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# Using a Combined Method of Hierarchical Analysis and Monte Carlo Simulation in Order to Identify and Prioritize the Target Market Selection Criteria

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Applied mathematics in Engineering, Management and Technology 2 (2) 2014:466-475 www.amiemt-journal.com

Using a combined method of hierarchical analysis and Monte Carlo simulation in order to identify and prioritize the target market selection criteria (Case study: Food distribution companies of Mashhad-Iran)
Amir kariznoee
Ph.D. student of Industrial Management,University of Mazandaran ,Iran (Corresponding Author's E-mail: Amir.kariznoee@yahoo.com)

Monireh Bijandi

Student of Public Management in Ferdowsi University of Mashhad,Iran

Vajihe Mogharabi
M.A. Student of Information Technology Management, Shahid beheshti University,Tehran,Iran

Abstract The aim of this study is to identify and prioritize the key factors in selecting a target market in the food industry. In order to determine the components and subcomponents of this study, we have used previous researches in this area. In order to match these factors with the food industry situation and create a hierarchical structure, we have obtained the opinions of 323 experts about affecting factors on choosing a market in this industry with the use of questionnaire. Then, using a combination of hierarchal analysis process and Monte Carlo simulation and cooperation with 10 senior executives of distribution companies, the weight of each component and sub-component was determined. In general, four components and ten sub-components were examined in this study. After determining the weight of these components, the importance of each component in choosing a market has been prioritized. The results show that cost component is the most important criteria and market size, competitive environment, and culture are the other priorities respectively.
Keywords: target market selecting, hiererchical analysis process, MC-AHP, food industry

1.Introduction In today's competitive business environment, the means to survive and develop for companies in business environment is to respond quickly to the customer needs and produce goods according to their tastes, preferences, and circumstances. Thus, selecting an appropriate target market is one of the significant steps in organizational development and maintenance (Andersen and Strandskov, 1998). In fact, choosing the appropriate target market in today's competitive environment create an ability for companies to make more share of total demand. Therefore, organizations need to select the appropriate market for representing their products. In order to make the best choice, organizations need to consider more components. Many researches have been done to recognize the components related to the market selection. Since these components are different in terms of countries and industries, suitable components for market selection in each industry and environment should be recognized (Andersen and Buvik, 2002). In order to select the best market, we need to define the main components and then prioritize them in terms of planning and budgeting. Furthermore, managers are advised to consider priorities in decision-making process (Cavusgil, 1985). According to previous studies, organizations in different environments apply different ways to determine the components of market selection (Young and Feigin, 1978). The point is that market selection criteria are not

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Applied mathematics in Engineering, Management and Technology 2 (2) 2014 A. Kariznoee et al words, understanding the performance of these criteria has a significant effect on using those criteria (Paterson et al, 2009). Treadgold mentioned in his study in 1990 that close proximity to the market is the most criteria in market selection. Hortacsu has developed this concept and asserted that proximity consists of proximity in ethics and culture, geographical proximity and economical proximity. McDonald and Dunbar (1995) divided market attractiveness factors into three classifications that are rate of growth, market size, and profitability. This classification is similar to Abrat's view (1993) which considered customer attraction capability, competitive situation, market size, potential market growth and market suitability with organizational goals and resources as the most important factors in market selection( Zhande, 1996). In another study, Kiani Abari (2012) has tried to represent a model for selecting an appropriate target market using FAHP and TOPSIS methods. At first, Criteria are weighted through FAHP method. Then, markets have been prioritized by the use of TOPSIS technic. For entering a market, a company needs to provide a list of potential markets and make its marketing attempts based on them. In fact, the company should decide what kinds of markets are appropriate for its functions. Willingness or unwillingness to enter a market depends on the types of products, geographical factors, revenue, and population of target market, political, cultural, and economic environments. After obtaining markets lists, it is needed to prioritize and winnow them. 3. Research methodology The aim of this research is to recognize and prioritize the most important market selection criteria in food industry of Mashhad. To this end, 30 criteria were selected through literature review and marketing experts. Then, these criteria were distributed through 350 marketing experts in the form of questionnaire. They were asked to choose 10 superior criteria for market selection in food industry. From the whole 350 questionnaire, 323 questionnaires were returned. In order to prioritize and allocate weights to these criteria, we used a combined method of hierarchical analysis and Mont Carlo simulation, which are described in the following part. 3.1.Analytical Hierarchy process (AHP) AHP method is a multiple criteria decision making techniques which invented by Thomas L. Saaty in 1970. In summary, AHP method consists of following stages: Definition of problems, goals and results Determination of decision elements (criteria, sub-criteria and alternatives) and turning them into a hierarchical structure Drawing paired comparisons between decision elements by decision makers Recognizing the relative weights of decision elements using paired comparisons matrix Determination of compatibility factors to ensure the judgments of decision makers Determination of total weight of alternatives First, AHP method turns the multi-criteria decision-making issue into the hierarchy of decision elements (goals, criteria and alternatives) related to that issue. Goals, criteria, and alternatives are sorted into the hierarchical structure like a family tree. There are at least three levels of hierarchies: the overall goal is placed at the first level, multiple- criteria that evaluate the alternatives are at the middle level, and decision alternatives are placed at the low level. Second step contains the comparisons between alternatives and criteria. When the issue was analyzed and its hierarchy was made, prioritizing procedures will begin in order to determine the relative importance of criteria in each level. Paired comparison begins from second level and finishes at final level. Paired comparison is made for criteria in each level with regard to their levels of influence and based on the specified criteria in the higher level.

