BWM - Best-Worst Method

Overview

BWM requires only 2n−3 pairwise comparisons (BO and OW vectors) instead of n(n−1)/2 in AHP, greatly reducing cognitive burden. The consistency indicator ξ* ∈ [0,1] measures how well the comparisons satisfy the transitivity requirement - ξ*=0 is perfectly consistent. The reference consistency index (Table 1 in Rezaei 2015) gives maximum acceptable ξ* per n.

Output

Weight, higher is better

Data

Crisp, expert input required

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Expert-driven weighting, Supplier selection

How it works

1. 1

   Identify Best (B) and Worst (W) criteria from expert.

   $$B\in \{c_j\},W\in \{c_j\},B\ne W$$

   Rezaei 2015, p.51 Sec.2.1

2. 2

   Pairwise vectors A_B = (a_{B1},…,a_{Bn}) and A_W = (a_{1W},…,a_{nW}) on 1-9 scale.

   $$A_B=(a_{B1},\dots ,a_{Bn}),A_W=(a_{1W},\dots ,a_{nW}),a_{ij}\in \{1,2,\dots ,9\}$$

   Rezaei 2015, p.51 Eqs.(1)-(2)

3. 3

   Solve the original nonlinear minimax model for weights and consistency.

   $$\min \xi \text{s.t.}|\frac{w_B}{w_j}-a_{Bj}|\le \xi ,|\frac{w_j}{w_W}-a_{jW}|\le \xi ,\sum w_j=1,w_j\ge 0$$

   Rezaei 2015, p.52 Eqs.(3)-(4)

Fits when / Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• ξ* > 0.30: comparisons are highly inconsistent - re-elicit from the decision-maker.

Works with

How to cite