How AHP model helps business make location decisions

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Mengzi, the Chinese greatest ideologist and representative of the Confucian, once said 'the right time does not guarantee the success unless you are also in the right terrier'. He emphasised the importance of terrier for the success. In the financial world, the success of companies is measured by their abilities to maximise profits and grow their business capabilities, 'terrier' is referred as the location for business activities. Therefore, according to Mengzi's view, we can say that the success of companies depends largely on the location of their business activities. Location by definition is where something is distributed and connected to other things (Webber, 1984). Business location therefore does not just mean the geographies where organisation's business activities are located, but also refers to other concepts that relate to business activities, such as labour, transportation and market. A good business location decision can provide the organisation with an advanced step to success, as its business activities will be perfectly connected with other related things. Business location decision, the customer service levels, transportation decision and inventory management together form the four key planning concepts of designing the organisation's logistic system (Ballou and Masters, 1993). Hence, the business location decision is significantly important for organisations, and it has attracted increased attention from variety of perspectives, such as academic, business and government.

The aspects of business location decision include location decision for organisation's management offices, manufacture, warehouse, distribution centre and outlets. According to intention and expectation of organisation to its future business capacities, it can be analysed into three categories, (Webber, 1984). The first category of location decision is to add capacity to the organisation such as locate a business initially, or relocate and expand its business into new geographies, this is the location decision which usually being faced by the organisation. Second, the organisation tries to rearrange its business capacity, for example, focusing on operations in certain areas and closing down others. The third category of location decision is to reduce the capacity by closing down the operation wholly, this happens when the organisation collapsed. The first two categories of the location decision are same as the investment decision, and the third one is on the opposite site, which is the decision to withdraw the investment. Therefore, the business location decision can be viewed as a concept which measures the presence of opportunities in the market for doing business (investing or disinvesting), and it relies on organisation's abilities to seek and hold opportunities.

Once the organisation is established, it always tries to grow by continuing to invest in the business (Webber, 1984). There are two sources of finance which can be used to finance grow of the organisation, one is the reinvestment of its own profit, the other one is to seek the investment from other business communities. No matter which source of finance is used, the organisation's own profits are important. This is why the organisation always does its best to maximise its profits by reducing down operation cost. In the opinion of the scientists of economic that the business location decision has impact on organisation's ability to maximise its profits, since a right location can help organisation attract attention of customers and investors, and reduce the operation cost, i.e. transportation cost, cheaper land cost (Kuo, Chi and Kao, 1999). It will also affect organisation's marketing and operation strategies setting, cost of investment, and performance of operation (Yang and Lee, 1997), for the reasons of these activities will be carried out according to the situation of the selected location. Taking restaurants as an example, if the selected location for the restaurant is near stations, the main customers of the restaurant are passengers and they are usually busy with travelling, and they do not have the time to enjoy their meals, therefore, in order to maximise their profits, the size of the restaurant in such areas should be small, and its main products should be fast food which can serve the customers quickly, furthermore, the prices of products are charged higher than the prices of the same products being charged in other areas; but if the selected location for the restaurant is near schools, its main customers will be students, who usually have no income, thus the prices should be cheap and the types of the food should be varied and health, in terms of the size of the restaurant should be large enough for these customers to chat during the meals. In conclusion, the location decision is strategically important for the organisation, as it will affect the organisation's subsequent periods' strategies setting and performance of operation, eventually, its abilities to maximise profits and grow business capacities. Hence, in order to be success, the organisation should pay a large amount of time and resource to the location decision-making.

The location decision-making is a complex and long term related strategic process. It includes the consideration of organisation's objectives and operation strategies, and all other aspects in relation to business location, such market that organisation tries to serve, the situation of transportation, and the capabilities of suppliers and customers in the area. Usually there are four steps for making business location decision. Step1, decide what factors will be used to evaluate alternatives, step 2, identify factors that are important to business location decision, step 3, identify the suitable alternatives of business location, step 4, use the factors developed in step 1 and step 2 to evaluate the alternatives and select the best alternative (ErtuÄŸrul & KarakaÅŸoÄŸlu, 2008).

Business location decision is a multi-criteria decision-making (MDM) problem, since there are numbers of quantitative and qualitative criteria being considered in the process of decision-making, such as labour cost, operation cost, taxes, transportation cost, customer bases, and industrial regulation and government policies. The quantitative criteria are easy to assess by the decision-makers for the reason of there are measurement units/absolute values being assigned to them. However, the assessments for qualitative criteria are challenging, as there is no measurement unit or absolute value being allocate to them and they are assessed by the preference of decision-makers. Every decision-maker has his personal preference which might be different from other decision-makers', even decision-maker's personal preference might be changed over time. And therefore, in order to assist decision-makers with consistent preference in ranking the order of criteria during the decision-making is a typical problem being faced by researchers (Li and MA, 2008). After decades of studying and researching, there are varieties of models and approaches have been developed to solve this problem, such as Data Envelopment Analysis, Fuzzy integrated hierarchical decision-making approach and Analytical Hierarchy Process (AHP) model, and so on. Among these models, the AHP decision model is more preferred by the researchers and decision-makers.

The AHP model was developed by Saaty in 1980. It is a widely used model by decision-makers for variety types of decisions, such as a firm uses AHP model to select suppliers, business location and operation implementation, and the government uses it to plan construction, and assess performance of companies. AHP is a flexible and useful model which uses simply techniques to help decision-makers solve the complex decision problem, i.e. techniques of linear programming, comparison and rating alternatives. And finally reach the best decision upon decision-makers' knowledge and judgements.

One of the techniques of AHP model is to rank the alternatives based on comparison of pairwise preferences outlined by the decision-makers (Saaty, 2008). In order to compare the pairwise preferences, the AHP model breaks down the complex decision problem into several measurable and manageable alternatives, and then forms a hierarchy according to the importance and priority of each alternative to others, the more preferred the higher level of hierarchy the alternative is in. The main difference of AHP from other decision models is that it quantifies decision-makers' judgements by allocating a weighed value to each alternative, and the weighed value is given on the basis of the preference of the decision-makers. The final decision is reached through the use of decision-makers' knowledge and judgements on the overall level of preference of alternatives (Yang and Lee, 1997).

In this dissertation, I will concentrate my work on following areas:

The importance of business location decision for an organisation.

The AHP decision model and how it is used to help business make location decisions.

Here, only the first category of location decision is discussed, namely the location choice made initially for starting-up an organisation, relocating or expanding the organisation's operation after establishment.

This dissertation is structured as follows. In section 2, there is a literature review on findings of researches that carried out by scientists for business location decision, key factors being considered for location choices, and the models/approaches have been developed for location decision. A description and discussion of the AHP decision model for business location selection are in section 3. In section 4, an illustration of process of applying AHP decision model to a real life location decision problem is established. The implication of using AHP decision model to make business location decision and the conclusion are in section 5.

2. Literature Review

2.1 The business location decision

In today's high competitive marketplace, organisations are mainly competing in prices of their products and services, as there are massive of same or similar products and services available in the world wide market, which can serve the most needs and requirements of customers equally; and customers always want to pay the lowest prices for the best products and services they can get without considering where producers/providers are (Canel and Khumawala, 1996). Hence, for missions of maximising profits and growing their business capacities, organisations must be able to identify the most profitable locations for their business activities that enable organisation to reduce its operation cost and keep the satisfaction of its customers (Webber, 1984).

Due to the high competitive level and recent changes in global economic activities, more and more concerns have been paid to customers satisfactions when considering the selection of business locations. Ballou and Masters, (1993) had stated that business location decision is in the second stage of designing organisation's logistics systems, which immediately after the planning of customer service level and before the decisions for inventory management and transport. They emphasised that business location decision is strategically important to the overall logistics system design. That is the locations of organisation's variety facilities (manufacture, warehouses, distribution centres and outlets) should be in a point which can be convenient and ease of reach for both suppliers and customers. This idea is also agreed by Kuo, Chi and Kao (1999), they had pointed out that a favourable location should be able to attract eyes of customers and be convenient and easy assessable for them. From the point of forecast of future competition, Drezner and Drezner (1998) had considered that the best business locations for an organisation should be the one that enables organisation to capture the market share in the competitive business environment. Therefore, the business location decision is very important for an organisation's abilities to maximise its profits and having a significant impact on organisation competiveness (Bhatnagar, Jayaram and Phua, 2003).

