Development of TOPSIS Techniques

Transcription

1 Chapter 3 Development of TOPSIS Techniques 3.1 THE STANDARD TOPSIS The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) was originally proposed by Hwang and Yoon[26]. The standard TOPSIS method attempts to choose alternatives that simultaneously have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. The positive ideal solution maximizes the benefit criteria and minimizes the cost criteria, whereas the negative ideal solution maximises the cost criteria and minimizes the benefit criteria. TOPSIS makes full use of attribute information, provides a cardinal ranking of alternatives and does not require attribute preferences to be independent[13]. To apply this technique, attribute values must be numeric, monotonically increasing or decreasing, and have commensurable units. 3.2 THE STEPWISE PROCEDURE FOR IMPLEMENTING TOPSIS[26]: After forming an initial decision matrix STEP 1: Form the normalised decision matrix = =1,2, ;=1,2,.. -(3.2.1) where and are original and normalized score of decision matrix, respectively. P a g e 18

2 STEP 2: Construct the weighted normalized decision matrix = (3.2.2) where is the weight of the criterion. STEP 3: Determine the positive ideal and negative ideal solutions. The positive ideal solution is given by ={,,. }where =max ;min (3.2.3) The negative ideal solution is given by =,, (3.2.4) where =min ;max STEP 4: Calculate the separation measures for each alternative. The separation measure from positive ideal solution is =, i=1,2,3,.m (3.2.5) The separation measure from negative ideal solution is =, i=1,2,3,.m (3.2.6) STEP 5: Calculate the relative closeness to the ideal solution given by = (3.2.7) P a g e 19

3 where 0< <1 Select the alternative with closest to DEVELOPMENT OF TOPSIS AND APPLICATIONS: The recent trend of TOPSIS papers has shifted towards applying the combined TOPSIS rather than the stand alone TOPSIS. These combinations have made the classical TOPSIS method more representative and workable when handling practical and theoretical problems. Tools commonly used to extend the TOPSIS method include the fuzzy set approach, group decision making approach, Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), entropy method, mathematical programming and genetic algorithm. The fuzzy set approach seems to be the most commonly used method in TOPSIS. The classical TOPSIS assumes that alternative ratings and criteria weights are crisp numbers whereas the fuzzy TOPSIS utilizes linguistic variables and fuzzy numbers to handle problems with imprecise information. TOPSIS sometimes involves group decision making as groups of experts make most crucial and significant decisions in organizations. Decisions made collectively tend to be more effective than decisions made by an individual. Many authors have used the AHP method in combination with TOPSIS to determine criteria weights. The ANP, the more general form of AHP is sometimes used. Moreover, the TOPSIS method has been combined with multi objective mathematical programming to identify the optimal compromise solution from the optimal solution set. A hybrid integration of entropy method with TOPSIS to determine criteria weights has also been developed. The TOPSIS performance has been compared with other MCDA, MCDM methods including AHP, ELECTRE, PROMETHEE, P a g e 20

4 VIKOR, DEMATEL and SAW. Since 2010, there has been a considerable growth in the number of papers published on TOPSIS. Literature review for fuzzy TOPSIS using SCOPUS gives 4,010 published papers. After 2006, usage of fuzzy TOPSIS increased dramatically. In 2013 alone, 154 articles use the fuzzy TOPSIS approach.[9]. Fuzzy TOPSIS based studies can be grouped into three groups. The first group develops new fuzzy TOPSIS methodologies or modify the existing approaches.notable contributions include that where Ye and Li[44] modify TOPSIS method using possibility theory. Kahraman et al[10] develop a fuzzy hierarchical fuzzy TOPSIS method. Chen and Wei[15] extend Chen and Hwang s[12] methodology and use linguistic terms expressed as fuzzy triangular numbers to describe the weights of each criterion. Shahanagi et al[39] use a new fuzzy group TOPSIS approach for vendor selection. The second group uses the existent approaches in a specific problem area. Kannan et al[28] use fuzzy TOPSIS for green supplier ranking. Wang[43] evaluates financial performance of Taiwan container shipping companies while Chu[16] uses fuzzy TOPSIS to solve facility location selection problem. The third group combines different decision making techniques and develops hybrid methods. Mandic et al[34] develop an integrated fuzzy muticriteria model for assessing financial performance of banks. Tsaura et al[42] use a hybrid approach to evaluate the service quality of airlines. Fuzzy TOPSIS has been extended using intuitionistic fuzzy numbers, hesistant fuzzy sets and type 2 fuzzy sets. P a g e 21

5 Behzadian et al[3] provide a state-of-the-art survey of TOPSIS applications in order to taxonomise the research on TOPSIS applications and methodologies. The classification scheme contains 266 scholarly papers from 105 journals since the year With respect to application, supply chain management and logistics was found to be the most popular topic. This was followed by design, engineering and manufacturing systems and thirdly by business and marketing management. Health, safety and environment management, Human resources management, energy management, chemical management and water resource management relatively contained a small portion of TOPSIS applications. P a g e 22