AHP Final Report

A DECISION SUPPORT SYSTEM FOR HOTEL SELECTION USING THE AHP

METHOD

developed under the Final Year Work or Project of the 5th year of the Electrical and Computer Engineering graduation course in collaboration with Adaptive IDE

Lda.

July 2005

Supervisor/Orientating Professor: Professor José Soeiro Ferreira (FEUP)

ADAPTIVE’s Project Partner:

Eng. Hugo Caldeira Project developed by Filipe Alexandre Camacho [email protected] Frederico Vilas Boas [email protected] João Bernardo Câmara [email protected]

FEUP/LEEC-PSTFC – A Decision Support System for Hotel Selection using the AHP method - July 2005 2

INDEX

1.Motivation.......................................................................................6

2.Introduction ....................................................................................6

3.Case Study ................................................................................. .. 10

3.1 Evolution of the initial case study ................................................11

4.E-Tourism: Current scenario and trends............................................. 11

5.Theory ......................................................................................... 12

5.1 Decision Support Systems...........................................................13 5.1.1 The scope of DSS in e-commerce ............................... 13 5.1.2 History of DSS implementation in the Tourism industry..... 14 5.1.3 Taxonomies of a Decision Support System .................... 16 5.1.4 Taxonomy of the proposed DSS .................................. 18

5.1.5 Evaluation features for our DSS ..................................... 18 5.2 AHP – what is it all about?..........................................................19 5.3 The reason behind choosing AHP..................................................25 5.4 Information Systems Technologies ...............................................27

6.Design of the AHP model .................................................................. 29

6.1 Individual Travel Selection....................................................... 30 6.2 Group Travel Selection ..............................................................32 6.3 Proposed Procedure / Hierarchical Structure ...................................34 6.4 AHP applied to GDSS: How to do it? ...............................................35

7.Implementation .............................................................................. 37

7.1 Introduction...........................................................................38 7.2 Description of the search engine..................................................44 7.3 Individual Travel Selection: implementation ...................................45

7.3.1 Construction of the judgement matrixes ....................... 47

8.Testing......................................................................................... 50

9.Conclusions ................................................................................... 52

10.Annex......................................................................................... 55

11.References .................................................................................. 58


Acronyms and Symbol Listing

EIS - Executive Information Systems

GDSS - Group Decision Support Systems

ODSS - Organizational Decision Support Systems

OLAP - On-Line Analytical Processing

AHP - Analytic Hierarchical Process

HTML – HyperText Mark-up Language

CSS - Cascading Style Sheets

PHP – Hypertext Pre-processor

SQL – Structured Query Language

B2C – Business to Customer

ACM - Association for Computing Machinery

AJAX - Asynchronous JavaScript and XML

EVM – Eigenvalue Method

ANSI –American National Standards Institute

ISO – International Organization for Standardization

WAMM - Weighted Arithmetic Mean Method


Picture index Fig.1 – A brief history of DSS ................................................................... 8 Fig.2 - The five distinct components of a DSS .............................................. 9 Fig.3 - Operating structure for the DSS: sequence of events ...........................10 Fig.4 – A typical AHP structure ...............................................................20 Fig.5 – AHP structure for the individual travel selection ................................31 Fig.6 – The AHP structure adopted in Jablonsky et Lauber..............................33 Fig.7 - Proposed Hierarchical Structure for Group Travel phase .......................35 Fig.8 – Aggregation of the individual judgments into the group’s judgment

matrixes for group decision .......................................................37 Fig.9 – Database’s E/R model ................................................................43 Fig.10 – Use of the PHP and SQL in the DSS ................................................43 Fig.11 – Selection boxes for attribute insertion ...........................................44 Fig.12 – Search engine with selection boxes and hotel listing ..........................45 Fig.13 – Pair-wise comparison of criteria ...................................................46 Fig.14 - Testing our implementation using the Expert Choice: ranking of

alternatives ............................................................................51 Fig.15 – Ranking of alternatives obtained by the application...........................51 Fig.16 – Example’s hierarchical structure ..................................................55


Table index Table 1 – AHP’s 1-9 scale ......................................................................21 Table 2 and 3 - Example of the two types of matrixes, criteria matrix and

alternatives matrix: pair-wise comparison and local weights ..............22 Table 4 – Average random consistency......................................................25 Tables 5 to 15 – Database Entities and their description................................41 Table 16 to 21 – Database associations and their description ..........................42 Table 22 – Conversion between the 0-10 scale and the AHP scale.....................48 Table 23 – Comparison of consistency ratios: Expert Choice vs. Application ........52 Table 24 – Example’s criteria pair-wise comparison......................................55 Table 25 – Normalized and respective local weights .....................................56 Table 26 to 29 – Pairwise comparison of alternatives with respect to criteria......56 Table 30 – Example’s Normalized Judgement Matrixes ..................................56


1. Motivation

The origin of this project dates to late February, early March, after

ADAPTIVE, an entrepreneurial company based on Funchal requested an application

for its tourism contents webpage. The idea behind the requested application was a

client-support system for assisting webpage’s visitors in finding the hotel/resort or

other type of tourism lodging that best suited their interests. Such relevant

interests were pointed out like the price tag, facilities available, services and

others. Besides this application should target an individual user that wishes to

select a hotel.

After a first phase of exchanging information between the Final Year Report

students and the company, a proposal for implementing the web application was

made to the Project orientator. Before the acceptance of the proposal, a road-map

was proposed for achieving all the goals listed in the proposal.


2. Introduction

Have you ever wanted to book the best place in your favourite holiday’s

destination that fitted the exact bill for your perfect vacation? That resort or hotel

that has all the services in the perfect spot for assuring the perfect time, all this

while still fitting in your desired price tag?

And what about if you wish to travel in a group that may hold different ideas

concerning their perfect holidays…it’s all about finding the place that can offer the

best solution for all the members. Surely no one expects the impossible, or a

“heaven” sent compromise between all members which may be well out of reach.

But a solution that could approximate all members’ choices is possible and

desirable.

The big problem is that this type of decision is usually disregarded of any

analytic base: of course it’s hard to say to someone who is planning his/hers

holidays to grab a piece of paper and a pencil, and get “analytical” with some kind

of mathematic algorithm.

Rather the challenge is to incorporate this mathematical analysis and create

a proper interface in order for it to be user-friendly and sufficiently accessible to

all kinds of people, computer educated or not.

This is the scenario for which our project was guided, namely a web

application that supported decision making by a user or a group of users. In this

point, research through literature (papers, online documents and major tourism

boards’ web pages) indicated no similar implementations of the same nature,

which gave the green light for further studying of the scenario.

After some studying, it was found that the baseline theory associated with

this project lies on Decision Science, an increasingly important field of Operations

Research, with applications in so many different environments that range from

biotechnologies, medicine, informatics, logistics and management…in fact the

scope of Decision Sciences can be found in almost every sector of global economy.

In our case the implementation will be of course based on information

systems technologies. Such type of system is commonly known as a Decision

Support System (DSS), defined by Sprague and Carlson1 as an ‘interactive

computer-based systems that help decision makers utilize data and models to


solve unstructured problems’ although many other definitions are available in a

more or less complete way.

Its origins date back to 1965 and treads closely with the evolution of

computers and information systems. Also it is considered that the concept of DSS

became an area of research of its own in the middle of the 1970s, before gaining

intensity during the 1980s.

In the middle and late 1980s, Executive Information Systems (EIS), Group

Decision Support Systems (GDSS), and Organizational Decision Support Systems

(ODSS) evolved from the single user and model oriented DSS.

Beginning in about 1990, data warehousing and On-Line Analytical Processing

(OLAP) began broadening the realm of DSS. As the millennium approached, new

Web-based analytical applications were introduced (Figure 1).

Fig.1 – A brief history of DSS

There are many different types of classifications used by many different

authors, regarding a DSS. Also different models exist for a DSS although the

differences between them aren’t as significant as one may suggest.

Building upon the much different architectures Marakas 2 proposed a general

architecture made out of five parts:


Fig.2 - The five distinct components of a DSS

KE – knowledge engine - contains the mathematic models, working databases.

DBMS – Data Base Management System

MBMS - the model-base management system

The knowledge engine is the one that comprises the mathematical

structuring of the decision making problem using an appropriate model to

accomplish this.

This was the main concern in the documentation phase of our project,

finding a mathematical model that effectively introduced decision making for

scenario in hand, firstly considering only an individual and finally for the group

travel selection .

