Comparison of Multi Criteria Decision Making Methods SAW and ARAS: An Application to Performance of Indian Pharmaceutical Companies

While assessing the performances of companies, the decision makers to take not only a single criterion for making the right decisions in to account, but also a number of other relevant criteria that could affect the performance. Because when it is necessary to make the best selection among several option, Multiple-Criteria Decision Making (MCDM) methods are used. This study is to provide insight in to the applicability of method Simple Additive Weightings Method (SAW) and Additive Ratio Assessment (ARAS) method under MCDM techniques to evaluate the performance of Indian Pharmaceutical companies during the study period 2006-2019. The seventeen evaluation criteria’s were used in the application. The constructed model was analysed using both SAW and ARAS method. The study results showed that the best performance belongs to Glico Smith Kline Pharma Limited in SAW method and Sun Pharmaceutical Industries Ltd in ARAS method and worst performance belongs to Ranbaxy Laboratories Limited in both methods. By comparison, both methods revealed the similar rankings of companies during the study period.


Introduction
The Indian industrial sector has undergone regulatory changes as the consequences of the economic reforms between 1988 and 1991. India moved away from 'control' era towards the "open" economy model. It should bring out a dramatic change in Indian Pharmaceutical companies. Firm's performance is dependent on both financial and non-financial conditions of the firm. For this purpose, profitability, assets utilization, liquidity, working capital efficiency, long-term solvency, market value and foreign trade measures are grouped under financial indicators and other indicators such as sales and marketing strategy, consumer satisfaction, technological issues, human resources and growth variables are grouped under non-financial indicators. However, in this study, an attempt has been made to analyse the financial indicators only which help to measure the financial performance of selected Indian Pharmaceutical companies.
In many real world decision problems, a decision maker has set of multiple conflicting objectives. The decision must be compared according to many criteria (Turskis et al., 2009). The problem of a decision maker is to evaluate a finite set of alternatives in order to find the best one, to rank them from the best to worst or to describe how well each alternative meets all the criteria simultaneously . There are many methods of determining the ranking of a set of alternatives in terms of a set of decision criteria. In a multicriteria approach, the researchers to build several criteria using several views. Multi-Criteria Decision-Making(MCDM) is one of the most widely used decision methodology used in science, business and government and help to improve the quality of decisions by making the decision making process more efficient. The MCDM represents one of the fastest growing fields of operation research. It has over the time bound its application in solving various decision making problems.

Indian Pharmaceutical Industry-Sectorial Background
Published by SCHOLINK INC. India is a leading exporter of generic drugs across the globe and as demand expands across the globe, Indian pharmaceutical industry aspires to become the world's largest supplier of drugs by 2030.
Indian pharmaceutical companies played an important role in the global fight against the coronavirus pandemic that had affected over 3 million people across the world. Hydroxychloroquine has been identified by the US Food and Drug Administration as a possible treatment for the . India, one of the largest producers of anti-malarial drug Hydroxychloroquine, has seen spurt in demand in recent weeks. India has sent the drug to over 50 countries over the last few weeks including United States.
However, in the last couple of years, Indian pharma industry has faced several challenges such as higher level of customer consolidation, increased competition and number of product approvals, increased pricing control, transient impact of demonetisation and continued to face destructions from regulatory bodies. Further, our strong position as a global supplier of high quality and affordable medicines has also been impacted due to recent compliance challenges and low productivities. The profits are under severe pressure. Hence, the continued viability of Indian pharma industry is of strategic concern for the government, industry and stakeholders.

Justification for the Study
Financial performance of firms is subject to continuous monitoring. Good financial conditions leads to growth and development and guarantee satisfaction to all stakeholders. On the other hand poor performance may lead to negative consequences for the achievement of goals of all the stakeholders involved. An evaluation of financial performance is a multidimensional assessment based on multiple criteria including profitability, asset utilisation, liquidity, working capital efficiency, solvency and market value measures. For this reason, developing a ranking of entities so as to make comparisons among them by using Multiple Criteria Decision Making (MCDM). While taking a decision, there might be many alternatives with distinct criterions. The MCDM is an approach designed for the evaluation of problems with a finite or an infinite number of choices.

