OCRA Method

Operational Competitiveness Rating Analysis

1994 Celik Parkan 4 Steps

OCRA (Operational Competitiveness Rating Analysis) is an MCDM method used to evaluate and rank alternatives based on operational competitiveness, particularly when alternatives are evaluated using input (cost) and output (benefit) criteria.

Video Demonstration

Step-by-Step Algorithm

Calculated cell

Source cells in formula

Form the decision matrix

Create the decision matrix with $m$ alternatives and $n$ criteria :

\[ X=\begin{bmatrix} x_{11} & x_{12} & \cdots & x_{1n}\\ x_{21} & x_{22} & \cdots & x_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ x_{m1} & x_{m2} & \cdots & x_{mn} \end{bmatrix} \]

$x_{ij}$ presents the performance value of ith alternative on jth criterion, m and n are the numbers of alternatives and criteria respectively.

Alternative	$C_1$	$C_2$	$C_3$
$A_1$	10	20	30
$A_2$	15	25	35
$A_3$	25	15	35

Criterion type: C₁ Output (Benefit) C₂ Input (Cost) C₃ Output (Benefit)

Weights: $w_1=0.7279$ · $w_2=0.2009$ · $w_3=0.0712$ (Entropy method)

Aggregate performance

Formula

First, calculate the aggregate performance for the input (cost) criteria :

$$ I_i=\sum_{j=1}^{p}w_j\frac{x_{ij}-\min_i x_{ij}}{\min_i x_{ij}} $$

For the output (benefit) criteria, calculate :

$$ O_i=\sum_{j=1}^{q}w_j\frac{\max_i x_{ij}-x_{ij}}{\min_i x_{ij}} $$

Here, $I_i$ represents the aggregate input performance and $O_i$ represents the aggregate output performance of alternative $A_i$.

This step measures the relative disadvantage of each alternative for input and output criteria.

Alternative	$I_i$ (Input: $C_2$)	$O_i$ (Output: $C_1, C_3$)
$A_1$	0.0670	1.1038
$A_2$	0.1339	0.7279
$A_3$	0.0000	0.0000

Reference values: $C_1$: $\max=25$, $\min=10$ · $C_2$: $\min=15$ · $C_3$: $\max=35$, $\min=30$

Linear performance

Formula

The aggregate performances are converted into linear performance values by subtracting the minimum value :

$$ I_i^{\prime}=I_i-\min_i(I_i) $$

$$ O_i^{\prime}=O_i-\min_i(O_i) $$

The best performance in each group is assigned a value of zero, providing a common reference point for the alternatives.

Alternative	$I_i^{\prime}$	$O_i^{\prime}$
$A_1$	0.0670	1.1038
$A_2$	0.1339	0.7279
$A_3$	0.0000	0.0000

Minima subtracted: $\min(I_i)=0.0000$ (at $A_3$) · $\min(O_i)=0.0000$ (at $A_3$)

Global performance and rating

Formula

Combine the linear input and output performances to obtain the global performance :

$$ G_i=I_i^{\prime}+O_i^{\prime} $$

The OCRA rating is obtained by comparing the global performance values :

$$ G_i>G_k \quad\Longrightarrow\quad A_i >A_k $$

A lower $G_i$ indicates less overall disadvantage, meaning better performance. The alternative with the smallest $G_i$ is ranked first.

Alternative	Global Performance ($G_i$)
$A_1$	1.1708
$A_2$	0.8618
$A_3$	0.0000

Global performances (lower is better): $G_3=0.0000 < G_2=0.8618 < G_1=1.1708$
Final ranking: $A_3 \succ A_2 \succ A_1$

OCRA Algorithm Flowchart

START

Form the decision matrix

Aggregate performance

Linear Performance

Global performance and rating

END