The mathematical model used for this phase of our project was the Analytic

Hierarchical Process (AHP) a popular multiple-criteria decision making tool based

on hierarchical structure. Some of its attracting features, among others, are the

capability of synthesizing qualitative, as well as quantitative info into the decision

making process. More on AHP and its implementation this will be the subject of a

more detailed explanation later on.

The final stage of the project is the implementation phase, the construction

of the DSS using information systems technologies, such as HTML, CSS and PHP4.

These are popular tools in database programming nowadays.


Fig.3 - Operating structure for the DSS: sequence of events


3. Case Study

3.1 Evolution of the initial case study

In a bid to attract more visitors and to transform ADAPTIVE’s tourism

contents web page a new web application was proposed. The company wanted an

application that supported a search engine through its hotel database, but that also

supported customer support in the form of optimizing customer’s personal

preferences, for example amount of money willing to spend, type of hotel wanted,

services, location, facilities etc…This application shouldn’t be directed only for the

individual but also for group travel. Finally it should present to user a

recommendation based on customer’s inputs.

The scenario presented to us at the beginning of the project involved, at

first, only a theory baseline for the proposed client-support travel selection system

with emphasis on a searching and adapting an optimization model that could

implement the described system. This was to be followed by testing for result

analysis, using appropriate software for this matter.

After the documentation phase the goals of the project broadened to include

the implementation, which replaced the previous phase of testing by mean of

already developed software available. This new step in fact brought into the scene

information systems technologies, like database programming languages, like PHP,

SQL and HTML.

In brief…

The goals: build a model that effectively implemented decision support making to

the user. The requirements for the implementation, other than the interface, were

to take the theory model built for an individual and “translate” it into a web

application. An appropriate interface should also be put in place.


4. E-Tourism: Current scenario and trends

The Internet has made possible numerous products that have enhanced the

tourism industry, coming from the typical online brochure of a hotel/tourist

destination to incorporate multimedia and online services in its contents opening

the way for new profit/services possibilities.

In fact, owing to their intangible and digital characteristics, tourism

products may no longer be needed because tourists will communicate directly with

hotels and airlines electronically. Or meaning the tendency to avoid intermediaries

in the process. Despite this only a marginal part of the tourism profit is generated

online.

For e-commerce this means that tourism business activities will have to go

beyond the already present online reservation and offer the customers other value-

added services, if the need of intermediaries is to be reduced. Clearly this will

require innovation and sheer entrepreneurship.

In fact, the slow adaptation to e-commerce innovations leads to high

product similarities and severe price competitions among web site operators, as

well as low total tourism market share, as already stated. Also it has been signified

that a more consumer-oriented web-based tourism information system to support

users in travel-related information search, product bundling, and travel planning,

and so on is strongly desired. This is clearly the next step in e-tourism3.

Another important factor in designing this client customized services passes

also in gaining the trust of the customer and the creation of sufficient incentives

for stimulating the curiosity of customers in the business proposition (Nysveen and

Lexhagen3).


5. Theory

In this part we will give some insight into the theory behind our project,

concerning all the subjects mentioned in the introduction.

Firstly we have to make additional remarks to our DSS and also to situate it

into the actual scenario of e-commerce and e-tourism. Also we will devote some

space to the theory behind AHP, since it will be one of the cornerstones of this

project.

This will be dealt in the form of exposing the algorithm and then

consequently show the way in which the AHP theory was incorporated into our case

study problem.

5.1 Decision Support Systems

5.1.1 The scope of DSS in e-commerce 4

The rapid advancement of Internet and Web technologies and the fast

growth of e-commerce applications in recent years have brought strong impacts on

the strategies and processes of business conductions. Many innovative business

models have emerged in the e-commerce environment such as market-oriented e-

Shop, e-Procurement, e-Auction, e-Mall, Third Party Marketplace, Virtual

Communities, Value Chain Service Provider, Value Chain Integrator, Collaboration

Platforms, Information Brokers, and Trust Service Provider.

Major identified e-commerce characteristics include global markets, virtual

organizations, 24/7 operations quick responses, competitive pricing, secure

transactions, multimedia and hypermedia documents, interactive processes,

personalized and customized services, value-added information, innovative

products and services, etc.

The growing Business-to-Consumer (B2C) applications and increasing market

competition have stimulated the needs for more information-intensive and

decision-oriented online consumer-support systems and services that could

incorporate personalized needs and interests in all searching, deciding, and

purchasing processes. As stated previously, in e-tourism the current trend is for


tourism information systems to offer extended decision-making support in tourist

travel planning.

It is obvious that the desired e-commerce-oriented consumer decision and

transaction process is relatively more complex than the traditional buying process,

since it may contain online activities such as product search and discovery, product

and vendor evaluation, price and contract negotiation, transaction and payments,

post-purchase services and dispute resolution.

Moreover, when planning and transaction services for consumer groups or

communities are concerned, extended group decision support capabilities should

be developed and provided.

Therefore, how to apply innovative e-commerce related models and

technologies to facilitate the web-based consumer decision and transaction process

that supports individual and group decision making with expert-level qualities

becomes critical for sustaining e-business competitiveness. As a result, more

sophisticated concepts and advanced technologies for designing the consumer-

oriented intelligent decision support system need to be developed to meet the

increasing market demands.

An intelligent consumer-oriented DSS can be generally identified as a web-

based DSS that provides generic and specific application functions, information

resources, model and knowledge computing mechanisms, as well as communication

facilities to efficiently and effectively assist consumers in making personalized and

group decisions through all phases of the decision and transaction process.

Potential business applications of the consumer-oriented DSS range from

online customized shopping, personalized insurance planning, personal financial

and investment portfolio management, to individual or group travel planning.

5.1.2 History of DSS implementation in the Tourism industry 4

Since the very beginning of this project, a thorough search was made via

internet to position our proposed project and confront it with already developed

products in the DSS area.

The search involved mainly online libraries and other scientific database

warehouses, like ScienceDirect.com also the online ACM Portal (Association for


Computing Machinery). Also the search complemented several tourism portals, like

Opodo (www.opodo.com, a large travel portal for reservations and flights owned by

the main European airliners), Expedia (www.expedia.com, a U.S based tourism

portal with more or less the same scope as Opodo), and Kayak (www.kayak.com, a

U.S online travel search engine). The objective with visiting these previous sites

was to get a feedback on the type of technologies besides the already omni-present

search engine.

Most of these sites indeed already incorporated many up-to-date

technologies, like AJAX, which is an intelligent way to save channel bandwidth by

only refreshing the desired part(s) of a webpage and also CSS, which provides for

some stunning interfaces and easier manipulation of styles inside a web page.

As for examples of web applications tourism focused DSS’s, these were few

and far between. One of the most relevant was A Web-Based Consumer-Oriented

Intelligent Decision Support System for Personalized E-Services 4, which dealt

with presenting an integrated framework for developing web based consumer-

oriented intelligent decision support systems to facilitate all phases of consumer

decision-making process in business-to-consumer e-services applications,

culminating with an example given for e-tourism. This paper, in the literature

review part, indicates that in commercial websites, currently exists ‘some efforts

to assist customers in searching and selecting products and services have been

reported’, or in other words, client-support for decision aiding.

The paper goes on to state some examples, like General Electric Plastics

(www.geplastics.com) which provides datasheets, engineering calculator, and

material selection tools on the company web site to help customers in analyzing

product needs and getting an effective material solution. It concludes this

literature review by stating that ‘although the needs to offer more powerful

capabilities for consumer decision support on the web sites are widely recognized,

the facilities already provided to the consumers are still limited to specific

products and tasks and thus unable to support full-stage and high-quality decisions.

The other part of special interest is the application of the proposed

integrated framework in the e-tourism web application. Several prototype systems

were developed for both the e-tourism and e-investment applications using the

proposed framework and design methodologies, using as background the tourism in

New Zealand. In one of the these there is a system for evaluating package tours in

which consumers select their preferences and weights about destination region,


trip length, price, accommodation rank, departure date, and features, as well as

specify the level of matching. Users can then submit the request to get a list of

matched tour packages for their inspection.

Another interesting application is a page for designing personalized tour plan

in which consumers can design their own trip plan by selecting and bundling

destinations, hotels, and restaurants in daily basis.

Other page is aimed at group travel: community voting that allows

community members to vote on original and alternative trip plans. Before they

make the vote, users can check the content of each trip plan. After inserting a new

vote by someone, new vote counts of all trip plans appear on the ‘number of votes’

column.

Even another great example of value-added online service: the page has a

tour plan bidding session that allows travel agencies to bid on posted group trip

plans. The time interval for submitting a bid, the current lowest bid, and the name

of the associated bidder are also shown in this page.

Finally another application illustrates a continuing recommended personal

insurance portfolio plan in which insurance types, principal, duration, and premium

are shown in response to a consumer’s need and preferences.

A final note is required to say that these described systems are only

prototype at the moment, after we tried to retrieve more information in the net

for better understanding of features and technologies

5.1.3 Taxonomies of a Decision Support System 5

After a basic introduction to DSS, we need to explain in more detail the

architecture exposed in the introduction. But in a first glance there is firstly a need

for classify our DSS, in light of current types of DSS available nowadays.

Work on the taxonomy of DSS has been conducted since the development of

DSS. As with the definition, there is no all-inclusive taxonomy of DSS either.

Different authors propose different classifications. This classification is in

general done at three levels:

• user level, the level of interaction between user and system,


• conceptual level refers to the goal for which the DSS was designed,

type of operation, data manipulation…

• technical level, if the system is based in one single computer or

distributed around a large organization

At the user-level, the paper differentiates passive, active and cooperative

DSS: a passive DSS is a system that aids the process of decision making, but that

cannot bring out explicit decision suggestions or solutions, while an active DSS can

bring out such decision suggestions or solutions. A cooperative DSS allows the

decision maker (or its advisor) to modify, complete, or refine the decision

suggestions provided by the system, before sending them back to the system for

validation. The system again improves, completes, and refines the suggestions of

the decision maker and sends them back to her for validation.

The whole process then starts again, until a consolidated solution is

generated.

At the conceptual level, it differentiates Communication-Driven DSS, Data-

Driven DSS, Document-Driven DSS, Knowledge-Driven DSS, and Model-Driven DSS.

A Model-Driven DSS emphasizes access to and manipulation of a statistical,

financial, optimization, or simulation model. Model-Driven DSS use data and

parameters provided by DSS users to aid decision makers in analyzing a situation,

but they are not necessarily data intensive.

A Communication-Driven DSS supports more than one person working on a

shared task: examples include integrated tools like Microsoft’s NetMeeting.

Data-Driven DSS or Data-oriented DSS emphasize access to and manipulation

of a time-series of internal company data and, sometimes, external data.

Document-Driven DSS manage, retrieve and manipulate unstructured

information in a variety of electronic formats.

Finally, Knowledge-Driven DSS provide specialized problem-solving expertise

stored as facts, rules, procedures, or in similar structures.

At the technical level, the paper differentiates between enterprise-wide DSS and

desktop DSS.

Enterprise-wide DSS are linked to large data warehouses and serve many

managers in a company. Desktop, single-user DSS are small systems that reside on

an individual manager’s PC.


5.1.4 Taxonomy of the proposed DSS

We are now in a position to classify our DSS according to the taxonomy

shown:

So at user-level we can see that since our DSS can classified as active since the

system will deliver a recommendation of the hotels that best suit the user/users

preferences, from the initial input of desired characteristics/features of the ideal

hotel (like price, location, services available etc…).

It cannot though be considered cooperative since the system doesn’t refine

the optimization: the only possibility for the user is to start again and choose new

parameter inputs for the consequent optimization, as the AHP method as we will

see later on, doesn’t allow for changes during its implementation.

Also we can say that the DSS is model-driven since it will optimize the

alternatives according to the AHP algorithm.

Finally and looking at the system from the technical level we can point out

that the DSS will be of desktop type since the DSS will be run always from a single

PC although this single workstation will permit decision making for a group.

5.1.5 Evaluation features for our DSS

In this part, we need to clearly specify the aspects or features that will be

used for assessing DSS performance.

One element for further improving/upgrading this project is to put in place a

common framework that will allow for the use of this application (of course with

some differences in its implementation) in other tourism destinations.

This means that the system must have some flexibility in order to adapt to

contrasting destinations, like for example a skiing destination. If we look to the

available literature dealing with DSS’s, one can see that the main drawbacks in its

design are:

• Poor maintainability, that illustrates that a decision-maker

sometimes has to leave the focus on decision making and has to spend

some time and attention in maintenance of the DSS.


• Poor flexibility, which means that DSS’s are often too much

application-specific, with difficulties in updating/upgrading

In fact and given the nature of our proposed DSS, we can consider flexibility

for different tourism destinations as the main factor in evaluating our application.

5.2 AHP – what is it all about?

For the present problem there is a need to address the way in which users

will express their preferences/wishes and evolve from there to a ranked

prioritization of alternatives according to the expressed characteristics.

The Analytic Hierarchical Process (AHP), created by Thomas Saaty13 in the

1970’s, is an excellent tool for optimization procedure in multi-criteria

environment, when several alternatives are presented to the user.

It allows as we already stated the capacity to synthesize both quantitative

and qualitative information into a hierarchical model, by means of pair-wise

comparisons of alternatives of criteria and then of alternatives to the criteria

proposed in the decision problem. The method is comprised of the following steps:

1. Structure a problem in the form of a hierarchy with objectives,

criteria and alternatives.

2. Asks for judgments regarding a decision-maker’s relative preferences

for criteria and alternatives and represent those judgments with

numbers.

3. Use the numbers to calculate the priorities of the criteria and

alternatives in the hierarchy.

4. Complete the synthesis of these results to determine the ‘best’

alternative.

Step 1 – Structuring of the decision problem into a hierarchical model

It includes decomposition of the decision problem into elements according to

their common characteristics and the forming of a hierarchical model having

different levels.


The simplest AHP model has only three levels, namely Objective, Criteria

and Alternatives. This phase is a fairly important part of the method so as to

represent the decision making problem faithfully. Saaty13 recommends care in

designing the model so that the structure effectively represents the problem in

hands.

Fig.4 – A typical AHP structure

Step 2 – Making pair-wise comparisons and obtaining the judgment matrix.

Next, the decision-maker expresses his/her opinion regarding the relative

importance of the criteria and preferences among the alternatives by making pair-

wise comparisons using a nine-point system ranging from 1 (the two choice options

are equally preferred) to 9 (one choice option is extremely preferred over the

other).

If, however, one criterion is preferred less than the comparison criterion,

the reciprocal of the preference score is assigned. The use of reciprocals yields the

property such that (ai,j).(aj,i)= 1, where ai,j, the preference score of criterion i to

criterion j, aj,i, preference score of criterion j to criterion i and aj,i=1/ai,j .

The AHP scoring system is a ratio scale where the ratios between values

indicate the degree of preference. The nine-point scale has been the standard

rating system used for the AHP. Its use is based upon research by psychologist

George Miller, which indicated that decision makers were unable to consistently

repeat their expressed gradations of preference finer than ‘seven plus or minus

two.’


Intensity of

importance

Definition

Explanation

1

3

5

7

9

Equal importance of both elements

Moderate importance of one

element over another

Strong importance of one element

over another

Very Strong importance of one

element over another

Extreme importance of one element

over another

Two elements contribute equally to

the property

Experience and judgement slightly

favour one element over another

Experience and judgement strongly

favour one element over another

An element is strongly favoured and

its dominance is demonstrated in

practice

The evidence favouring one element

over another is of the highest

possible order of affirmation

Table 1 – AHP’s 1-9 scale

Step 3 – Local weights

In this step, local weights of the elements are calculated from the judgment

matrices using the eigenvector method (EVM).

The normalized eigenvector corresponding to the principal eigenvalue of the

(judgment) matrix provides the local weights of the corresponding elements.

To do so, there is the need to define the comparison matrixes which makes

the pair-wise comparisons between each criterion of the decision model.

After knowing the preferences of the user by an interface used to capture

the more preferable criterion, these are represented in a matrix which compares

the criteria with respect to the main goal (Fig:4 Table A), calculating the local

weights of each criterion has to the user.


Secondly, the need of comparing each alternative with respect to each

criterion (criterion 1…, criterion n), will give respectively the local weights of each

alternative

However other comparisons must be made in order to capture the relation of

preference between possible alternatives. For that reason other matrixes are

needed in order to calculate the local weights, there are built n+ 1 matrix as n,

number of criterion.

A: Comparison of criteria with respect to goal

Criteria C1 C2 C3 Local weights

C1 1 5 4 0.400

C2 3 1 5 0.394

C3 1/4 1/5 3 0.128

B: Comparison of alternatives with respect to Criteria 1

Criteria 1 A1 A2 A3 Local weights

A1 1 1/3 5 0.279

A2 3 1 7 0.649

A3 1/5 1/7 1 0.072

Table 2 and 3 – Example of the two types of matrixes, criteria matrix and alternatives matrix: pair-wise comparison and

local weights

Step 4 – Aggregation of weights across various levels to obtain the final weights

of alternatives.

Once the local weights of elements of different levels are obtained as

outlined in Step 3, they are aggregated to obtain final weights of the decision

alternatives (elements at the lowest level).

For example, the final weight of alternative A1 is computed using the following

hierarchical (arithmetic) aggregation rule in traditional AHP:

Final Weight of A1 = ∑i

(Local weight of A1 with respect of Criterion Cj) ×(Local weight of Cj )


The final weights are calculated using the local weights of each alternative

regarding each criterion and the local weights of each criterion as shown in the

expression above.

This expression will calculate the priorities which each alternative.

Notice that the sum of all final weights must be equal to a unit (1). This will prove

that the method used is being well followed as well as confirming all the steps

made before.

The final values reached (estimate weights) inform (to contemplate explicit

or implicit knowledge) about the possible alternatives and the way they are used to

satisfy the selected criterion, as well as the importance of these criterion in order

to reach the goal of the better alternative to choose from.

Taking this into regard we have reached a result where we can affirm which

alternative is more preferable from the user point of view.

Step 5 - Inconsistency and Sensitivity Analysis

In making a sequence of pair-wise comparisons, especially for systems that

have five or more criteria and/or alternatives, we would expect that the estimates

of the unknown weights, as reflected by the weight estimates (ratios) given in

answer to the pair-wise comparison questions, need not be exact or consistent.

The AHP measures inconsistency by comparing the DM’s data to a set of

random results that assumes, for the same size matrix, that the estimates were

random. Saaty developed a measure of inconsistency, called the inconsistency ratio

(IR) that is based on fundamental theoretical results on the size of the largest

eigenvalue for the matrices in question.

This ratio measures transitivity of preference for the person doing the pair-

wise comparisons. To illustrate the meaning of transitivity of preference, if a

person prefers choice A over B, and B over C, then do they in consistent fashion

prefer A over C?

This index provides a useful check because the AHP method does not

inherently prevent the expression of intransitivity of preferences when ratings are

being performed.

The AHP consistency index compares a person’s informed preferences ratings

to those generated by a random preference expression process:


An arbitrary but generally-accepted as tolerable level of inconsistent

preference scoring with the AHP is less than or equal to 10% of the total number of

judgments.

Calculation of the Inconsistency Ratio (IC)

The process of acquiring the values so we can reach the final result is

divided into 4 steps:

1. Synthesizing the pair-wise comparison matrix 2. Calculating the priority vector for a criterion 3. Calculating the consistency ratio 4. Selecting appropriate value of the random consistency ratio

1st. Calculate the weights with respect to the initial matrix of criterion and its local weights (criteria weights). 2nd. Calculate the inconsistency index with respect to the criterion weights and the weights driven in Step 1:

∑=

=n

i weightscriteriastepofvectorfinal

n 1max _

1___1λ

n: degree of the matrix

3rd. Calculate the Inconsistency ratio: IC

1

max

−−

=n

nIC

λ

4th. Compare the IC ratio with the random index (RI) with respect to the corresponding n.

RIIC


Table 4 – Average random consistency

In order to get a better understanding of the various steps described in this

part we have included an example of AHP application in annex. This example will

give the reader a better insight into the methodology of the AHP as well as a more

intuitive feel for it.

5.3 The reason behind choosing AHP

At the phase of documentation, it became apparent that AHP has a wide

application scope, being regarded as a powerful tool for multi-criteria decision

making for both individual and group. The method was firstly designed for a single

user but the capabilities of the algorithm were extended to achieve group decision

making. Its robustness, flexibility and the fact that it synthesizes the final results

vertically according to the structure followed for the decision making problem.

Another fact is that AHP copes well associated with other tools, like linear

programming, fuzzy logic and other methodologies (Machado 6).

Disadvantages found with AHP relate to the following according to

Goodman7:

• Verbal to numeric scale conversion – decision agents that use the AHP’s

verbal comparison mode have their judgements automatically converted to

the 1-9 numeric scale, but the correspondence between the two scales is

based on non-tested theory base. For example if A é judged to be weakly

more important than B, the AHP assumes that A is 3 times more important

than B, which may not be the case at all. There is some argumentation that

factor 5 is too strong to denote the notion of strong preference.

• Inconsistencies imposed by the 1-9 scale – in some cases the pair-wise

comparisons under the 1-9 scale may lead the decision agent to commit

several inconsistencies. For example, if A is considered to be 5 times than B

Size of

matrix, n 1

2

3 4 5 6 7 8

9

10

Random

consistency

0

0

0,58

0.9

1.12

1.24

1.32

1.41

1.45

1.49


and B is 5 times more important than C that should make A 25 times more

important than C; but that is not possible, due to the fact that the scale

goes from 1 to 9.

• Significance of responses to the questions – the weights are obtained

without any reference to the scales in which the attributes are measured,

which may mean that the questions are interpreted differently, and possibly

wrong, by the each of the decision makers.

• Rank Reversal – this can be easily understood by the following example: if a

company had to choose a city for establishing a new sales office, and that

the method gave the following global ranking of alternatives: 1st

Albuquerque, 2nd Boston, and 3rd Chicago. However if a new city, Denver,

was proposed to the already existing set of alternatives and if we repeated

the application of the method in order to accommodate the new alternative.

Even if the relative importance of the attributes remains the same, the new

analysis gives this ranking: 1st Boston, 2nd Albuquerque, 3rd Denver and 4th

Chicago reversing the ranking of the Boston and Albuquerque. This comes

from the characteristic that all weights are normalized to give a total sum of

1.

• The number of comparisons can be large – while the existing redundancy

inside the AHP method can be interpreted as a technical advantage of the

method (because it allows the verification of the previously made

comparison), it can, on another way, require a large amount of judgements

by the decision maker. For example a seven alternative problem with 7

attributes will take 168 pair-wise comparisons, which puts difficulties on the

application of the method. In our implementation, however, this won’t be a

reason for concern since the AHP will be mostly based on database lists.

Even with these drawbacks, the method has great intrinsic value due to the

hierarchical structuring of a problem and the facilitation of the dialogue between

decision makers. In this fashion, the AHP is perfectly adapted as long as its

limitations are taken into account. A good example of this, is the large number of

DSS applications that incorporate AHP as a decision making tool.


Turning our attention to group decision, many refer to AHP ‘as well suited

for this task due to its role as a synthesizing mechanism by means of its capability

to accommodate both tangible and intangible characteristic, individual values and

shared values’ (Lai 8). Also it can help structure a group decision so that the

discussion centres on objectives rather than on alternatives.

5.4 Information Systems Technologies

The project will use information systems methodologies in order to achieve

the task of ‘translating’ the model built on the AHP algorithm, for the two

possibilities listed (individual or group travel).

We will use PHP to implement the database scripting and SQL to develop the

necessary queries between application and database. A brief description of both

these technologies follows:

PHP

PHP stands for a recursive acronym of Hypertext Pre-processor and is

defined by its creators as [9] ‘an open-source server-side scripting language for

creating dynamic Web pages for e-commerce and other Web applications’.

PHP is described as an interpreted language that has absorbed a mixture of

features from procedural languages like C, object oriented languages like Java,

shell languages like Bash, a similar multi-parented language Perl, and various other

languages.

It is intended for writing small portions of code that are embedded in HTML.

The PHP code is run on the server, and is used to generate the dynamic portion of

the HTML, that depends on the values entered into forms by users of web browsers,

and the content of databases on the server. It is concise, and has many powerful

library functions. However, features such as the lack of declarations and type

checking make it a poor general purpose language for writing large programs.

Nowadays, its implementation at a global scale is a testimonial to its

capacity of providing [9] ‘simple and universal solution for easy-to-program


dynamic Web pages’ as well as to an intuitive syntax which facilitates learning to

anyone with basic programming skills.

Also because it is an open-source product, allows the support of a large

group of open-source developers worldwide. This provides users with excellent

technical support and bugs are found and repaired quickly.

Other feature is the excellent connectivity to most of the common databases

(including Oracle, Sybase, mySQL, ODBC and many others), and its integration with

various external libraries, which allows the developer to do anything from

generating PDF documents to parsing XML and other.

Another key advantage of PHP, when compared to other scripting languages

such as ASP or ColdFusion, is that it is open-source and cross-platform, suitable for

today's heterogeneous network environments.

Given this and according to [9], PHP is accounted ‘as today's fastest-growing

technology for dynamic web pages’ and according to a specialized internet

technology survey (conducted by Netcraft, www.netcraft.com/survey/ ) ‘PHP can

now be found on more that 6 million domains, and is growing at a rate of up to

15% each month’.

SQL 10

Structured Query Language (SQL) is the most popular computer language

used to create, modify and retrieve data from relational database management

systems.

The language has evolved beyond its original purpose to support object-

relational database management systems. It is an ANSI/ISO standard.

SQL allows the specification of queries in a high-level, declarative manner.

For example, to select rows from a database, the user need only specify the

criteria that they want to search by; the details of performing the search operation

efficiently is left up to the database system, and is invisible to the user.

SQL standard was first introduced in 1986 although its beginnings date to the

70’s. As the name implies, SQL is designed for a specific, limited purpose —

querying data contained in a relational database. As such, it is a set-based,

declarative computer language rather than an imperative language such as C or


BASIC which, being programming languages, are designed to solve a much broader

set of problems

Compared to general-purpose programming languages, this structure allows

the user/programmer to be less familiar with the technical details of the data and

how they are stored, and relatively more familiar with the information contained in

the data. This blurs the line between user and programmer, appealing to

individuals who fall more into the 'business' or 'research' area and less in the

information technology area.

The original vision for SQL was to allow non-technical users to write their

own database queries. While this has been realized to some extent, the complexity

of querying an advanced database system using SQL can still require a significant

learning curve.

Although SQL is defined by both ANSI and ISO, there are many extensions to

and variations on the version of the language defined by these standards bodies.

Many of these extensions are of a proprietary nature, such as Oracle

Corporation's PL/SQL or Sybase and Microsoft's Transact-SQL.

It is also not uncommon for commercial implementations to omit support for

basic features of the standard, such as the DATE or TIME data types, preferring some

variant of their own. As a result, in contrast to ANSI C or ANSI Fortran, which can

usually be ported from platform to platform without major structural changes, SQL

code can rarely be ported between database systems without major modifications.

There are several reasons for this lack of portability between database systems

such as:

• The complexity and size of the SQL standard means that most

databases do not implement the entire standard.

• Many database vendors have large existing customer bases; where the

SQL standard conflicts with the prior behaviour of the vendor's

database, the vendor may be unwilling to break backward

compatibility.


6. Design of the AHP model

After a thorough description of the AHP method, it’s time to create the AHP

structures that will carry translate the scenarios exposed for the individual & group

travel selection.

We will derive a model for each of the two cases using the already exposed theory.

6.1 Individual Travel Selection

In interpreting the individual travel selection one should first identify clearly

the elements that we will want to integrate into our structure. From the case study

presented it’s obvious that the alternatives will be hotels or other kind of tourist

lodging. This was made clear when the goals were exposed.

Secondly and since the decision making resides only in an individual, the

goal is to optimize the client’s input preferences for his/hers desired vacation

lodging. The final part is to identify the criteria for which we wish the customer to

do the pair-wise comparison in the 1-9 scale. The issue is identifying the right

parameters that will describe completely our scenario.

This part was carefully accompanied with responsible of ADAPTIVE, through

swapping of views and ideas about the subject: after some discussion, three

criteria items were selected:

• Location of the hotel

The location determines the type of vacation available; for example a hotel

located near the mountains will be more suited for hiking and other mountain

terrain activities, although it doesn’t exclude the possibility of doing beach

activities. Another example is if the individual is looking for a typical beach

vacations a resort located with direct access to the sea will be the obvious choice.

Each hotel has a classification in terms of the types of locations at our

disposal (Sea, Mountain and Centre). We will use the 1-9 scale for facilitating the

conversion for the AHP method.


• Price

The price range is an obvious criterion in travel/hotel selection problem.

• Quality of Accommodation

This was the criteria that raised more doubts about its existence. In fact one

can say that price is directly related to the quality of the accommodation and thus

the parameter being useless. This is because the AHP method recommends care on

the selection of criteria based on mutual exclusion of criteria.

However, and after some research around the hotels of Madeira in general,

one can see that for example there were quite a few hotels of 3 stars that had a

very similar price compared to 4 star ones. This was also the case with some 4 and

5 star hotels although in a less significant manner. For this reason and because the

number of stars in a hotel determines certain quality parameters of services and

infrastructures, we decide to include the quality of accommodation in our

structure. The star rating will serve as guarantee of services for the user.

The next step is to define the hierarchical structure, based on the previous:

Fig.5 – AHP structure for the individual travel selection

As we see the structure is a very simple AHP structure with 3 levels. One

final note is about the number of alternatives at our disposal: in the scheme

presented the alternatives are supposedly as many as the user wants.


Let’s not forget that before the optimization procedure there is a search

engine that will limit the alternatives according to the preferences of services,

infrastructures, nearby facilities and/or services etc…the search engine will be

properly detailed in the implementation phase.

6.2 Group Travel Selection

The Individual Travel Selection didn’t pose much work on the documentation

due to the fact that it is a classic application of the AHP method, as seen in

numerous books/papers on the subject.

For the Group Travel Selection we wanted to continue to use AHP as it would

permit considerable savings in the implementation of the web application. So the

emphasis was in finding adequate literature that dealt with Group Decision Support

System (GDSS) in a multi-criteria environment preferably in theory for the purpose

of orientating our work in this stage of the project. The first task involved

consulting papers and/or other types of information (web sites, etc…) that

employed some kind of a Group Decision Support System (GDSS).

After this stage several papers were considered, but we decided to base our

implementation of the Group Travel stage on two papers, namely Group Decision

Making and Hierarchical Modelling 11, by Jablonsky and Lauber, Group Decision

Making in Multiple Criteria Environment: A case using the AHP in software

selection 8 by Vincent S. Lai, Bo K. Wong and Waiman Cheung and finally

Aggregation of analytic hierarchy process models based on similarities in

decision makers' preferences 12 by N.Bolloju.

Analysis of the documentation fetched

The structure of a Group Decision Support System (GDSS) adopted in

Jablonsky et Lauber11 used, as already mentioned, AHP as the main core of the

decision making structure:


Fig.6 – The AHP structure adopted in Jablonsky et Lauber

The proposed hierarchy presented here suggests a set of levels for which we

will give a brief description. The article assumes that there is an inherent conflict

in the decision making process, so it proposes that the Level 1 (or goal of the

problem) must be an apparent compromise between the members of group (that

may have different weights in the final decision). The paper later goes on to

quantify this “compromise” into an index.

For our case however the goal of looking for a compromise between all is not

important, so the analytical study presented in the paper on how to reach a

compromise between the members wasn’t considered. So for this matter our goal is

to find the alternative, given each member’s weight in the decision process that

best suits the group’s wishes with no special care for conflict resolution (we

assume that the AHP already considers this implicitly in its implementation for

group decision).

The remaining levels are relatively straightforward: Level 2 represents each

member’s view of the perfect location for their holidays (or Party to the Conflict in

the original structure), Level 3 the criteria (the same as in the individual Travel

Selection) and finally in Level 4 the alternatives available to choose from.

The relations between levels derived from the hierarchy can be converted

into a numerical form and interpreted as follows:


• Level 2 - evaluation of the importance of the parties to the conflict with

respect to the given decision problem - weights of the parties to the

conflict

• Level 3 - evaluation of the importance of the criteria with respect to the

individual parties to the conflict - weights of the criteria

• Level 4 - evaluation of the scenarios - local priorities (with respect to the

given criterion and the given decision maker) and global priorities

(synthesized from the local preferences) are the direct basis for the final

decision (finding the consensus, ordering of the scenarios, etc.).

The priorities of the scenarios/alternatives lead apparently in the typical

case to the different results when the parties to the conflict are taking into

account individually.

That is the basic aim of the conflict resolution is to find such approach that

will make it possible, e.g. based on an interactive procedure, getting from the

local priorities of the parties to the conflict to global priorities.

6.3 Proposed Procedure / Hierarchical Structure

In this step we will show the hierarchical structure for the Group Travel

Selection, according to the remarks made in previous step:


Fig.7 - Proposed Hierarchical Structure for Group Travel phase

6.4 AHP applied to GDSS: How to do it?

As stated before, the AHP algorithm is applied to our problem in very similar

conditions comparing to the individual travel selection: firstly the AHP is applied

individually to each individual.

Secondly, the weight in the decision making process (again for each

member) as well as the aggregation of the individual preferences are introduced

into the problem following the Weighted Arithmetic Mean Method, as shown in

Bolloju12.

From this document that describes methods for synthesizing a group

decision, two different methods are presented: the geometric mean method (GMM)

and the Weighted Arithmetic Mean Method (WAMM).

The reason why WAMM was chosen is because the several members of the

group may have radical differences in their judgment about the most suitable

alternative. The subject of the aggregation procedure will be detailed below:

• STEP 1: INPUT DATA

In first notice, each one of the group’s members must fill in a text box, with

personal data as well as his/hers preferred location (remember that it can be a


beach resort or a country cottage for example) for their proposed vacations. Then

each member designates its importance in the group decision (from 0 to 1, meaning

1 the total decision for the group and that the sum of importances cannot be

higher than 1). The data is stored in database tables

Finally a listing of all hotels that comply with the alternatives chosen by all

users is displayed. The users can eventually discuss the alternatives and remove

any of them if they wish so. The remaining alternatives enter the individual AHP.

• STEP 2: INDIVIDUAL AHP

After this is done, the AHP is implemented in roughly the same way as in the

individual choice. For each comparison matrix the user makes the pair-wise

comparisons between for the three selected criteria. The criteria remain the same:

PRICE, QUALITY and LOCATION.

The only difference is in the matrix that relates the LOCATION criteria with

the alternatives offered. In this case, the matrix follows the type of LOCATION

chosen by this individual alone.

After the insertion of data into the 4 tables per member, prioritization of

alternatives is made for each member. The next step will aggregate the individual

results.

• STEP 3: PASSING FROM INDIVIDUAL PRIORITIES TO GLOBAL

PRIORITIES

After the prioritizing of the alternatives is computed, we use the Weighted

Arithmetic Mean Method for achieving the prioritized group alternatives. This is

done by aggregating the corresponding matrix for each of the group members. For

example, and imagining that the group is composed of three elements, there will

be 4 aggregating matrixes: each matrix is built in following manner:


Pairwise comparison matrix Member 1



Aggregated comparison Matrix Group

Fig.8 – Aggregation of the individual judgments into the group’s judgment matrixes for group decision

in that each member of the aggregate group matrix,

∑ == n

k kijkaggregatedij awa1 ,, . ,

with k depicting the kth member of the group, i the line of matrix and j the column of the aggregate group matrix.

This process is followed for the other matrixes which results in the 4

predicted ones.

After these matrixes are computed, we simply derive the local weights and

the final weights in the same manner as in the individual case.


7. Implementation

7.1 Introduction

In this part we will detail the implementation of our DSS, following the

derived models for the knowledge engine already described in the previous parts.

The 1st stage in the implementation is to build an entity-association model for

describing our database. The E/A model must not though to be considered

definitive since it may not describe all the perceived restrictions, due to its

subjective nature but it will, nonetheless, establish a design approach to our

database.

In the E/A model, the scenario we wish to depict is illustrated by means of

entities and its relations between them. The relations between them are pretty

much straightforward so description of it is relatively scarce.

Also before designing a fully functional search engine we have to consider

the entities/attributes that we will use to describe a hotel or other kind of tourism

lodging. Considering all the possible information about tourism lodging we selected

the following entities (bold) and its respective attributes (underlined):

• Chain of hotels: name of chain.

• Unit info: name of hotel, the type of hotel, phones, e-mail, star

rating, website, prices for each kind of available room. Other

important feature is the classification in a 0 – 10 scale of the 3 types

of location, Sea, Centre and Mountain. This was made by measuring

the distance of each hotel to the nearest sea access, to the city

centre (in our case the historical centre of Funchal) and mountain

access, respectively.

• Services made available by the hotel: these include paid or free and

include for example internet access, parking, or organized trips

(whether it may refer to land or sea).

• Location, with street and postal address, and most importantly the

type of accesses that the hotel possesses: for example if a hotel has

direct access to the ocean, or in case of a mountain lodging to hiking

trails or to other leisure activities grounds. Also descriptions of the


views from the hotel are available. Finally there is a classification of

the hotel according to the accesses and location: beach, rural,

mountain and city (called nearby). This classification is not limited to

one single choice: a hotel can be classified as beach and city for

example.

• Types of rooms available: description of rooms and their number

• Food, describes if type of meals (half-board, full board) or the

customer has facilities for self catering.

• Facilities, describes the facilities available in the hotel (for example,

tennis courts, swimming pools etc…)

Entities

Chain

Fields Type Null? Links for Commentaries namechain varchar(30) No Name of the hotel chain

Facility

Field Type Null? Links for Commentaries namefacil varchar(20) No type of facility

Food

Field Type Null? Links for Commentaries namefood varchar(20) No type of food

Location

Field Type Null? Links for Commentaries

access varchar(15) Yes Type of access that an hotel or hotels gots

views varchar(10) Yes Type of view that an hotel or hotels gots

nearby varchar(15) Yes If it nearby or close from a place

street varchar(50) Yes The address of a certain hotel

zip1 varchar(4) Yes Postal code. The first four digits.

zip2 char(3) Yes Postal code. The last three digits.


municipally varchar(20) Yes Municipally –> name Municipality

Municipally

Field Type Null? Links for Commentaries name varchar(30) No Name of the municipality

Roomtype


nametype varchar(25) No Name of the type of room

Service

Field Type Null? Links for Commentaries nameserv varchar(20) No Name of a service

Typeserv


name varchar(10) No If it is paid of free the service

Unit

Field Type Null? Links for Commentaries nameunit varchar(30) No Name of the unit numstar int(11) Yes Number of stars

type varchar(10) No Type of unit phone1 varchar(21) No phone2 varchar(21) Yes

fax varchar(21) Yes website varchar(60) Yes email varchar(40) Yes

pricemin int(30) Yes Minimum Price that hotel can offer

pricemax int(30) Yes Maximum Price that hotel can offer

namechainu varchar(30) No chain -> namechain

Name of the chain that a hotel belongs

streetunit varchar(30) No location -> street The address of the unit

sea int(11) No Ranking 0 to 10 for the implementation of AHP

concerning Location

mountain int(11) No Ranking 0 to 10 for the implementation of AHP


concerning Location

center int(11) No Ranking 0 to 10 for the implementation of AHP

concerning Location

User


ticket int(6) No

The user will have a certain ticket that will be used for identifying all users at will be grouped on Group Decision Making

Tables 5 to 15 – Database Entities and their description

Associations

Choose

This table was created to keep the hotels that were chosen on Hotel Search and all

the ranking values that were used for the AHP method.

Field Type Null? Links for Remarks

nameunitch varchar(30) No unit -> nameunit

Name of unit of the chosen ones

priceminch int(30) Yes Ranking values of Minimum Price

numstarch int(10) No Ranking values of Maximum Price

seach int(11) No Ranking values of Location (sea)

mountainch int(11) No Ranking values of Location (mountain)

centerch int(11) No Ranking values of Location (centre)

Chooses

A ticket is going to be attributed for every user that will associate with the unit he has chosen.


nameunitcho varchar(16) Não unit -> nameunit


ticket int(6) Não user -> ticket

got

Field Type Null? Links for CommentariesNameunitgot varchar(16) No unit -> nameunit

Nameservgot varchar(20) No service -> nameserv

typeserv varchar(5) Yes

gotan

Field Type Null Links for Commentariesnameunitgotan varchar(16) No unit -> nameunit

nametypegotan varchar(25) No roomtype -> nametype

gots

Field Type Null? Links for Commentariesnameunitgots varchar(16) No unit -> nameunit namefoodgots varchar(15) No food -> namefood

pricefood decimal(5,2) Yes

offers

Table 16 to 21 – Database associations and their description

Field Type Null? Links for Commentariesnameunitoffers varchar(16) No unit -> nameunit

namefacil varchar(20) No facility -> namefacil


Fig.9 – Database’s E/R model

The database technologies used were SQL, PHP 4.0. One idea already

present for future upgrading this DSS is to use new technologies like AJAX and

SQLite which will provide better usage of resources as well and better

interface/usability from the user’s point of view. Other powerful tool for upgrading

the interface is RICO, an open source JavaScript library for creating rich internet

applications, compatible with AJAX.

Fig.10 – Use of the PHP and SQL in the DSS


7.2 Description of the search engine

The user when accessing the web application will encounter an interface

which will be divided on two important sections:

1. Selection of attributes

2. Display of hotel units (according to selected attributes).

Fig.11 – Selection boxes for attribute insertion

Description of the search selection boxes

In the top-left one can find the price scroll bar: the user will use it to define

the upper limit for the price tag in the hotel search.

The user can also choose hotels of a particular star rating: this selection is

made on the following text box right below the price scroll bar. One might wonder

if this will affect the AHP method since one of the criteria is the Quality. In fact if

a selection of hotels that has the same star rating enters the attribute comparison

all the derived local weights in the pair-wise comparison for Quality for each hotel

are the same, not influencing in pervious manner the derived global priorities (for

the Quality criteria) that will then follow to the final solutions.


The other selection boxes follow from our description of the database

entities and attributes indicated earlier such as the access, municipality of the

desired hotel, desired facilities and services, views from the hotel or type of food

services offered by the hotel.

The initial step is to illustrate all the hotels from the database; the next step

is when an attribute is chosen by the user a new request will be asked to the

database by filtering a new search.

After the display of the hotels, the user has an option of eliminating any of

listed hotels on the page. In any case the user must select the alternatives that he

wishes to go ahead using the AHP.

Fig.12 – Search engine with selection boxes and hotel listing

In the next step, the AHP model is introduced. We will describe separately

the implementation for the two mentioned case (individual and group travel).

7.3 Individual Travel Selection: implementation

In the individual case, the search engine used will be equal to one described

previously. So in this part we will detail the implementation of AHP method to our


case, following the established design. The 1st part is to introduce the pair-wise

comparison between the criteria.

Fig.13 – Pair-wise comparison of criteria

Some notes: the scale is not in the usual form of the 1-9 scale as described

earlier but varies between -9 and 9. This is because we need to differentiate the

relation between the pair-wise: for example, if we say that A is -5 compared to B

according to our conversion means B is 5 compared to A, in the 1-9 scale.

After this step, the information needed to accomplish the method is

complete. The next step is to perform the pair-wise comparisons between

alternatives regarding each criterion proposed. All data is contained in the tables

of the database, and classified in a 0-10 absolute scale.

For achieving the 1-9 AHP scale (for the pair-wise comparison of

alternatives) we will use the numeric difference between the values of each

respective attribute regarding LOCATION, PRICE and QUALITY for each of two

alternatives. This difference will then be mapped into the 1-9 scale by means of an

appropriate table of conversion that will be described in next step. After this, the

matrixes are filled in with the appropriate values taken from the lists saved on the

database.

As already mentioned, we will have in any case 4 matrixes, one comparing

criteria vs. goals the other three are the judgements matrixes (pair-wise


comparison of the alternatives with respect to the criteria). These matrixes will all

be square (number of rows equal to number of columns).

7.3.1 Construction of the judgement matrixes

As stated earlier the user input ends at the pair-wise comparison of the

criteria. The values that we are going to input into the following matrixes

(judgement matrixes) are retrieved from the hotel lists in the database.

Construction of the Judgement Matrix regarding Price

One problem was how to interpret the various prices of the different types

of rooms available. To make matters worst the type of rooms differed quite

significantly which made comparison of these difficult and also most importantly

the prices varied quite a lot.

After some discussing we decided that the minimum price of each hotel

should be the one to be used. This decision was made after we observed that the

minimum price offered a good indication of the hotel’s general price tag.

The next point is to explain the conversion from the 0-10 scale to the AHP’s

1-9 scale. The problem arises from the fact that the 1-9 scale is a relative scale,

i.e. a classification on the 1-9 scale only has meaning if we compare two

alternatives at a time. Because of the nature of this scale, for each time that the

AHP method is applied to the selected alternatives, we classified the prices in 0-10

scale in the following manner:

The hotel with the most expensive price is classified with 10. All the other

hotels with remaining prices are classified using a simple linear transformation.

This procedure is followed every time that the user enters the chosen alternatives

into the attribute comparison.

The following issue is: two alternatives with values in the 0-10 scale that we

need to convert to the 1-9 scale. Since we are dealing with an absolute scale (the

0-10 scale) we can say that for example that if A has 10 as its price value and B

only 5, we can say that A is twice more expensive or that the difference between

them is 5. This difference will be used to convert into to the AHP 1-9 scale, by

using the following table:


Numeric Difference

between alternatives

(in 0 -10 scale)

AHP

conversion

(1-9 scale)

Description

0

1

If alternatives have the same value, alternatives have

the same importance.

1

2

3

3

If the alternatives have a maximum difference of at

least 3, then we consider one alternative to be

moderately important over the other.

4

5

5

If the difference is considered to be relevant (4,5 or 6)

we say that one is more important than the other

6

7

8

7

The difference between alternatives are quite

noticeable, making one much important than the other

9

10

9

The difference between alternatives are so high, that

one says that one alternative is extremely important

compared to the other

Table 22 – Conversion between the 0-10 scale and the AHP scale.

Construction of the Judgement Matrix regarding Location

As mentioned before, each hotel’s location is characterized in terms of

distances to the sea, mountain and city centre accesses. This is done by using the

0-10 scale once again. Then the LOCATION matrix will be filled with values

obtained using the same conversion table of the AHP 1-9 scale for comparing

alternatives.


In this case the minimum value of the 0-10 scale (0) means that the hotel

has direct access to a specific location while, for example, 10 would mean that the

hotel is very far from that location.

Example:

Pestana Carlton Hotel is a 5 star hotel with the following location attributes:

1. Sea – 0

2. City Centre – 2

3. Mountain – 8

This classification means that the hotel has direct access to sea, is close to the city

centre and is far from the mountains.

Construction of the Judgement Matrix regarding Quality

The 0-10 scale was adopted for conferring consistence and equal conversion

for each of the three criteria. Of course this was also the case with the Quality

criteria.

For each time that the alternatives are entered into the Attribute

Comparison the application assigns 10 to the one with the highest star rating. All

the remaining star rating values are mapped into the 0-10 scale.

As it was the case with the previous criteria, the conversion table is used to

get to the values in the AHP scale needed for filling the QUALITY matrix.

Inconsistency Analysis Implementation

The inconsistency analysis was made following the theory background

described in theory part of this report. For each of pair-wise comparison matrixes,

we will derive the consistency’s ratio.

This step is needed for assuring that the results that will come from our

application will be meaningful and not biased by intransitivity from the user.


8. Testing

This part is entirely dedicated to the testing of the application. Emphasis

will be put into asserting features/characteristics of our built DSS derived from

testing and of course validating the results obtained.

Firstly the search engine was tested, and to check if any bugs aroused from

it: a wide range of values were introduced and the search engine performed quite

nicely: the hotel listing was consistent with the search parameters also the

application only allowed progression to the attribute comparison phase if the user

selected 2 alternative, at the least, as it was predicted; also the application had a

limit for the maximum number of alternatives in order for us to check and

calculate (the Average Random, RI, index has only values for matrixes for a

maximum of 10 alternatives) the consistency ratio. Next was the testing the

attribute comparison, in which the AHP method was implemented. After some

initial bugs related to wrong insertion of values in the matrixes at our scripting

code, we began the testing according to following steps:

1. Checking if the database inserted the correct values in the matrixes.

The database sends all the values that are inserted in the pair-wise

comparison matrix info in the 0-10 scale, and the application

converts them to the 1-9 AHP scale.

2. If the insertion of values into the application is valid, we must test

the local weights derived by the application, as well as the final

results achieved by the application. This step was achieved by using

the Expert Choice, a decision-making software based on the AHP

method.

In the first step, we had some errors in the insertion of the values which was

quickly solutioned. Also the application effectively converted the values sent by

the database in the 0-10 scale into the AHP’s scale.

For the second step, as mentioned, we used the Expert Choice for assessing

the accuracy of our results. The software requires building a structure and making

pair-wise comparisons between criteria and between alternatives regarding a

criterion.


This was done using the data inserted into the application’s tables. For the

example depicted 3 hotels were chosen:

• Pestana Carlton Hotel, a 5 star hotel, with direct access to sea, quite

close to the centre but far from the mountain area. The minimum

price is 135 €.

• D.Pedro Garajau, a 3 star hotel, quite close to the sea, away from city

centre and far from the mountain area. The minimum price is 33 €.

• Hotel da Ajuda, a 4 star hotel, close to the sea, not distant to the

centre but far from the mountains. Minimum price is 72 €.

Fig.14 - Testing our implementation using the Expert Choice: ranking of alternatives

Fig.15 – Ranking of alternatives obtained by the application

The results achieved are exactly the same as the ones given by our

application which means that the AHP method was correctly followed in the

implementation process. The application example follows in electronic format

inside the CD, with all details, about the pair-wise comparison made for criteria

and alternatives as well as for the consistency analysis.

Finally we need to check the consistency values given by our

implementation. The software also performs the inconsistency ratio for each of the

pair-wise comparison matrixes.


The Expert Choice gave very similar results to the ones obtained in our

application. The differences were minimal and are probably related to the

rounding of intermediate values.

Consistency ratios Expert Choice Application

Criteria 0.13 0.1183

Price 0.06 0.0564

Quality 0.04 0.0333

Location 0.13 0.118

Table 23 – Comparison of consistency ratios: Expert Choice vs. Application


9. Conclusions

As we have seen the current trend in e-tourism is to offer new and

innovative services that bring added-value to worldwide users.

Customers will progressively leave the tendency to consider internet based

tourism services as merely only a way to book their stay in a tourism destination to

discover a new array of services that will enable them to personalize and customize

their wishes/preferences. This in term will mean an improvement in customer

satisfaction. Clearly with the phenomenon of globalization, which prompted the

current competition between holiday destinations, any comparative advantage will

tell a difference at the end. Also with internet connections reaching millions of

homes worldwide and brand new markets, especially from developing countries like

China, prompts a new dimension to the universe of potential customers.

In conclusion, innovation and customer satisfaction are the key words

nowadays for the e-tourism based services.

The developed web-application presented here aimed at implementing a

client-support system based on a DSS, in selecting a hotel, given the user’s input

parameters regarding the 3 chosen criterions.

The interaction implied into the system will allow more and better quality

info to the user and also considerable time-saving. This last remark is taken under

assumption when compared to the hotel search is based on a typical tourism

contents web-page.

Another great feature is that when the AHP method is used in implementing

the decision-making process, it allows direct confrontation between the

alternatives. Also this confrontation is visible to the user thus enabling more insight

into the selected alternatives from the user’s standpoint.

Finally, AHP is able to confer consistency to the user’s inputs in the deriving

a solution. The method provides feedback to the user about inconsistency

introduced by the user in pair-wise comparison of criterion by means of an index.

This can be for example if a user decides that Price is extremely important

compared to Quality, Quality is more relevant than Location and finally Location is


more valued than Price. There’s obvious inconsistency in the process of this

judgment*.

In conclusion, these are strengths of the method which prompted its

selection as the decision-making tool of this project.

Also the testing done on the previous chapter validated our approach of

implementing the AHP in a model-based framework for our database: the results

obtained from our application compared with those of the Expert Choice software,

yielded the same values. The same applies to the consistency analysis, as stated in

point 8 of this report.

Future upgrades to this project relate to the use of more powerful database

related technologies, such as AJAX, which is a smart way to reduce bandwidth by

refreshing only the sections of the webpage selected by the user as opposed to the

refreshing of all the webpage.

Also the interface would be greatly improved by integrating JavaScript

libraries for creating enriched applications inside the webpage. The use of SQlite

would also allow considerable gains in interface/usability aspects.

As for the application’s flexibility for different holiday destinations other

than Madeira’s tourism, we can say that is inevitable that some work would have to

be done in order to adapt it to, for example, a skiing destination.

The main advantage is that the model framework (application of the AHP

method) would be left almost intact. However redesign would have to be done on

the interface and on the E/R model of the database (defining different entities,

attributes and associations if needed).

* Note: testing these inputs results in an inconsistency index well over 3 for the example where a

consistent decision should result in a CR < 0.1.


10. Annex

Example of the AHP application example

Problem: A company wishes to expand its activities and is looking to establish in a

new location to accomplish this objective. After an earlier study, the company

chose three locations (L1, L2 and L3) and selected 4 criteria for the choosing

between them.

Criteria

• Land price

• Distance to suppliers

• Technician’s Quality

• Labour Cost

Solution:

Hierarchical Structure

Best Location

Land Price Distance Technician’s Quality

Alternative 1 Alternative 2 Alternative n

Labor Costs

Fig.16 – Example’s hierarchical structure

Criteria Pair-wise comparison

Criteria Land Value Distance Tech.Qual. Labour Cost Land Value 1 1/8 1/2 3 Distance 8 1 5 7 Tech.Qual. 2 1/5 1 3 Labour Cost 1/3 1/7 1/3 1

Table 24 – Example’s criteria pair-wise comparison


Normalized Matrix and respective local weights

Criteria LandValue Distance Tech.Qual. Labour Cost Local Weights Land Value 0.0882 0.0852 0.0732 0.2143 0.1153 Distance 0.7059 0.6813 0.7317 0.5000 0.6547 Tech.Qual. 0.1764 0.1362 0.1463 0.2143 0.1683 Labour Cost 0.0294 0.0973 0.0488 0.0714 0.0617 Sum of input values from the previous table

11.3333

1.4679

6.8333

14.0000

1.000

Table 25 – Normalized and respective local weights

Pair-wise comparison of the alternatives with respect to the criteria

Land Value L1 L2 L3 Distance L1 L2 L3 L1 1 4 2 L1 1 5 1/4 L2 1/4 1 1/6 L2 1/5 1 1/9 L3 1/2 6 1

L3 4 9 1

Tech.Qual. L1 L2 L3 Labour Costs L1 L2 L3 L1 1 1/4 1 L1 1 1/4 2 L2 4 1 7 L2 4 1 5 L3 1 1/7 1

L3 1/2 1/5 1

Table 26 to 29 – Pair-wise comparison of alternatives with respect to criteria

Judgement Matrixes Normalized and with local weights

Land Value L1 L2 L3 L.W L1 4/7 4/11 12/19 0.5222L2 1/7 1/11 1/19 0.0955L3 2/7 6/11 6/19 0.3823

Table 30 – Example’s Normalized Judgement Matrixes

Ranking of alternatives:

2531.02014.0)0617.0(1524.0)1683.0(2364.0)6547.0(5222.0)1153.0(1 =×+×+×+×=L

2151.06806.0)0617.0(7208.0)1683.0(0623.0)6547.0(0955.0)1153.0(2 =×+×+×+×=L

5318.01180.0)0617.0(1268.0)1683.0(7013.0)6547.0(3823.0)1153.0(3 =×+×+×+×=L

Conclusion: L3 is the favourite.


Consistency check

Step 1: Calculate the weights with respect to the initial matrix of criterion and its

local weights (criteria weights)

=

2498.07149.08505.24664.0

0617.01683.06547.01153.0

13/17/13/1315/12751832/18/11

Step 2: Calculate the inconsistency index with respect to the criterion weights and

the weights driven in Step 1

∑=

=n

i weightscriteriastepfromdrivenweights

n 1max _

1___1λ

maxλ 1738.40617.02498.0

1683.07149.0

6547.08505.2

1153.04664.0

41 =

+++=

Step 3: Calculate the Inconsistency ratio, IC

0579.03

41738,41

max =−=−−=

nnIC λ

Step 4: Compare the IC ratio with the random index (RI) with respect to the

corresponding n

0644.090.0

0579.0 ==RIIC ( 1.0≤ ), which means that the decision is consistent.


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Englewood Cliffs, N.J., Prentice-Hall, 1982

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Proceedings of the 4th Informing Science Conference, June 19-22 Krakow, Poland

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Ano 4, n.2, p. 61-85, Universidade Presbiteriana Mackenzie, 2005

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York, Wiley, 2000

8 Lai, Vincent S., Wong, Bo K., Cheung, Waiman, Group Decision Making in Multiple

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134-144


9 PHP Scripting Language,(Online) available at http://www.zend.com/zend/

aboutphp.php, July 2005

Note: Zend Corporation was founded by the creators of PHP

10 SQL – Wikipedia, The Free Encyclopedia (Online) available at

http://en.wikipedia.org/wiki/SQL, July 2005

11Jablonsky J., Lauber J., Group Decision Making and Hierarchical Modelling,

Proceedings of the 12th MCDM Conference, Hagen, Germany, Spring 1997

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13Saaty, T.L.,The Analytic Hierarchy Process, RWS Publications, Pittsburgh 1990

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