## 1.INTRODUCTION

Nowadays, commercial companies increase the profitability with respect to the competitive environment issues, globalization of markets, and shortening of product life cycles, and rapid technological development should have become a pioneer of diversity.In such circumstances, new product development is considered with respect to companies’ important achievements in the field of high technology because of efforts to respond to consumer preferences and new markets. A brand must continuously introduce new products or redesign them. To minimize risk, managers try to succeed in the field of new product marketing research. However, optimal product line design is problematic (Papadimitriou and Steiglitz, 1983). A number of marketing studies have been done applying optimization algorithms with dynamic programming (Kohli and Sukumar, 1990), the beam search (Nair *et al*., 1995), genetic algorithms (Balakrishnan *et al*., 2004), and Lagrangian method (Camm *et al*., 2006). Almost in all optimization methods which solve design problem, a production line has been used for global optimal solution. Reasonable achievements in the field of operation research seem to solve product design issues complexity since expertise in marketing and engineering is requires. In this context, to gain optimal solution for customer preferences is very important for a brand. Diversity may cause too heavy costs for modern technologies and production (Balakrishnan *et al*., 2004). The fact is that optimization is to increase market share and profit in which design lines can take place. Consumer preferences are important for managers and especially for brands that many products have in the market share. To solve such problems, best solutions should be used. It is possible for producers and builders to lead a specific product line. It is, therefore, very important for managers to give a true picture of the wide range of consumers replacing suitable diversity. Inappropriate production line design may not change the expected share from that brand. Thus, taking into consideration various factors to diversity may lead to the optimal solution of market share. This can be done by two methods: using a population-based optimization algorithm or running the algorithm many times with different values for the tuning parameters. The second method is deceitful because constraints should be entered continuously. In addition, all optimization methods of the production line assume that the market is static. And the current companies do not want to introduce one or more new products (Alexouda and Paparrizos, 2001; Steiner and Hruschka, 2003; Tsafarakis *et al*., 2011).

In the area of diversity optimal level of trade markers, we can refer studies conducted by Michalek *et al*. (2011), which they considered production lines design useful for many of new products by using optimization methods. Results indicated that optimal level of products in the production line increase profitability. Yang (2011) used hybrid systems for designing new mobile product and optimization of system. In this study, support vector regression (SVR) and Multi Objective Genetic Algorithm (MOGA) were integrated and the results showed that customer needs should be considered in the design of new products.

Using combined method of particle swarm algorithm and leaping algorithm to optimize industrial production lines in both discrete and continuous modes, Stelios *et al* suggested that using the artificial intelligence would provide better yield for companies in relation to concepts of customer relationship and strategic management of production. Chen *et al*. (2012) used Bayesian Nash equilibrium and particle swarm optimization (PSO) to maximize the diversity of quality. Foster. and Ferguson (2013) designed a car production line using multi-objective optimization genetic algorithm in a study and they showed that this approach improved the car production. Foster *et al*. (2014) used discrete genetic algorithm optimization technique to maximize the diversity of their production. The advantages of this method resulted in saving in calculations and increased brand share in the market. Wang and Yeh (2014) used modified particle swarm algorithm (MPSO) to design the production line. In this paper, they compared the MPSO performance with standard PSO (SPSO), and Genetic Algorithm (GA). The results showed that MPSO is better than SPSO and GA in terms of reliability and rate of convergence. Wu and Chen (2014) designed production lines and pricing for smart phones in a competitive market (with high product diversity). In the study, discrete choice model and genetic algorithms were used to optimize the prices of smart phones. Saridakis *et al*. (2015) introduced new vehicle models in production lines tailored to customer needs in their study. In this study, swarm intelligence mechanism was used to optimize the degree of product differentiation in vehicle models. Sampling was performed among 1,164 passenger car consumers and the results showed that the diversity in models of car production lines led to increased customer satisfaction.

In summary, it can be said that each brand’s product diversity has an important role in the final selection of the brand consumers. The main purpose of the current study was to investigate factors affecting brands share of Kalleh, Pegah, and Sabah according to diversity. The results offer profitable information for cheese product brands (Kalleh, Pegah, and Sabah) on market share and guide their decisions in determining the optimum diversity of the product from every brand. Firstly, the relationship between diversity of every brand and share of every brand in Mashhad market is estimated by seemingly unrelated regression equations. Secondly, the optimal value of every brand’s diversity is obtained using particle swarm optimization algorithm (PSO).

