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

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

Kalpesh D. Maniya (C. K. Pithawalla College of Engineering and Technology, India)
DOI: 10.4018/978-1-4666-9885-7.ch006
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Abstract

This chapter present the study of comparative assessment of Grey Relational Analysis (GRA) method and Multi Objective Optimization on the basis of Ratio Analysis (MOORA) method with considering two distinct weight determination methods named Analytical Hierarchy Process (AHP) method and Entropy method for ranking and selection of Two For One (TFO) machine used in Textile industry. TFO machines are used in textile industry to improve the properties of yarn by twisting. The ranking performance of GRA method and MOORA method is compared with each other with reference to ranking order obtained using different weight determination method and it explore effectiveness and simplicity of MOORA method for selection of best TFO machine.
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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 = {Ai for i = 1,2,3,…n} be a set of alternative, C = {Cj for j =1,2,3,…,m} be a set of decision criteria or attributes, W = {Wjfor j =1,2,3,…,m } be a set of weight of criteria Cj and Xij = Performance measure of alternative Ai when it examined with criteria Cj. 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 Wj. 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 Wj 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

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