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Applied mathematics in Engineering, Management and Technology 2 (2) 2014 A. Kariznoee et al Paired comparison should be done through putting questions to the decision maker. For example, it is asked that which scales from one to nine should be allocated as a scale for determining the importance of criteria regarding the decision goal. (Table 1). Note that middle numbers 2,4,6,8 are used for correcting the comparison. Table 1: paired comparisons in AHP method Numbering classification 1 3 5 7 9 Intuitive judgment Same preference Average preference Strong preference Very strong preference Infinitely preferable 2,4,6,8 are middle values

3.2.Mont Carlo simulation In simulation method, instead of creating a formula for problem solving, the "Model" is analyzed for several times (depending on the required accuracy) in probable conditions and the results of each experiment are recorded. Then, with analyzing the obtained statistics, reliable results of actual performance of the real system will be available. It is clear that the experience of repeating the process for several times only would be practical and reasonable by using a computer. In fact, a "Monte Carlo" Simulation technique is one of the most efficient simulation techniques in industrial engineering, maintenance, and industrial management. In this technic, besides having probability distribution functions and influential factors on system design, probable events those effects on system are removed by using random numbers. In addition, system reaction to these events is examined. The term "Mont Carlo" had become common by physicists who were working on the project to build a nuclear weapon in Los Alamos national Laboratory of America in 1940. Monte Carlo method is a computational algorithm that uses random sampling. Mont Carlo methods are usually used for Simulation of physical, mathematical, and economic systems. On the other hand, Mont Carlo method is a class of computing algorithms that rely on repeated random sampling to calculate their results. Furthermore, Mont Carlo methods are mostly used to simulate mathematical or physical systems. Because of their reliance on repeated calculations and random numbers or pseudo-random numbers, these methods should be run by a computer. When deterministic algorithms are not able to calculate the exact answer, this method can be used. There is no single Mont Carlo method, but rather this term is applied to a wide range of employed methods. Anyway, these methods follow a specified pattern: 1Definition a limitation for possible inputs. 2Generation the random inputs from that limitation. 3Perform specific calculations with use of obtained inputs. 4Merging the results of each calculation in final answer. 3.3.A combined method of AHP and Mont Carlo simulation In order to increase the ability to conduct a better examination and winnow the lists of alternatives, Rosenbloom (1996) suggested adding Mont Carlo simulation model to the traditional AHP method. This model reduces the decision making risk and represents more acceptable results. Moreover, it helps decision makers to be more flexible in comparison with AHP method. In this method, when a decision maker is not sure about the decision, triangular distribution, which determine minimum, maximum and the most probable points, is used. Although it

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Applied mathematics in Engineering, Management and Technology 2 (2) 2014 A. Kariznoee et al is a new model, many researchers [such as Banuelas and Antony (2004), Kleija et al (2003), Shuliang and Zheng (2009), have used this method in decision-making process. 3.4.Influential components and subcomponents on market selection in the food industry Since MC-AHP method is used in this study, hierarchical structure should be provided for all components and subcomponents. The hierarchical structure was formed by extracting components and subcomponents from literature and experts opinion.

Fig.1- Hierarchical structure of market As figure1 displays, 10 main subcomponents have divided into 4 groups so that paired comparison would be done easier. These four groups include cost, competitive environments, culture of consumption and market size. The cost component consists of product transportation to the new markets, advertising costs, the cost of actions related to market recognition and setting up a distribution firm, warehouse and so on. Since, competition in a market that was already saturated with similar products requires a very high risk, competitive environment, which includes existence of similar products in market and regulations and rules, are the most important factors that affect the market selection in food industry. The culture of consumption, which includes consumerism and dominant culture and religion, has a significant impact on market selection. For example, in some communities, the first customer preference is to buy a kosher food. Market size is another component that was considered both in literature and experts opinions. Douglas (1982), Samli (1977), and Root (1994) show high regard for market size as the most significant factor in market selection. 3.5.Identifying the weights of components by applying MC-AHP Method As previously mentioned, we used the combined method of hierarchical analysis and Mont Carlo simulation to determine the weights of components in order to minimize the risk of decision-making. In this method, after drawing the hierarchical decision tree, the related data of decision-making elements are collected in the form of random variables by using questionnaires related to paired comparisons. Paired

