A hybrid method using experiment design and grey relational analysis for multiple criteria decision making problems
Introduction
There are many multiple criteria decision making (MCDM) problems in manufacturing industry. Different from single criterion decision making problems, in multiple criteria decision making problems, a decision maker (DM) has to choose the most appropriate alternative that satisfies the evaluation criteria among a set of candidate solutions. For that the evaluation criteria are frequently in conflict with each other, how to make a scientific decision becomes a difficult problem [1].
A number of methods have been proposed for solving MCDM problems such as scoring models [2], simple additive weighting [3], axiomatic design [4], analytic hierarchy process (AHP) [5], technique for order preference by similarity to ideal solution (TOPSIS) [6], preference ranking organization method for enrichment evaluation (PROMETHEE) [7], and multi-objective optimization on the basis of ratio analysis (MOORA) [8]. Almost all the methods above mentioned require the relative importance of each criterion which is supplied by weights. The result is sensitive to the change of weights [9], i.e., different weights will produce different results. When weight changes, the whole mathematical calculation process has to do all over again, which may be impracticable and ineffective for DMs, who may not have a strong mathematical ability.
As decision making requires multiple perspectives from different people, most organizational decisions are made in groups. To make the group decision making process as efficient and effective as possible, multi-criteria group decision making (MCGDM) method is proposed. In practice, subjective and objective information may need to be processed simultaneously in MCGDM problems that may contain uncertainties. Aiming at the uncertainties of subjective information and objective information, based on fuzzy sets [10] and fuzzy logic [11], several fuzzy MCGDM methods have been proposed and proved to be very effective technique to increase the level of overall satisfaction in MCDM problems [12], [13], [14]. However,the calculation of fuzzy MCGDM method is difficult. So a new method has been proposed in this work which is easy to use and adaptable.
Grey system theory provides a mathematical means to deal with poor, incomplete, and uncertain information. It is first developed by Deng [15], [16],to study the uncertainties in system models, to help in prediction and decision making.In grey systems theory, according to the degree of information, if the system information is fully known, the system is called white systems, if the information is unknown, it is called black systems. A system with information known partially is called a grey system. The grey system theory includes five major parts: grey prediction, grey relational analysis, grey decision, grey programming and grey control [16], [17]. Grey relational analysis (GRA) as an important part, reflects the trend relationship between an alternative and the ideal alternative, but it cannot reflect the situational relationship. In order to improve this situation, some steps of the GRA have been modified just as the normalized formula, the ideal and non-ideal alternative had been considered at the same time, etc. [18], [19].
In this paper, a new hybrid MCDM method using design of experiment and grey relational analysis, also called DoE-GRA method, is introduced. Three different MCDM problems in real-time manufacturing applications will be solved using the DoE-GRA method. According to the results, the DoE-GRA method is featured by less sensitive to weight changing, it is simple and fast calculation, robust and practical. It could help the DM get the most appropriate alternative in complex MCDM problems.
The remaining sections of the paper are organized as follows: Section 2 presents the methods;Section 3 describes the applying process of the DoE-GRA method in detail; Section 4 demonstrates the applicability and potentiality of the DoE-GRA method in solving different MCDM problems.Finally, conclusions and future works are discussed in Section 5.
Section snippets
Grey relational analysis
In this paper, among the most popular MCDM methods, the GRA method is selected because of its advantages compared with others. Table 1 depicts the comparative performance of some of the most widely used MCDM methods with respect to their computational time, simplicity, mathematical calculations involved and stability [1], [8]. From Table 1, it is revealed that in all aspects, the GRA method clearly outperforms the other MCDM methods which proves its universal applicability and flexibility as an
Example of the application process of DoE-GRA method
An illustrative example is presented to particularize the DoE-GRA application process and validity of its result in the rapid prototyping (RP) process selection. RP process can be defined as a group of techniques used to quickly fabricate a scale model of a part or assembly using three dimensional computer-aided design data. Byun and Lee developed a decision support system for selection of a RP process using the modified TOPSIS method [26]. Chakraborty [8] applied MOORA method and İç [6]
Applications to other MCDM problems
In order to demonstrate the applicability and potentiality of the DoE-GRA method in solving different MCDM problems, the following illustrative examples, flexible manufacturing systems (FMS) and automated inspection systems (AIS) selection problem, are analyzed in this section.
Discussion and conclusion
It is very important for DMs to make a choice among varies alternatives in the manufacturing industry. It is also a MCDM problem. Some methods, such as AHP, TOPSIS, GRA, PROMETHEE and MOOR, are usually used for solving this kind of problems. This paper proposes a new MCDM method, i.e., the DoE-GRA method. Design of experiment and grey relational analysis are used together to identify critical criteria and their interactions of a MCDM problem by fitting a polynomial to the experimental data in a
Acknowledgements
The author is grateful to the editor and the anonymous referees for their insightful and constructive comments and suggestions, which have been very helpful for improving this paper. This research was supported by the National High Technology Research and Development Program of China (863 Program) No. 2011AA09A104.
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