SECA - Simultaneous Evaluation of Criteria and Alternatives

Overview

SECA derives criterion weights simultaneously with alternative appraisal - no weight elicitation from the decision-maker is needed. β controls the trade-off between maximising total appraisal (β→1) and minimising inter-alternative variance (β→0). β=0.5 is the recommended balanced default. The optimisation is non-linear (NLP) and requires a suitable solver.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Linear normalisation (min-max) to [0,1].

   $$r_{ij}=\frac{x_{ij}-x_j^{\min }}{x_j^{\max }-x_j^{\min }}\text{ (benefit)};r_{ij}=\frac{x_j^{\max }-x_{ij}}{x_j^{\max }-x_j^{\min }}\text{ (cost)}$$

   Keshavarz Ghorabaee et al. 2018, p.268 Eqs.(1)-(2)

2. 2

   Solve non-linear optimisation to determine weights w_j and appraisal scores A_i simultaneously by maximising a combination of total appraisal and minimising variance.

   $$\max f(w)=\beta \sum _{i=1}^m{A}_i-(1-\beta )\sum _{j=1}^n{\sigma }_j^2(w);A_i=\sum _{j=1}^n{w}_j{r}_{ij},{\sigma }_j^2(w)=\frac{1}{m}\sum _{i=1}^m(w_j{r}_{ij}-{\bar{r}}_j{w}_j{)}^2;\text{s.t.}\sum _j{w}_j=1,w_j\ge 0$$

   Keshavarz Ghorabaee et al. 2018, p.269 Eqs.(3)-(6)

3. 3

   Rank alternatives in descending order of A_i.

   $$\text{rank}(A_i)=\text{rank by descending }{A}_i$$

   Keshavarz Ghorabaee et al. 2018, p.270

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• NLP solver sensitivity: different solvers or starting points may yield slightly different weights - always verify solver convergence.

Works with

How to cite