The trend in recent business location decision has made organisation to consider opportunities of locating its business activities in foreign countries, where it can gain potential competitive edge, and to treat the implications of location choices as an essential element of its overall business plans and strategies (Cantwell, 2004, Badri, 1999, Ho and Lau, 2007). The advanced technologies of transportation and communication have been providing a solid ground for organisation to locate its business activities all over the world. These advanced technologies include the development of highway system in the world wide places, and improved telecommunication techniques. The improved highway system has offered fast access among countries, and eventually, reduced the transportation cost among organisation's different business locations, suppliers and customers. The advanced telecommunication techniques have made organisation's management easily to control its business activities which are expanded widely (Yang and Lee, 1997, Martin and Rogers, 1995).

These advanced technologies together with the increased globalization have made the less developed countries more popular and attractive to many organisations as their business locations. Most of the big companies in today's market are multinational companies; they usually locate their management centre in their home countries, manufacturing facilities in a foreign country and the final assembly of the products in another foreign country or in their home country. While receiving the potential benefits from there, e.g. lower labour cost and favourable regulations issued by these countries, the organisation also faces numbers of challenges, such as culture, economic, politic and language differences (Ho and Lau, 2007, MacCarthy and Atthirawong, 2003).

Due to the strategic importance of organisations' business location decision and the recent changes in global economic and politic activities, namely the increased globalization, advanced technologies of communication and transportation, and increased rely on knowledge and information (Canel and Khumawala, 1996), business location decision has drawn an increased attention from both perspectives of academic and business. Many literatures have been published to address the problems of making business location decision.

According to the particular problem of business location decision that they are addressed, those literatures can be classified into two types. One is focused on discussing the location factors that critical to the consideration of selecting a business location, the other one is to address the models or approaches that can be used by decision-makers to reach the best location decision. The summaries of those literatures are outlined in Table 1.

Although a lot of works have been carried out by vierity perspectives to handle the problem of business location decision, it is still a complex and difficult task for organisations and decision-makers. This is due to its vita important to organisations' operation and overall strategy and performance, the limited knowledge and experience of decision-makers, the recent and continuing changes in the global economic activities, the changeable influence of the critical location factors over time and the existence of limitations of the location decision models. In order to solve this problem, the decision-makers need to have a wide range of skills (i.e. forward planning and managerial skills) and acquire enough information that relate to the potential suitable locations (Webber, 1984).

Table 1 The summaries of literatures that for business location decision

Literatures that discuss the location factors

Authors Location factors addressed

Fulton (1955) Labour, size of community, transportation, power

supply, government policies

Fulton (1971) Labour, size of communities, transportation, power

supply, financing opportunities

Martin and Rogers (1995) Public infrastructure

Canel and Trade barrier, customers, competition, regulation,

Khumawala (1996) markets, resource, cost

Jayaraman (1998) Transportation

Bhatnagar, Jayaram Cost, infrastructure, business services, labour,

and Phua (2003) labour, government, market, suppliers, competitor

MacCarthy and Costs, labour, infrastructure, suppliers, customers,

Atthirawong (2003) competition, quality of life, legal and regulatory

framework, economic factors, government and

political factor, social and cultural factors, sites

Badri (2007) Transportation, labour, raw materials, markets, industrial sites, utilities, government attitude, climate, community,

political situation of foreign country, global competition

and survival, economic factors

Ho and Lau (2007) Tax, labour, government policy and attitude, economic factors, regulation

Literatures that address location decision models

Authors Location decision models addressed

Canel and A mixed-integer programming approach

Khumawala (1996)

Yang and Lee (1997) Analytic Hierarchy Process

Badri (1999) Analytic Hierarchy process and goal programming approach

Alberto (2000) Analytic Hierarchy Process Methodology

MacCarthy and Analytic Hierarchy Process

Atthirawong (2002)

Ho and Lau (2007) Stepwise approach, maximization approach, conceptual


ErtuÄŸrul and Fuzzy AHP and fuzzy TOPSIS methods

KarakaÅŸoÄŸlu (2008)

2.2 Key Location factors

Location factors play a vita function in the process of business location selection, they are the criteria which used by the decision-makers to evaluate the identified alternatives of business location, and they have to be cohesive to the overall strategies of the organisation as their influence on organisation's missions, operation and marketing activities. Their influence and importance to the organisation are depending on type of industry which organisation is operating in i.e. labour will be the most influential and important factor for location decision of organisation operates in the labour-incentive industry; compared to the transportation system will be the most vital factor for organisation operates in the transport industry (Ho and Lau, 2007, Yang and Lee 1997).

The influence and importance of location factors on organisation's business sites selection are changing over time. From research of US industry location, Fulton (1955) recognised some of the most influential location factors to business sites, such as labour, transportation and community size. Furthermore, in this article, he forecasted few important changes in these location factors during next 10 years, and i.e. the labour force would grow in size to meet the increased need of skilled labour. In 1971, Fulton recalled his options in 1955 by confirming the continuous importance of these location factors, and recognised the major changes of some of location factors, such as for labour, many new sources of labour forces were discovered and used, and the demand for skilled labour had increased and would continue to increase, i.e. demand for systems analysts and other technical persons.

There are many new factors are introduced into the consideration of business location both international and national. These factors include trade barriers, international competition, additional resources, economies of scale, synergy, power and prestige Canel and Khumawala (1996), foreign workers, Protection of Foreign Investment, likely competitors' reaction to site, (Bhatnagar, Jayaram and Phua, 2003), location of suppliers, government structure, consistence of government policies, community addtidues towards business and industry, schools, churches, hospitals, recreational opportunities, population trend, and education system, (MacCarthy and Atthirawong, 2003), attitude of worker, anticipation of growth of market and marketing services Badri (2007).

From the review of Badri (2007), Bhatnagar, Jayaram and Phua (2003), Canel and Khumawala (1996), Chan, Kumar and Choy (2007), Doeringer, Evans-Klock and Terkla (2005), Fulton (1955 and 1971), Ho and Lau (2007), MacCarthy and Atthirawong (2001 and 2003), Martin and Rogers (1995), some of the most discussed factors that influence organisation's business location decision are labour, market, raw materials, transportation, government and political factors, economic factors, legal and regulation framework, quality of life, site consideration, and social and culture factors. The summaries of these most influential factors are analysed in Table 1. According to their different functions, Badri (2007) has analysed these critical factors into three fundamental categories, namely, markets, labour, and community environment.

Table 2 The summaries of the most influential location factors

Critical Factors Sub-factors

Labour Availability of labour, labour cost, quality of labour, attitudes

of labour towards to work, labour unions, wage rates.

Market Status of existing market, trend of the market, profitability of market, distance to market, cost of serving the market, further expansion opportunities, competition levels, size of the market, the trend and level of consumer's income, population trend, demand trend, marketing services, consumers' characteristics.

Raw Materials Availability of raw materials, distance to suppliers, credibility of suppliers, alternative suppliers, cost of transportation to suppliers, location of suppliers, and warehouse for raw materials.

Transportation Cost of transportation to market, suppliers, warehouses and outlets, facilities of transports, such as facilities of airway, railway and highway, the quality of delivery system in the site, and trucking services.

Government and Government policies on construction, industry, tax and

Political factors investment.

Economic factors Tax policies and incentive, strength of the currency, standard of living, government aids, financial incentives, tariffs, inflation, interest rates, exchange controls, country's debt.

Legal and regulation Compensation laws for employment, insurance law,

Framework employment law, environmental regulations on pollution, waste and noise, legal system, requirements for setting up local corporations

Quality of life Trend and level of consumers' income, quality of education system and hospitals in the site, crime rate, standard of living

Site consideration Existence of modes of transportation, quality of life, cost of land, space for future expansion, quality of site utilities and communication systems, climates, quality of transportation system, quality of water, gas, electricity and other power supply, financial and non-financial lending institutions

Social and Culture

factors Language, culture, and customer characteristics

As mentioned in introduction, according to measurability, location factors can also be classified into two categories, quantitative and qualitative. Quantitative factors, such as cost of labour, cost of land and financial incentives, can be measured on their numerical values. However, for the qualitative factors, i.e. credibility of suppliers and legal framework, as there are no measurement units or numerical values being assigned to them, they are measured by the preference of decision-makers, which are very subjective. Due to there is a large amount of quantitative and qualitative factors affecting business location decision and the difficulty of making trade-offs among these factors, the problems of making business location decision are complex and difficult (Badri, 1999).