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Applied mathematics in Engineering, Management and Technology 2 (2) 2014 A. Kariznoee et al comparisons are determined as a certain number in AHP method. Nevertheless, in this method, paired comparisons are the random variables that follow a specific distribution. (Usable, 2002) Mont Carlo simulation method is based on showing compound random of probable situations of uncertainties that might occur in a project. A computer is needed to display different situations that occur in uncertainties. In Mont Carlo simulation method, probability distribution function of uncertainties, which have identified in previous risk management stages, is determined by experts of project management team and experiences of previous projects at the first stage. In this study, we used random variables or triangular distribution function for making paired comparison. Because, from expert's point of view, paired comparisons could not have a specified certain number. Each expert is asked to make paired comparison with regard to three approaches: optimistic, most probable, and pessimistic. Thus, there are three numbers for each paired comparison. In second stage of Mont Carlo process, the numbers of simulation runs are determined. The number of runs depends on complexity and dimensions of project and the importance of under examined risks. In each implementation of Mont Carlo method, a random number is generated for each uncertainty between lower limit and upper limit of related uncertainties based on triangular distribution in which frequencies follow probability distribution function of uncertainties. Thus, in each implementation, a set of answers, which are in one to one correspondence with uncertainties, are generated that show one of the probable situations of utility. In this study, each time that simulation is implemented a random number with triangular distribution function, which its bounds were determined by decision makers suggestions, is allocated to the paired comparisons and its compatibility is examined. Then alternatives are prioritized by AHP method. This process will be repeated until the risk of decisions that based on three approaches (pessimistic, most probable, and optimistic) is minimized. It means that the parameter will obtained with enough accuracy (rosenbloom, 1996). Components paired comparison and alternative comparison were done using a triangular distribution at the interval between 1/9 to 9. After collecting information with the use of EXCEL software, Mont Carlo simulation is repeated 1000 times (In this study, we reached the sufficient accuracy (involving 3decimal digits) of weights with 1000 iterations. The obtained distribution did not change with more iteration) and the results were entered into the AHP method to determine the weights of each components. In fact, in simulation process, decisionmaking expert only choose one number of three input numbers randomly for each pair of comparison with the proviso that the probability of the chosen number proximity to the middle number is more likely. This process is similar to the fact that thousands of people are asked to make paired comparisons. In order to clarify the subject, a part of this process has been described in following. For example, experts were asked to determine the weights of main components in the form of paired comparison using clock spectrum. Table 2 shows this process. Table 2- Paired comparisons Market selection Market size Culture Competitive environment Market size 1 0.22 0.25 1 0.31 0.50 1 0.79 0.78 1.26 1 1.27 culture 3.27 1 2.00 4.63 1 2.70 Competitive environment 1.28 2.00 4.00 0.37 0.50 0.79 1 1 1 cost 0.40 0.20 0.13 0.50 0.25 0.30 0.80 0.51 0.50

As table 5 shows, three numbers are used for each paired comparison that respectively shows pessimistic, probable, and optimistic paired comparisons. Thus, we can tell that the expert asserts his/ her opinion in the form of triangular distribution. Then Excel software selects a number randomly with use of the obtained distribution. The selected number should be between lower limit and upper limit of that distribution and the number is likely to be closer to the middle number. In next stage, the numbers, which are selected randomly from this distribution, are put in paired comparisons table.

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Applied mathematics in Engineering, Management and Technology 2 (2) 2014 A. Kariznoee et al Table 3- Paired comparisons Market size Market size culture Competitive environment cost 1 0.271 0.337 1.545 culture 3.685 1 1.572 2.599 Competitive environment 2.971 0.636 1 2.637 cost 0.647 0.385 0.379 1

The information of this table is entered into AHP method as inputs. Then the weights of each main criterion will be obtained simply. Table 4- The weights of main criteria Competitive Market size Culture environment 0.353 0.112 0.145

Cost 0.391

Weights

The next step is to determine the compatibility or incompatibility of paired comparisons. We can calculate the compatibility rate with following relations: (5) (6) (n) is equal to the number of criteria that are compared. RI is the function of (n): if n=3 then RI =0.58. If n=4, then RI is equal to 0.90; and if n=5, then RI=1.12. Regarding the information of table 4, the rate of compatibility is calculated for related comparisons of main criteria. Table 5- Calculation of compatibility rate AX 1.447 0.450 0.587 1.608 λ max= Ci= Cr= Compatibility criteria result 4.075 0.025 0.028 Cr

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