pairwise comparisons, and export the expert response.

Survey answers are held in this browser session only. Export the completed response JSON before closing or refreshing the page.

Import questionnaire JSON

3. AHP Analysis

Load one or more completed expert response JSON files to calculate weights, consistency, and alternative ranking.

Import completed expert response JSON

4. Results and Interpretation

Review the calculated priority weights, consistency checks, and final ranking.

Individual and group consistency checks

Criteria Weight Distribution

Alternative Ranking

AHP Hierarchy Structure

Review the decision hierarchy used in this calculation: goal, criteria, optional sub-criteria, and alternatives.

Pairwise Comparison Calculations

Trace the calculation from the aggregated pairwise judgements and any objective data normalisation through local priorities and consistency checks. Select any calculation below to view the detail.

Decision Matrix and Weighted Calculation

The final matrix combines each alternative's local priority under every leaf criterion or sub-criterion with its global weight.

Scenario Planning: Test Weight Sensitivity

Test whether the preferred alternative changes when one criterion or sub-criterion receives more or less importance.

About Analytic Hierarchy Process

Analytic Hierarchy Process is a structured method for multi-criteria decision-making. It asks experts to compare criteria, optional sub-criteria, and alternatives in pairs, converts those judgements into priority weights, and combines the weights into an overall ranking.

Guidance

Define the decision goal, criteria, optional sub-criteria, and alternatives in the questionnaire design section.
Choose whether each final evaluable criterion or sub-criterion is subjective judgement or objective measured data. Objective items need a direction such as higher-is-better or lower-is-better.
Export the blank questionnaire JSON and send it to the expert or decision-maker.
The expert imports the questionnaire, answers each pairwise question, and exports the completed response JSON.
Load one or more completed response files into the analysis section, enter measured values for any objective leaf criteria, and calculate the ranking.
Review consistency ratios before using the ranking to support a decision.
Optionally turn on Scenario Planning after calculation to test whether changes in criterion importance alter the preferred alternative.

Methodology, Assumptions, and Limitations

Formula Logic

Notation
E = number of experts, n = number of compared elements, a_ij^(e) = expert e's judgement comparing element i with element j, w_i = priority weight

Reciprocal pairwise matrix
a_ji = 1 / a_ij, a_ii = 1

Multiple-expert aggregation
A_ij = (∏_e=1^E a_ij^(e))^1/E

Row geometric mean
GM_i = (∏_j=1ⁿ A_ij)^1/n

Normalised priority weight
w_i = GM_i / ∑_k=1ⁿ GM_k

Sub-criteria global weight
g_ij = w_i × u_ij, where w_i is the parent criterion weight and u_ij is the local sub-criterion weight

Final alternative priority
S_a = ∑_l=1^L g_l × p_al, where g_l is a global leaf weight and p_al is alternative a's local priority under leaf criterion l

Objective criterion, higher is better
p_ai = x_ai / ∑_a x_ai

Objective criterion, lower is better
p_ai = (1 / x_ai) / ∑_a (1 / x_ai)

Sensitivity scenario
w′_k = s, w′_j = w_j × (1 - s) / (1 - w_k)

Consistency Ratio

Consistency vector
(Aw)_i / w_i

Principal value
λ_max = (1 / n) ∑_i=1ⁿ ((Aw)_i / w_i)

Consistency index
CI = (λ_max - n) / (n - 1)

Consistency ratio
CR = CI / RI

RI is Saaty's random index for a matrix of size n. A CR around 0.10 or lower is commonly used as review guidance, not proof that the judgement is objectively correct.

Saaty Scale

Ratings use 1 equal, 2 equal to moderate, 3 moderate, 4 moderate to strong, 5 strong, 6 strong to very strong, 7 very strong, 8 very strong to extreme, and 9 extreme preference.

Assumptions

Experts can make meaningful pairwise judgements, objective values are measured consistently, criteria and sub-criteria are relevant to the decision, and alternatives are comparable under each leaf criterion.

Limitations

AHP supports structured judgement but does not remove bias. Objective criteria are normalised decision inputs, not proof that the selected measures fully represent performance.

FAQ

What is the Saaty scale?

It is a 1 to 9 judgement scale used for pairwise comparison. A value of 1 means equal importance or preference, while 9 means extreme importance or preference.

Can several experts answer the same questionnaire?

Yes. Send the same questionnaire JSON to each expert, then load multiple completed response files in the analysis section. The tool aggregates judgements using a geometric mean.

Can AHP use objective data as well as expert judgement?

Yes. Mark a final criterion or sub-criterion as objective when alternatives can be compared using measured values, such as cost, on-time delivery percentage, emissions, or lead time. The tool normalises those values into local priorities while still using AHP criterion and sub-criterion weights.

Can AHP use sub-criteria?

Yes. Use one sub-criteria level when a main criterion needs a clearer breakdown. The tool compares sub-criteria under their parent criterion and multiplies local sub-criteria weights by the parent weight to create global leaf weights.

What does consistency ratio mean?

It checks whether the pairwise comparisons are reasonably coherent. A high consistency ratio means the expert should review the answers before the ranking is used.

Is my survey data uploaded?

No. This tool reads, calculates, and exports JSON files in the browser. No server upload is used by this static page.