Comparative Study of GRA and MOORA Methods: A Case of Selecting TFO Machine

1. Introduction

Multi attribute decision-making (MADM) is a special branch of operation research which deals to take the decisions in presence of multiple criteria from the set of alternatives. The MADM is being used in many fields and applications of engineering and science. The MADM methods are becoming more important as potential tools for solving complex real world problems in which multiple criteria involves in the selection process. Many MADM methods are reported in the literature for selection, evaluation, and ranking of alternative in decision making problem; a few important methods are; Simple Additive Weighing (SAW) method (Fishburn, 1967), Analytical Hierarchy Process (AHP) method (Saaty, 1980), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method (Hwang and Yoon,1981), Grey Relational Analysis(GRA) method (Deng, 1989), Preference Ranking Organization method for Enrichment Evaluations (PROMETHEE) method (Brans and Vincke,1985), Elimination Et Choice Translating Reality (ELECTRE) method (Roy, 1991), COmplex Proportional ASsessment (COPRAS) method (Zavadskas et al., 1994), VIšekriterijumsko KOmpromisno Rangiranje (VIKOR) method (Opricovic, 1998;2011), Multi Objective Optimization on the basis of Ratio Analysis (MOORA) method (Brauers, 2004; Brauers and Zavadskas,2006), Additive Ratio Assessment (ARAS) method (Zavadskas and Turskis, 2010), Preference Selection Index method (Maniya and Bhatt, 2010).

A typical assessment and selection of alternatives based on multiple attribute is a multi-stage process as described in the following.

• Stage 1 - Assessment of Alternative and Attributes: The solving of any types of MADM problems start with the defining alternatives and these alternatives are specified by different criteria. Let, A = {A_i for i = 1,2,3,…n} be a set of alternative, C = {C_j for j =1,2,3,…,m} be a set of decision criteria or attributes, W = {W_jfor j =1,2,3,…,m } be a set of weight of criteria C_j and X_ij = Performance measure of alternative A_i when it examined with criteria C_j. These considered alternatives and selection criteria are represented in the form of data or decision matrix.

• Stage 2 - Normalization of Attributes Measures: The process of transforming data from its value into a range of zero and one is called normalization. In multi attribute decision-making problems, attributes or criteria have different performance measuring units. Hence, a normalization procedure is required in MADM approach to transform performance rating with different data measurement unit in a decision matrix into a compatible unit.

• Stage 3 - Define the Weight of Attributes: The assignment of weights plays a key role in the decision making process, in which the weights indicate the importance of each attribute with attributes. The weights indicate the decision makers preference about the attributes importance relative to others. In general, attribute weights are denoted by W_j. In most of MADM methods employ AHP method or Entropy method for determination of weights of attributes.

• Stage 4 - Aggregation: An aggregation procedure is used to combine normalized decision matrix and attributes weight W_j to achieve an overall preference value for each alternative on which the overall ranking of alternative is based.

• Stage 5 - Ranking and Selection of Alternatives: Finally¸ all the alternatives will be ranked according to the overall preference value calculated in stage-4. Finally, alternative is ranked first whose overall preference value is the highest and it will be considered as the best alternative for a given application. Finally, general methodology of MADM methods is shown in the Figure 1.

Figure 1.

Methodology of MADM methods