## 2.MATERIALS AND METHODS

### 2.1.The Optimum Diversity of Three Brands (Kalleh, Pegah, and Sabah)

To obtain the optimal value, five modes of diversity (glass, tin, cream, UF 100 to 250 grams, and UF 300 to 500 grams) for three brands (Kalleh, Pegah, and Sabah) were obtained by total of brands’ shares from seemingly unrelated regression model. n_{11}, n_{12}, n_{13}, n_{14}, n_{15}, n_{21}, n_{22}, n_{23}, n_{24}, n_{25}, n_{31}, n_{32}, n_{33}, n_{34}, and n_{35} are 15 states of Kalleh, Pegah, and Sabah diversity and include glass, tin, cream, UF100 to 250 grams and UF 300 to 500 grams for three brands of grocery store. Applying seemingly unrelated regression approach and Stata software were used for factors affecting brand share.(1)(2)(3)

The objective function is the sum of the market shares (Kalleh, Pegah, and Sabah) which is a function of the five modes of diversity of three selected brands, maximized considering the following formula:(4)

Also, restrictions of the sum of the shares in the market according to formula (5) are calculated as (Kohli and Sukumar, 1990; Tsafarakisetal, 2011; Tsafarakis *et al*., 2013):

Applying PSO algorithm, optimized amount of diversity (Kalleh, Pegah, and Sabah) is obtained, and PSO algorithm is executed using MATLAB software. PSO algorithm was used regarding the brands’ diversity.

The implementation of PSO algorithm for this search is following figure:Figure 1

### 2.2.Particle Swarm Optimization

PSO is a meta-heuristic technique. The basic idea was introduced by Eberhart, a computer scientist, and Kennedy, an expert in the field of social psychology in 1995 (Kennedy and Eberhart, 1995). PSO algorithm is based on the production of a random population inspired by social behavior of animals such as bird flocking or fish schooling. The population is called a swarm, and each population member is called a particle (Kennedy and Eberhart, 1995; Eberhart and Kennedy, 1995; He, 2004). The basic idea of PSO is that each particle is moved in search space to find the optimum point and the best situation that is the best individual position of the particle, stored in various stages; this value is called (*P _{best,i}*) at each search step. Particles exchange information about the situation to help each other to find the optimal situation. Each particle uses a particle, having the best match (i.e., the best global situation of the community (

*P*) to adjust its pace). After finding the two best values, the particle updates its velocity and positions according to the following formula (Kennedy and Eberhart, 1995; Eberhart and Kennedy, 1995):(6)(7)

_{best}

${V}_{id}^{t-1}$, ${V}_{id}^{t}$ and ${X}_{id}^{t}$ are the velocity vector in the previous cycle, the velocity vector in the current cycle, and the position vector of particle *i* in the current cycle along the d^{th} dimension, respectively. ${P}_{best,t}^{t}$ is the best position in the history of particle *i* along the d^{th} dimension in cycle t. ${G}_{best}^{t}$ is the best position in the history of all the particles along the d^{th} dimension in cycle t. *c*_{1} and *c*_{2} are acceleration coefficients. *r*_{1} and *r*_{2} are two independent random numbers distributed uniformly in the range of [0, 1]. ω is the inertia weight factor.

### 2.3.Data

The sample of project data of Noushad and Pegah Milk Industry in 2014was extracted from 435 grocery stores in Mashhad. Selected brands were Kalleh, Pegah, and Sabah, the major shares of cheese products of Mashhad market. In terms of cheese variety including glass, tin, cream, UF 100 to 250 grams, and UF 300 to 500 grams for three brands of Kalleh, Pegah, and Sabah, five main features were considered for a diversity of brands.

## 3.RESULTS AND DISCUSSION

### 3.1.Estimating SUR system

Before estimating equations system with SUR method, simultaneous correlation between the residuals should be tested. Therefore, the Brush Pagan LM test statistic was used. In the following table, statistic Brush Pagan is significant at 0.01. The null hypothesis is rejected, and the correlation between the residuals is not rejected. Therefore, equations must be estimated by seemingly unrelated regression.

The results are provided for three brand shares (Kalleh, Pegah, and Sabah) along with interpretation. Based on the findings (Table 2), factors affecting Kalleh brand share were Kalleh glass diversity, Kalleh cream diversity, Kalleh UF 100 to 250 grams , and Kalleh UF 300 to 500 grams with coefficients of 0.527, 0.110, 0.123, and 0.238, respectively, which were positively significant, and only Kalleh tin diversity was not significant regarding Kalleh brand share. Pegah glass diversity, Pegah cream diversity, Pegah UF 100 to 250 grams diversity had significant and negative relationship with Kalleh brand share. Table 1

Pegah tin diversity had not significant effect on Kalleh brand share, and only Pegah UF 100 to 250 grams diversity had positive and significant relationship with Kalleh brand share. Also, Sabah diversity coefficients had not significant relationship with Kalleh brand share.

