ROV - Range of Value method

Overview

ū_i ∈ [0,1]. u⁺ and u⁻ represent optimistic (best weight assignment) and pessimistic (worst weight assignment) utilities. Their average ū provides a robust ranking that accounts for uncertainty in the exact ordering of criterion importance. ROV is particularly useful when the decision-maker knows the criterion weights but is uncertain about their exact values.

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

   Min-max normalisation per criterion direction.

   $$r_{ij}=\{\begin{array}{ll}(x_{ij}-{\min }_i{x}_{ij})/({\max }_i{x}_{ij}-{\min }_i{x}_{ij})& j\in J^{+}\\ ({\max }_i{x}_{ij}-x_{ij})/({\max }_i{x}_{ij}-{\min }_i{x}_{ij})& j\in J^{-}\end{array}$$

   Yakowitz 1993, p.1604 Eq.(1)

2. 2

   Best-case u^+_i = Σ_{j∈J+} w_j r_ij + Σ_{j∈J−} w_j (1−r_ij).

   $$u_i^{+}=\sum _{j\in J^{+}}{w}_j{r}_{ij}$$

   Yakowitz 1993, p.1605 Eq.(2)

3. 3

   Worst-case u^−_i.

   $$u_i^{-}=\sum _{j\in J^{-}}{w}_j{r}_{ij}$$

   Yakowitz 1993, p.1605 Eq.(3)

4. 4

   Range of Value u_i = (u^+_i + u^−_i)/2 and descending ranking.

   $$u_i=\frac{u_i^{+}+u_i^{-}}{2}$$

   Yakowitz 1993, p.1605 Eq.(4)

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

• Constant criterion column: normalisation denominator is zero - check E-4.

Works with

How to cite