**Abstract**

One of the major problems faced in engineering is the selection of the material which is most suitable for the product. Material selection from a large number with diverse mechanical, physical and chemical properties and choosing the best material which is the most satisfying for making the job is a very complex process. Material selection is important as it determines durability, reliability and cost of the product. Selection of suitable material which gives maximum performance with minimum cost is often observed to be a multi-criterion decision-making (MCDM) problem with different objectives. This chapter presents an integrated approach to select the suitable material to be used as base of induction cookware which can give maximum performance with minimum cost. In the integrated approach the weights of the criteria are computed using the cross-entropy method and ranking of the alternatives is done using the different MCDM methods. The methods are further illustrated with an example and the result obtained from different cross-entropy MCDM methods are compared for finding the most suitable method for serving the purpose.

**Keywords:** Cross Entropy method, Different MCDM methods, Comparison, Spearman's Rank correlation coefficient, Coefficient of Determination

### **1. Introduction**

In this present techno-economic scenario material selection poses one of the major challenges in industries. Selection of the improper material adversely affects the reputation of an organization and also reduces the profitability. Selection of the proper material is a step in the process of product design where it aims in increasing the performance with minimum cost. Material selection is also important from the perspective of sustainability of industries [1, 2].

In the recent years, traditional materials were replaced by more advance materials due to their mechanical and chemical properties. The materials were used for manufacturing from complex geometry to long lasting products. With the large number of readily available materials the process of material selection is done with the help of multi-criteria decision-making (MCDM) process.

Moreover, MCDM is the study concerned with optimal decision making and the modelling of deterministic systems. Its focus in the interdisciplinary field of application, clutching a wide range of quantitative techniques. Whereas, Industrial Engineering is about the enhancement, refinement, and installation of integrated systems of personnel, material, and equipment. Industrial engineering is also about processing of the information. MCDM integrated industrial engineering provide a rational approach to engineering and managerial problem solving through deliberate application of scientific methods. In the MCDM model, the set of available materials are called alternatives among which the best material is selected on the basis of the certain properties called criteria.

In practical scenario MCDM addresses the performance of different alternatives on the basis of information and resource limitations of a company or industry or organization, working towards the establishing of beneficial policies. The function of the decision maker is to guide the engineers, managers and administration by processing the information available in the industries.

#### **1.1 Entropy based Multi-Criteria Decision Making (MCDM)**

In today's hi-tech engineering world, MCDM have evolved as one of the most important tools of decision making in a complex situation. MCDM also help in taking decisions in a situation where there is little or no chance of any altercation. In the present socio-economic world where a decision of selecting the best is effected by a large number of criteria, MCDM plays a very important role in such aspects. Decision making is done based on various criteria which might be important equally or not. From the last statement it can be said that every criterion are weighted which help the decision maker in taking the decision. One of the major problems faced in MCDM problem is the assigning of weights to the criterion. Some of the different techniques of assigning weights to the criteria are 5Ws and H method, fuzzy method, cross-entropy method etc. Cook [3] and Vesna Čančer [4] used 5Ws and H technique; Kumar and Gag , Amiri *et al.*, Kemal Vatansever and Yiğit Kazançoğlu , Keshavarz Ghorabaee *et al.*, used fuzzy for determining the weights of different criteria. ZOU Zhi-hong *et al.* [5], Wei Liu and Jin Cui [6], Chia-Chang Hung and Liang-Hsuan Chen [7], Farhad Hosseinzadeh Lotfi and Reza Fallahnejad [8], Yuguo Qi *et al*. [9], Peiyue *et al.* [10], Kshitij Dashore *et al.* [11], Deepa Joshi and Sanjay Kumar [12], Anhai Li *et al.* [13], Harish Garg *et al.* [14], Zhang-peng Tian *et al.* [15], Elham Ebrahimi *et al.* [16], Harish Garg [17], Javier Martínez-Gómez *et al.* [18] used cross-entropy method for determining the weightage of the criteria for solving MCDM problem.

#### **1.2 Application of MCDM in material selection**

With increasing choice of materials and large number of manufacturing process available to the designers, the selection of an optimal material have become more complex and more challenging than before [19]. In order to address the issue of material selection researchers like Ashby proposed MCDM as one of the best tools. Ashby *et al*. [20] have identified three material selection strategies which are (a) free searching based on quantitative analysis, (b) checklist/questionnaire based on expertise capture, and (c) inductive reasoning and analog procedure. A large number of literature exist for selecting the suitable material for a product. Based on the Ashby work a lot of researches is carried out in this respect. Out of which some are reviewed. Milani *et al.* [21] studied the ways in which different criteria transformation techniques effects the result in TOPSIS method for selecting gear material. In the year 2006, R.V. Rao and J.P. Davim [22] developed a combined AHP-TOPSIS

*Comparison of Cross-Entropy Based MCDM Approach for Selection of Material in Sugar… DOI: http://dx.doi.org/10.5772/intechopen.98242*

model for selecting material to be used in non-heat-treatable cover material. Shanian A and Savadogo O. [23, 24], successfully applied TOPSIS in selecting material for a particular product design with maximum performance and minimum cost. Again in the same year Shanian A and Savadogo O. implemented the ELECTRE-I method for selecting material to be used in Bipolar Plates for Polymer Electrolyte Fuel Cells Applications. In this chapter, ELECTRE-I gave the same result with or without negative criterion. In 2008, Sharif Ullah and Harib [25] proposed an intelligent method for selecting material where informations regarding the design configurations, working conditions and design-relevant information were not known. According to Karande and Chakraborty [26], material selection is also an important factor for a product to strive in the competition in market because improper material selection may result in failure to fulfil customer and manufacturer requirements. In 2013a, 2013b, Shankar Chakraborty and Prasenjit Chatterjee [27, 28], observed that in case of material selection the ranking performance of VIKOR is far better than the TOPSIS and PROMETHEE methods. In the chapter the authors also concluded that the best and the worst is solely dependent on the weights of the criteria. They further added that time for selecting the most suited material could be reduced by identifying the criterion with maximum weight. In their second chapter COPRAS and ARAS methods were termed as the most appropriate method for gear material selection as the result obtained from both the method are quite similar and also both the techniques are fool proof techniques.

#### **1.3 Motivation**

Decision making theory plays a vital role where decisions have to be taken in cases the performance parameter differs from each other by a very small margin. There are different decision making methods which takes in account different mathematical concepts such as the best alternative is one which in a best way can compromise the conflicting scenario (VIKOR), the alternative which is farthest from the non-benefit criteria is the best alternative (MOORA), the alternative having the highest relative weightage for the benefit criteria is the best alternative (COPRAS) and so on. Hence when a decision is taken with different MCDM methods, the result may differ for each method. Alternative which is best by one method may not be the best by some other method. In problems like material selection each wrong decision is associated with some penalty. For such cases the weights of the criteria are so calculated that it reduces the penalty for not choosing the actual best alternative instead of choosing the predicted best alternative. Moreover, selecting materials in sugar industry is well known MCDM problem. But, the literatures fail to answer which method to apply for material selection and the risk involved for choosing a method. The literatures also do not explain the accuracy degree to which two or more selection methods would agree to the same decision. The main aim of this chapter is find a material suitable for manufacturing equipment in the sugar industry by different MCDM methods and also to find the degree to which all the methods would agree to the decision.

#### **1.4 Novelties**

Lot of researchers have worked in the field of MCDM and developed novel approaches for precisely selecting alternatives. Some of the novelties developed in this chapter are as follows:

1.Application of CE integrated MCDM approaches are used for selecting material in sugar industry.


#### **1.5 Structure of the chapter**

The chapter is organized into 7 sections. The first section is introduction which describes the importance of the material selection and the comprehensive literature related to the topic. Section 2 describes the preliminary concept of the methodologies used for the study. Section 3 summarises the steps of the MCDM methods and section 4 describes the case study that is considered for the present study. Section 5 is the comparative study of the result obtained from various MCDM methods. Section 6 discusses the summary of the findings and section 7 concludes the chapter.