For the aim of selecting the best location for organisation, decision-makers should be prepared for allowing a sufficient time to collect information about the potential business sites, and identify and evaluate the major influential and important location factors, as well as using the most adequate models/approaches to assist their decision-makings.

2.3 Business location decision models

The selection for business location is a complex and difficult multi criteria decision making problem due to it depends on a large amount of quantitative and qualitative factors. The process of location decision-making involves two stages, first, decision-makers need to establish site requirements and the level of importance of each requirement over others, according to the type of business that organisation is doing and its future plans. Second, decision-makers have to identify, analyse, evaluate and select the best location among alternatives based on the established site requirements and their relative importance (Yang and Lee, 1997). Therefore, it is necessary to develop some models which can assist decision-makers with consideration and evaluation of both quantitative and qualitative factors in the process of making a business location decision, as well as to trade-off the qualitative (objective) criteria of the organisation in terms of benefits, attitude & skill of labour, quality of life and government policy for each alternative of potential business location (MacCarthy and Atthirawong, 2002).

Following decades of studying and researching, a number of models have been developed to help decision-makers make a business location decision. Based on the nature of these developed models, they can be classified into two categories (Bhatnagar, Jayaram and Phua, 2003).

The first category of location decision models is focused on assisting decision-makers analyse and evaluate quantitative criteria that are cost-related, in the process of making a business location decision. These cost-related criteria includes: the assumed cost of land, labour and transportation, tax incentives and other cost-based criteria. The aim of these models is to minimise the total cost of establishing an efficient supply chain network (i.e. start-up and expansion cost, cost of labour and transportation, and warehouse cost) though putting restrictions on the number, size, distance and geographies of organisation business locations (management offices, manufacture, warehouse, distribution centre and outlets), while keeping satisfaction of its customers. The main limitation of this type of models is that they ignore qualitative criteria during consideration of business location selection, i.e. quality of life and utilities in the area, government policies and attitude of labour, despite these criteria are crucial for organisation's to gain competitive edge over its competitors (Alberto, 2000, Ballou and Masters, 1993, and Bhatnagar, Jayaram and Phua, 2003).

The second category of models takes both quantitative and qualitative criteria into the consideration of business location decision. Many of these models are mathematical models, whose main feature is to work out the priority of each factor over others by assigning a numerical value to them respectively and the selected location is the one with the highest overall scores. Usually, the numerical value is allocated according to the preference of decision-makers. This type of models includes: weighted checklist, AHP decision model, the multiple regression analysis, integer programming and non-liner programming (Chan, Kumar and Choy, 2007, Canel and Khumawala, 1996, Yang and Lee, 1997, MacCarthy and Atthirawong, 2002). Among these models, the AHP decision model is widely used by variety of decision-makers (Alberto, 2000, Badri, 1999, MacCarthy and Atthirawong, 2002, Saaty, 2008, Yang and Lee, 1997) that can be used to handle large and complex real-life multi-criteria decision problems. It involves steps of decomposition, pairwise comparison and allocating numerical values to the criteria of location decision.

Some of identified limitations of models in this category are stated as followings: it is not a adequate method for solving critical and larger sample problems, e.g. making a location decision for organisation's distribution centre; and it is not easy to decide the priority of some qualitative criteria over others, e.g. which factor is more important for the organisation operation in a particular location, the attitude of labour or quality if utilities in the location?; furthermore, the assessment of priority of qualitative criteria made by these models is very subjective and imprecise as the preference and judgement of decision-makers are hard to capture accurately and precisely; Therefore, by using this category of models to make a business location decision, the outcome is very subjective and depends on the preference, knowledge, experience and judgement of decision-makers (Bhatnagar, Jayaram and Phua, 2003, Chan, Kumar and Choy, 2007).

There is a common limitation for those two categories of location decision models that is the most of them lack of capability to handle the significant changes in today's business location decision problems and evaluate all necessary quantitative and qualitative criteria in the consideration of business location selection.

Despite the existence of limitations of location decision models, Saaty's Analytic Hierarchy Process (AHP) decision model is a very useful location decision model, in terms of handling the information and criteria (both quantitative and qualitative) during the consideration of making a business location decision.

Since the AHP decision model was founded, it has been widely used by decision-makers and researchers to handle multi criteria decision problems that in vierity of fields, such as planning, evaluating of performance and selecting the best alternative. Some of the applications of AHP decision models are summarised in Table 3.