Considering factors affecting Pegah brand share, Kalleh cream diversity, Kalleh UF 100 to 250 grams, and Kalleh UF 300 to 500 grams with coefficients of -0.057, -0.047, and -0.027 were, respectively, negative and significant, and Kalleh tin and glass diversity was not affective on Pegah brand share. Coefficients obtained from Pegah glass diversity, Pegah cream diversity, Pegah UF 100 to 250 grams diversity, and Pegah UF 300 to 500 grams diversity were 0.084, 0.209, -0.142, and 0.392 respectively, and only Pegah tin diversity coefficient was not significantly correlated with Pegah brand share. Also, Sabah diversity coefficient had negative and nonsignificant relationship with Pegah brand share. Assuming factors affecting Sabah brand share, coefficient of Kalleh diversity was negative, but only Kalleh cream diversity and Kalleh UF 100 to 250 grams were 0.031 and -0.033 significant. Pegah cream and tine diversity had negative significant relationship with Sabah brand share. Among factors affecting Sabah brand share, coefficient of Sabah UF 100 to 250 grams was positively significant.

This study is compatible with previous studies which have evaluated the effect of product diversity on increasing the share of each brand in the market leads, but increasing diversity of its competitors reduces their share in the market (Bayus and Putsis, 1999; Horrace *et al*., 2009; Edward *et al*., 2014).

### 3.2.Optimizing Diversity of Brands Cheese Products

According to the results of PSO algorithm, the optimum diversity values of brands are presented in Table 3. The optimum amount of brands of cheese product diversity included Kalleh glass diversity, Kalleh cream diversity, Kalleh tin diversity, Kalleh UF diversity 100 to 250 grams, and Kalleh UF diversity 100 to 250 gramsobtained, respectively, 1, 0, 1, 2, and 2, showing that some diversity of cheese are optimal product diversity and Kalleh UF diversity 300 to 500 grams, and Kalleh UF which are more than the other modes of diversity, and the optimal value for tin diversity is 0.

The optimum amount of brands of cheese product diversity included Pegah glass diversity, Pegah cream diversity, Pegah tin diversity, Pegah UF diversity 100 to 250 grams, and Pegah UF diversity 300 to 500 grams obtained, respectively, 1, 1, 1, 1, and 1 showing that the diversity scenarios for Pegah brand are one type of diversity with optimum value. For Sabah brand, optimum amount of Sabah glass diversity, Sabah cream diversity, Sabah tin diversity, Sabah UF diversity 100 to 250 grams, and Sabah UF diversity 300 to 500 grams were obtained 0, 1, 0 1, and 1,respectively. In other words, the optimal value is zero for Sabah glass, and cream and optimum value for other diversity scenarios is one.

Maximum diversity for optimum value of diversity between different states is related to Kalleh UF diversity 100 to 250 grams and Kalleh UF diversity 300 to 500 grams.

Also, Kalleh tin diversity could be removed from the consumer market according to optimum amount and required amount. In sum, based on the findings, Kalleh brand should remove tin cheese from the market, and Sabah brand should remove tin diversity and cream diversity from Mashhad markets, and UF diversity should have the most sales.

## 4.CONCLUSION

In conclusion, cheese brands (Kalleh, Pegah, and Sabah) should pay special attention to diversity in the cheese production in order to increase their shares. Results showed that factors affecting Kalleh brand share were Kalleh glass diversity, Kallehcream diversity, Kalleh UF diversity100 to 250 grams, and Kalleh UF diversity 300 to 500 grams, and only Kalleh tin diversity was not significantly effective on Kalleh brand share. Pegah glass diversity, Pegah cream diversity, Pegah UF diversity100 to 250 grams, and Pegahdiversity had significant and negative relationship with Kalleh brand share. Factors negatively and significantly affecting Pegah brand share were Kallehcream diversity, KallehUF diversity 100 to 250 grams, and Kalleh UFdiversity300 to 500 grams, and Kalleh tin and glass diversity was not significantly effective on Pegah brand share. Pegah glass diversity, Pegah cream diversity, and Pegah UF diversity 300 to 500 grams were positively and significantly related; only Pegah tin diversity coefficient was not significantly correlated with Pegah brand share. Also, Sabah diversity coefficient was negative, but not significant regarding Pegah brand share. Kalleh diversity was negatively correlated with factors affecting Sabah brand share; however, only Kalleh cream diversity and Kalleh UF 100 to 250 grams were significantly negative. Pegah cream and tin diversity had negative significant relationship with Sabah brand share. One of the factors having positive and significant effect on Sabah brand share was Sabah UF 100 to 250 grams. The optimum amount of Kalleh product diversity is higher than other competitors in the market. One of the main reasons is that Kallehbrand has a special share in Mashhad market in term of diversity. This study showed that Kalleh UF diversity 100 to 250 grams and Kalleh UF diversity 300 to 500 grams are more than other modes of diversity, and Kalleh brand must remove tin cheese from the market. Pegah’s optimum diversity value for each type of diversity is 1, and Sabah brand should remove tin diversity and cream diversity from Mashhad market, and Uf diversity should have most sales.