MCDM Methodology
The Multiple Criteria Decision Making is defined as the process of selecting one from set of available alternatives or ranking alternatives based on a set of criteria. The MCDM methods transform multiple criteria optimization in a single criterion decision-making optimization, which is much easier to solve.
There are different phases in MCDM process which includes criteria weight determination, normalization, aggregation and selection. A typical MCDM problem can be presented in the following form.
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In literature, various types of MCDM techniques like SAW, ARAS, TOPSIS, VIKOR, GRA, ELECTREE, MOORA and PROMETHEE are used to assess the performance of manufacturing companies by using ratios derived from the information contained in the financial statement. With such an approach one of the simplest and widely used MCDM method for evaluation and ranking of alternative is Simple Additive Weighting (SAW) and Additive Ratio Assessment (ARAS) methods.
Hence, in this study an attempt has been made to ranking selected Indian Pharmaceutical companies by using SAW and ARAS method.

Simple Additive Weighting (SAW) Method
Simple Additive Weighting (SAW) Method probably the simplest, best known and formerly often used MCDM method (Dragisa, 2013). The SAW method uses a simple aggregation procedure, which is presented using the following formula:

…… (3)
where Q i is the overall ranking index of i th alternative; w j is the weight of j jth Criterion, r ij is normalised the performance of i th alternative with respect of j th criterion, i=1, 2, …..m; and j=1,2, …..n.
In SAW method, the alternatives are ranked on the basis of their Q i in ascending order, and the alternative with the highest value of Q i is the best ranked. The best ranked, or the most preferable, alternative, based on the SAW method, can be determined using the following formula: Where r ij is the normalised performance rating of the i th alternative on j th criteria.
Step 4: Calculated the weighted normalised decision matrix.
The weighted normalised performance ratings [V = {V ij }] as calculated as follows: Where v ij is weighted normalised performance rating of i th alternative in the relation to j th criterion.
Step 5: Calculate the overall performance index for each alternative: The overall performance index S i, for each alternative can be calculated as the sum of weighted normalised performance ratings, using the following formula.
In the case of evaluating the alternatives, the degree of utility for each alternatives can be calculated using the following formula.

Q i =
Where Q 1 is degree of utility of i th alternative, and S o is overall performance index of optimal alternative, and it is usually 1. The largest value of Q i is the best and the smallest one is the worst.

Weighting by Entropy Method
Entropy has become an important concept in the social sciences as well as the physical Sciences (Capocelli & De Luca, 1973). In information theory, entropy is a criterion for the amount of uncertainty presented by the discrete probability distribution P i (Jaynes, 1957). Entropy is one of the most widely used objective waiting methods. If the data of the decision matrix is available then, the entropy method can be very useful to evaluate the weighting (Deng et al., 2000). The entropy concept was defined as a measure of uncertainty by Shannon (1948). This measure of uncertainty is given by Shannon (1948) with the following equation:

…… (7)
where K is a constant coefficient. Since the entropy expression is first found in statistical mechanics, it is called entropy of P i probability distribution. When all P i values take P i = and S has the greatest uncertainty.
Entropy can be used as the tool for evaluating criteria (Zeleney, 1974; Nijkamp, 1977)  criterion is ignored. The entropy method measures the uncertainty in the data set and measures the variance of the data set with this uncertainty value. For each criterion, the value of the variation value in the total variance gives the weight value of the criterion. The decision matrix for a MCDM problem comprises a definite quantity of information; entropy can be utilised as an implement in criteria evaluation.
The process of determining the weighted value for the criteria by the entropy method is summarised as follows: Let mxn-dimensional decision matrix of a decision-making problem with m alternatives and n criteria be given as follows: Where, X ij is the success value of i th alternative, in the j th criterion, i= 1, 2, .. Step 1: Since the criteria have different scales, a normalisation process is performed in order to make and evaluation. R = [r ij ] mxn normalised decision matrix calculated by the following formula.
The aim of normalisation is to obtain same scale for all criteria and so to make comparison between them. (Caliskan, 2013).
Step 2: The uncertainty measures for each criterion, entropy value, is found by the following equation: Where K = is a constant coefficient and 0 ≤ e j ≤ 1 are guaranteed. The value of e j is the uncertainty measure of the j th criterion or in other words, the entropy value.
Step 3: The degree of diversification d j for each criterion using the entropy value of the average information contained by the outcomes of criterion j can be obtained as Step 4: Finally, the weight values of the criteria are calculated by proportioning the degree of diversification of each criterion to the sum of the degree of diversification: as addition is clear.