Table 3 The applications of AHP decision models

Authors Key research

Yang, and Lee, 1997 Developed an AHP location decision model to support the facility location decision. Three potential sites, four key location factors and 12 sub-factors are considered in the AHP location decision model

Alberto 2000 The AHP model is implemented through a case study to address the problem of site selection.

MacCarthy and The AHP model is used to evaluate an overseas

Atthirawong, 2002 manufacturing plant. The companies are in Thailand, and therefore, the AHP model is being tested to see whether it can solve the problems of international location decision and cover the international location factors.

Hunjak and The AHP model is performed to evaluate and rate the

Jakovčević, 2001 performance of Croatian banks.

Kumar, S, Parashar, N The AHP is adopted to address the problem of

and Haleem, A, 2009 vendor selection for small, medium and large industries.

Amiri, 2010 The AHP is used to handle the problem of project selection, and to determine the priority rates of the criteria identified.

Saaty, Vargas and The AHP is used to quantify the relative priorities

Dellmann, 2003 of intangible resources.

The AHP decision model is also convenient to be used by combining with other

decision approaches or models, e.g. fuzzy TOPSIS methods, goal programming

approach, mixed-integer programming approach and linear programming (Amiri,

2010, Badri, 1999, Canel, and Khumawala, 1996, Saaty, Vargas and Dellmann


3. The Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is one of the most used decision models for handling the multi criteria decision problems, it allows decision-makers to decompose a complex decision problem into several elements, which are the overall goal of the decision, criteria and sub-criteria that influence the decision, and alternative solutions. These broken down elements can be managed more easily and readily by the decision-makers. The AHP model is very effective for synthesizing the information and evaluating both quantitative criteria (i.e. transportation cost) and qualitative criteria (i.e. government policy) within one model. The relative priority weights of importance of identified criteria and the ratings of alternatives are obtained through the use of pairwise comparison. By performing the pairwise comparison, a ratio scale is calculated for each of elements in the hierarchy according to the judgements of decision-makers made on their relative importance to the criterion that with respect to which they are being compared to. Because the utilization of the mathematic method of ratio scales, that is the values obtained for each element are just proportional not absolute, the AHP model is able to measure the judgements of decision-makers, which are usually inconsistent from one decision-maker to others. As long as the measurements obtained by different decision-makers are within the proportion, they are validated.

Due to the ability of evaluating the inconsistent judgements, the AHP decision model has been applied to handle a variety of decision-making which involve judgements of decision-makers on the consideration and evaluation of numbers of quantitative and qualitative criteria and alternatives. Some of identified applications of AHP decision model including vendor selection, project selection, evaluation of organisation's performance, and facility location. A set of recent applications of the AHP decision model is showed in Table 3.

The identified steps in the process of the AHP decision model are as followings:

1) Define the problem.

2) Decompose the problem into overall goal, criteria, sub-criteria and alternative solutions.

3) Structure a decision hierarchy, with the overall goal of decision at the top level, the criteria and sub-criteria at the middle levels, and the alternatives at the lowest level.

4) Carry out numbers of the pairwise comparison. Each time, two elements are chose from one level to compare their relative importance and priority to the criterion at the immediately higher level of the hierarchy with respect to which those two factors are being compared to. Then, by using the method of rating scale, the decision-makers can determine a numerical value to each of elements in the lower level based on its importance to the criteria at the next higher level that it is subsequent to. Usually, the element with more importance will be assigned a higher value.

5) Calculate the overall priority weights of criterion at each level of the hierarchy. And continue this process for each level of the hierarchy until the final decision is obtained (the overall priority weights of alternative solutions at the lowest level of the hierarchy are obtained, and the final solution for the decision should be the alternative with the highest priority weights).

The AHP is a very useful decision model for selecting a business location. A business location decision involves the consideration and evaluation of both quantitative and qualitative location factors and alternative sites. For which, the judgements of the decision-makers are needed. Different decision-makers will usually have different judgements on the importance of particular factor when compared with another factor, for example, a decision-maker might view the labour cost is more important than labour attitude to the labour factor with respect to which they are being compared with, others might view it in an opposite way; the AHP decision model provides a possibility to evaluate those inconsistent judgments of decision-makers when making a business location decision.

For using AHP decision model to handle the problem of business location decision, the first step that decision-makers need to do is to make clear the requirements and goal of the location decision, is it needed for the aim of finding a location for their management office, manufacture, distribution centre, warehouse or outlets?

After identifying the goal of the business location decision (i.e. find a location for organisation's manufacture), the decision-makers then have to identify the critical factors that important to the location (such as labour, transportation, and market) and sub-factors that with respect to the critical factors (e.g. attitude of labour and wage rate of labour are sub-factors of the labour), as well as the alternative sites that match the requirements of the location decision.

The third thing that decision-makers need to do is to form a hierarchy with the goal of the decision at the top level of the hierarchy, the critical factors and sub-factors at the middle levels, and the alternative solutions (i.e. location A, B and C) at the bottom level.

The importance and priorities of quantitative factors of location decision are easy to measure, as they have identical measurement units. However, for the qualitative factors that have no measurement units, they have been measured by the judgements of the decision-makers. The qualitative analysis is carried out by the use of pairwise comparison; this is also the key step in the AHP decision model. In order to conduct the pariwise comparison, the decision-makers need to select two factors from the lower level of the decision hierarchy to compare their relative importance and priority to the criteria at the immediately higher level, with respect to which they are being compared with. Through the use of pariwise comparison, decision-makers can assign a number between 1 and 9 to each of the compared qualitative factors. One of often used scale of preference between two factors was developed by Saaty (2008) with number 1 to 9. Number 1 represents the equal important of two factors, and number 9 shows the highest possible importance that one factor over another (Saaty, 2008). The details of the scale of preference between two factors are presented in Table 4.

Following the conduction of pairwise comparison, a comparison matrix with size n * n (n is the number of factors have been used in the consideration of location decision) is formed to indicate the priority ratings of elements for each level of the hierarchy, in which the values of principal diagonal are 1, for the reason of each factor is as important as itself. And the other values that in the comparison matrix will be the reciprocals of the earlier comparisons, that means if factor x has been allocated a number between 1 and 9 when it is compared with factor y, then factor y has the reciprocal value when compared with factor x. In order to explain this more clearly, the mathematical notation is used. Assuming the weights of factor x is denoted as wx and weights of factor y is denoted as wy, in the comparison matrix, the value of factor x compared with factor y will be shown as axy, which is equal to wx / wy. Supposing axy > 0, then the value of factor y compared with factor x will be denoted as ayx and ayx = (axy)-1. Repeat this process for all other location factors.

Hence, for general, let's assuming there are n number of location factors in the consideration of particular location decision and the formed matrix is denoted as Matrix A with size n * n, as for each time, two factors i and j will be chosen to make comparison (i = location factor 1, 2,…n, j = location factor 1, 2,…n, and i ≠ j ), their weights therefore can be denoted as wi and wj, i and j represent the compared factors respectively. The values of factor i compared with factor j are indicated as aij and which equal to wi / wj. And assuming aij > 0, then aji = (aij)-1. The ratios of aij are used to form the Matrix A.

Furthermore, as the consideration of business location involves the judgments and preferences of the decision-makers that are usually inconsistent and varied from one decision-maker to another decision-maker, therefore, the priority weights calculated from different decision-makers are different. The AHP decision model provides a possibility to evaluate the inconsistent judgments with a Consistency Ratio (CR). Before calculating the CR, it is needed to calculate the weights vector, which is calculated by using the equation Aw=λmax * w and λmax ≧ n, where A is the comparison matrix with size n * n, w is an eigenvector of order n, λmax is the maximum eigenvalue of the Matrix A and n is the number of factors at each level of the hierarchy, which is used to decided the order of the every matrix of the immediately higher level. λmax is then used to calculate the Consistency Index (CI) that equals to (λmax - n) / (n-1). Finally, use the equation CI / RI to calculate the CR for the set of judgments used in the process of location decision, where, RI denotes the Random Index for its corresponding random matrix, and value of RI depends on the order of matrix. If the value of CR ≦ 0.1, it means that the judgments and measurements of decision-makers about the relative priority weights of the factors, sub-factors and alternatives in the business location decision are consistent and acceptable (Kumar, Parashar and Haleem, 2009, Alberto, 2000). The table 5 shows the values of RI for varied Matrix Orders.

Table 4 The scale of preference between two factors (Saaty, 2008)

Intensive of Definition Explanation


1 Equal importance Two factors contribute equally to

the objective

3 Slightly more important Experience and judgement slightly

favour one factor over the other

5 Strong important Experience and judgement strongly

favour one factor over the other

7 Very strong important Experience and judgement very strongly favour one over the other and its importance is demonstrated in practice

9 Extreme important The evidence favouring one over the other is of the highest possible


2, 4, 6, 8 Intermediate value Used when the compromise between the references listed above is needed

1.1-1.9 The two factors are It is difficult to determine the most

very close accurate number to the factors as they are very close, but if these factors are compared with other contrasting factors, the small numbers might not be too noticeable, and they still represent the importance of the factors

The final step is to calculate the overall rating of each location factor, as well as the total rating of the alternatives at the bottom level of the hierarchy. Usually, the one with the highest rating will be the location that decision-makers are looking for. The overall priority weights of each location factor are the sum of the weights of the sub-factors, which are subsequent to it; and the total rating of each alternative site are calculated by adding together the weights of all the location factors (Alberto, 2000, Vaidya and Kumar, 2006,). The brief process of the AHP model for handling the business location decision problem can be found in Figure 2.

Figure 2 The brief process of the AHP model for business location decision

Step 1: Identify the goal of the location decision. (Location decision needed for management office or manufacture)

Step 2: Identify the critical factors and sub-factors of the location decision and the alternative sites

Step 3: Form a hierarchy showing the relationship among the goal, critical factors, sub-factors and alternatives

Step 4: Conduct the pairwise comparison and work out the priority of each factor.

Step 5: Calculate the overall rating of alternatives and select the most preferred location for the business activity

The strengths and weaknesses of the AHP decision model

The strengths of applying the AHP model to solve a decision problem, for example, the AHP model used for selecting a business location, have been analysed as followings:

It is able to rank alternative solutions in the order of their effectiveness in meeting the goal of the decision; the judgements made about the relative importance of each factor of the decision have been made in a good faith. It provides a possibility to evaluate the inconsistence of judgements of decision-makers.

It allows decision-makers to decompose a complex decision problem into several elements that are more easily and readily manageable by decision-makers.

It is simple to use, as it is based on the use of simple mathematical method of rating scales and pairwise comparison. The pairwise comparison leads decision-makers to put their effort on each of small elements of the complex decision problem.

It can be used for a wide range of decision-making, such as decisions for location selection, project selection and group decision-makings.

It can be used by combination of other models or methodologies, e.g. linear programming and mixed-integer programming approach.

On the other side, since the AHP was first used by the decision-makers and researchers, they have identified some weaknesses of the effectiveness of the AHP decision model when it is applied to solve a particular decision problem. These identified weaknesses of the AHP model can be analysed as:

(1) It only works when the formed matrix is a positive reciprocal matrix that is the number assigned to the factor should be positive. Moreover, in such type of matrix, if number 5 is assigned to factor x when it is compared with factor y, represents that factor x is much more important than factor y with respect to the criterion to which they have been compared, then 1/5 is used to define the importance of factor y when it is compared to factor x. These values of the importance obtained by using this method are just reasonable not absolute, some decision-makers might need some models which can help them determine the absolute or more actual values of importance of factors.

(2) It is hard to use when there are a large number of factors and alternatives, as the AHP model is focused on pairwise comparisons. If the number of factors and alternatives are large, the decision-makers might be confused or even missed some factors or alternatives when conducting the pairwise comparison.

(3) The solution of the decision problem can only be selected from the identified alternative solutions within the hierarchy. It is difficult to add a criterion or alternative solution.

(4) It is difficult to select the best solution from the existing alternative solutions, as sometimes the priority weights of alternative solutions might be very close, and each of alternative solutions has its own merits.

Despite the existence of these weaknesses, the AHP decision model is a very useful methodology for evaluating both the quantitative and qualitative factors in one model and to rank the alternative solutions in the order of their suitability to meet the requirements of the decision problem. In addition, the calculations involved in the model are simple which can be performed by everybody. However, keep in mind that the 'best' solution obtained by using the AHP model is just reasonable not absolute.

4. Application of AHP decision model for location selection

5. Implication and Conclusion