Grey Relational Analysis - One of the popular method used for Multi-criteria Optimization

Grey Relational Analysis

Grey relational analysis (GRA) or Grey analysis is a technique by measure the degree of estimate among sequences relating to the grey relational grade (GRG). 

It consist of four steps where normalizing of the input data is required, calculation of deviation sequence, estimation of grey relational coefficient and final the grey relational grade (GRG) will be estimated based on the weights. The weights can be calculated by using AHP method and CRITIC method also. 

The different steps used in the GRA method will be discussed here. The video tutorials and the solved case study spreadsheets  will be also shared. 

Steps in Grey relational analysis

Step 1 Normalizing the data - here the data consists of different dimensions, the target here the data need to normalized in between 0 to 1.

For Higher the better

For Lower the better

Step 2 Determining the deviation sequence by using the formula below

Step 3 Estimating the Grey relational Coefficient (GRC) by using the formula. 

Here the coefficient of determination or distinguishing coefficient values lies between 0 to 1. Most of the researchers consider the distinguishing coefficient value for GRA is 0.5, because to weaken the influence if the deviation sequence Delta_max gets too big. 

Step 4 the final step is grey relational grade (GRG) calculated by using this formula

Here, some of the researchers they estimate the weights by using some subjective weights methods like AHP method or objective weight methods like CRITIC. Some they also consider equal weights. If equal weights are consider w_k = 1.

Case study tutorial - step by step procedure for grey relational analysis - Milling of Aluminum Hybrid Metal matrix Composites

Download the Excel file, which is solved in the video