Sample Selection
The pharmaceutical industry has been chosen for this study because it is one of the important and fastest growing sectors in the Indian economy. Among 258 pharmaceutical companies in India, the selection of sample companies is based on the following criteria; companies which are listed in BSE; companies which provide financial data for the study period of 13 years and companies which have a market capitalisation above Rs.15,000 crores. On the basis of the above criteria ten companies listed on BSE are used as alternatives or Decision-Making Units (DMU) that includes leading pharmaceutical manufacturers operating in Indian pharmaceutical industry. The list of companies considered in the analysis is given in the Table 1 along with DMU number.

Results
In this section, in order to perform objective conclusions in terms of the applicability of SAW and ARAS methods, the influence which the weights of criteria, the used approaches and the applied normalization procedure have on the selection of the most appropriate alternative and obtained ranking orders of alternatives is taken in to consideration. This study presents the ranking results of selected Indian pharmaceutical companies based on objective criteria. These criteria and their sub-criteria adopted in this study are shown in Table 2. The financial ratios used in the study were selected from those which could provide information about earning capacity, utilization of resources, financial soundness and paying ability, debt coverage, management efficiency and investment valuation figures of the company.

SAW Method
The Indian pharmaceutical companies that have decision points, the superiority of which has to be determined through the constituted decision matrix lines, while in the columns, occur in the financial performance ratios which are the evaluation criteria's. Ten decision making units (alternatives) and 17 evaluation criteria's were used in the research. First, the standard decision matrix was set with dimensions (10x17) for the SAW method obtained from Indian pharmaceutical companies. The decision matrix related to the Indian pharmaceutical companies is presented in Table 3. weights obtained on the basis of entropy method are shown in Table 2. The procedure for obtaining weights of each criteria presented in Table 10 to 12. The magnitude of the weight value reflects the importance of the criterion. It is observed from  Table 4. After determining weights of the criteria and normalized decision matrix, then weightening of the normalized data matrix is done by multiplying normalized data matrix with the weight vector and presented in Table 5. The relative importance of the each alternatives based on SAW method according to the formula (3) and presented in Table 5. The ranking of the alternatives are given as per the value of relative importance given in the Table 5. From the table it can be seen that the three best pharmaceutical companies on the basis of SAW method are Glaxo Smith Kline Pharma Limited, Sun Pharmaceutical Industries Limited and Dr.Reddy's Laboratories Limited. It is also understood from the Table 5 that the least performer belongs to Ranbaxy Laboratories Limited during the study period.

ARAS Method
First of all, the decision matrix related to the Indian pharmaceutical companies is along with the optimal alternative such as maximum value in case of benefit criteria and minimum value in case of cost criteria has been identified and presented in the Table 6. The next step in ARAS method is normalization of decision matrix in order to eliminate the scale effect by using linear scale normalization-sum method and presented in Table 7.  While evaluating alternatives, it is not only important that the best ranked alternative should be determined, but also that the relative performances of the considered alternatives should be determined in relation to the best ranked alternative. For this purpose, it is needed to compute the degree of utility (Q i ) of each alternative based on ARAS method according to the formula (5) and presented in Table 9.
The considered alternatives are ranked by ascending Q i , i.e., the alternatives with the higher values of Q i , have a higher priority (rank) and the alternative with the largest value of Q i , is the best placed. The ranking of the alternatives are given as per the value of relative importance in the Limited. It is also understood from the Table 9 that the least performer belongs to Ranbaxy Laboratories Limited during the study period.

SAW and ARAS Methods-A Comparison
The comparison of results of SAW and ARAS methods are presented in Table 10.  It is inferred from the Table 10 that both MCDM methods, SAW and ARAS, revealed same rankings of companies in Indian pharmaceutical industry during the study period except two changes. According to SAW method the first rank is given to Glaxo Smith Kline Pharma Limited whereas in ARAS method, the first rank given to Sun Pharmaceutical Industries Ltd and the Cipla Limited given 6 th rank in SAW method, but in ARAS method, it is given 5 th rank according to their performance. Except the above changes, all other companies are obtained similar rankings according to SAW and ARAS method during the study period.

Conclusion
The

Note
Note 1. The process of determining the weighted value for the criteria by the entropy method is as follows: