Objectives
This lecture continues the waste incinerator siting case study from Lecture 1.1.1. We will use a GIS for the evaluation of several decision criteria. A preference elicitation technique is then used to determine the preferred site. The technique, called Analytic Hierarchy Process (AHP), is a multicriterion decision analysis (MCDA) method, which combines well with a GIS and provides a useful way of transforming data into decision, i.e. information. The Analytical Hierarchy Process Model was designed by T.L. Saaty as a decisionmaking aid.
AHP is especially suitable for complex decisions which involve the comparison of decision elements which are difficult to quantify. It is based on the assumption that when faced with a complex decision the natural human reaction is to cluster the decision elements according to their common characteristics. It involves building a hierarchy (Ranking) of decision elements and then making comparisons between each possible pair in each cluster (as a matrix). This gives a weighing for each element within a cluster (or level of the hierarchy) and also a consistency ratio (useful for checking the consistency of the data).
– University of Cambridge, Dept. of engineering, Institute for manufacturing
What you should learn to do
 Design a multicriterion decision analysis scheme
 Use GIS to evaluate the criteria
 Implement the AHP/GIS approach in Microsoft Excel
Table of contents
Multicriterion decision analysis
In the first lecture we saw how the geographical data could be processed to analyse decision. We identified five potential sites; we estimated the yearly volume of municipal waste to transport; and we computed the transportation cost from each commune to each possible site. These are just a few examples of relevant information that can be extracted from geographical data stored in a GIS.
Dealing with complexity in decision making
A GIS handles an enormous amount of data. Coupled with physical or economic models, it can transform the data into values for evaluation criteria, e.g. the cost of different alternatives, the population exposure to different levels of health risk, and the distribution of pollutant concentrations in different areas of a city. In two other lectures related to this topic, we will focus on network optimisation and on air pollution, with adapted analytical tools. We will then see how a GIS transforms raw geographical data into values for indicators and criteria.
In this lecture, we address the ultimate question in a decisionmaking process: How can a decision maker (DM) weigh different evaluation criteria so as to reflect correctly his preferences and deduce the preferred course of action? This is the socalled preference elicitation process that helps a decision maker to take the ‘correct decision’ in a complex environment. Multicriterion decision analysis (MCDA) is the scientific discipline concerned with this topic.
Coupling MCDA with a GIS
Figure 1 shows the way GIS and MCDA can be linked together. The GIS handles a quantity of data from various sources, most often with a spatial reference. The raw data can be presented as maps, or may be transformed by numerical models and then presented as maps, and finally transformed into indicators and criteria values. MCDA techniques transform the many indicators and criteria obtained through a GIS approach into a recommendation for the decision maker.
A variety of MCDA techniques
There are many techniques that have been developed to help decision makers rank alternative according to many criteria. Among the most celebrated techniques are
 MAUT (Multiattribute utility theory): a technique based on the paradigm of decision tree and risk analysis and using a cardinal utility function. For a coupling of MAUT with a GIS see Keisler and Sundell (1987).
 ELECTRE: a technique originally developed by B. Roy (1991) to incorporate fuzzy (imprecise and uncertain) logic into decision making by using thresholds of indifference and preference. The presentation of ELECTRE will be further developed in Topic 1.4 dedicated to MCDA.
 Compromise Programming (CP): This technique is used to identify solutions that are closest to the ideal solution, as determined by some measure of distance. The solutions identified to be closest to the ideal solution are called compromise solutions and constitute the compromise set. The ideal solution is the one that provides the extreme value for each of the criteria considered in the analysis. For a coupling of CP with a GIS see Tkach et al. (1997).
Exercise 1
Select a city that you know well. Consider the problem of siting a waste incinerator in the vicinity of this city. Explain the different studies that should be requested and the different criteria and/or indicators that should be computed to evaluate the possible courses of action. Describe in as much detail as much as you can the type of analyses that could be performed on a GIS.
Preference elicitation
Criteria evaluation
Data come from a series of measurements concerning a variety of phenomena. These measurements enter into the definition of criteria which influence the preference of the decision maker. Typically, a decision maker involved in a problem of locating a hazardous facility will use many criteria to evaluate the options. In our example of the waste incinerator, the criteria are organised in three groups: economics, environmental impact and sociopolitical acceptability.
 Economic criteria: investment cost, transportation cost, maintenance cost
 Environmental impact criteria: air pollutant emissions, increase in population exposure to immissions (the air pollutants that we breathe or which are deposited on the ground), population exposure to noise pollution
 Sociopolitical acceptability criteria: coping with the NIMBY effect (Not In My Backyard syndrom, i.e., a complete rejection of proposed plans by local citizens’ groups), respecting zoning laws, conforming with longterm urban development planning
Within each group, several criteria will be used to ‘measure’ different components of the economics, the environmental impact or the sociopolitical acceptability of the project under study.
GIS operations for criteria evaluation
GIS operations and physicalsocioeconomic models can be involved in the evaluation of each or many of these criteria. For example:
 Transportation costs can be obtained through network analysis
 Population exposure to pollution can be obtained through buffer analysis and application of a (longterm) pollution dispersion model, or of a noise model
 NIMBY groups, or ‘neinsäger’ communes, can be identified through analysis of past elections
 A preferred course of action can be recommended by a MCDA.
These measurements, evaluated according to many different criteria, can be combined together to produce a global preference indicator. Multicriterion decision analysis techniques provide systematic ways to perform this preference elicitation process. AHP and ELECTRE are two approaches to multicriterion decision analysis that we will explore in Chapter 1.4. In this lecture we use AHP without entering too much into the details of the underlying theory.
Multicriterion decision analysis is a process that transforms evaluation criteria into a preference ranking over a set of possible courses of action. These methods are used to shed light on complex decision processes. Multicriterion decision analysis techniques work well with GIS and can help transform data into information.
Quiz 1
Multicriterion decision analysis (MCDA) and GIS go together well because
 they both are adapted to the analysis of environmental decision problems.
 the concept of a GIS encompasses the multicriterion decision analysis paradigm.
 GIS can handle enormous amount of data. Data becomes information only if a model is used to transform the data into evaluations of possible courses of action. MCDA provides the information structuring needed for assessing complex decision problems.
 both GIS and MCDA have been invented by the same person.
Answer: 3
The Analytic Hierarchy Process
The Analytic Hierarchy Process (AHP) was developed by T. L. Saaty (1980) as a simple and yet powerful method for structuring almost any complex decision problem. The method is widely used in American decision science circles. You can find a long list of references on applications of AHP on the website
http://www.expertchoice.com/hierarchon/references/reflist.htm.
In Europe, other multicriterion decision analysis tools have been successful, like Electre.
The AHP method is based on two principles:
 Build a hierarchy of criteria, in the form of a graph where, on the left you have the decision and on the right you list the alternatives, among which you have preference.
 At each node of the hierarchy, weight the alternatives, normalise the results, and then sum the normalised weights for each alternative. The resulting set of weights gives the relative preferences of the decision maker at this level of the hierarchy for the object that are directly linked to the node. This weighing is carried out through a sequence of pairwise comparisons from which a consistent, normalised set of weights is calculated.
HIPRE is an AHP tool developed by the Systems Analysis Laboratory of the Helsinki University of Technology, and is available on the web at http://www.hipre.hut.fi/.
We have also implemented a very primitive version of AHP in an Excel file (criteria.xls) which you can download. The details of the method will be described in Lecture 1.4.1. But first, let us begin by applying the AHP method to our incinerator siting problem.
Pairwise comparison
The complexity in preference elicitation comes from the fact that our mind has difficulties comparing more than two things. For example, suppose one wants to compare three alternatives in terms of one criterion and give a degree of preference. The task is already complex (Figure 2).
Figure 2: Comparing three alternatives
We can easily make pairwise comparisons. For example we compare alternatives 1 and 2. We can take the analogy of a scale and give a ratio between ‘1’ and ‘9’ that will represent our level of preference for the most valuable of the two alternatives. A ratio equal to ‘1’ means that the two alternatives are equivalent. A ratio equal to ‘9’ means that alternative 1 weighs nine times more than alternative 2. Indeed, if we were weighing alternative 2 in comparison with alternative 1, we should obtain a ratio equal to ‘1/9’.
Figure 3: Comparing alternatives 1 and 2
We can repeat the pair wise comparison for another pair of alternatives (Figure 4).
Figure 4: Comparing alternatives 1 and 3
And then another pair (Figure 5).
Figure 5: Comparing alternatives 2 and 3
Thus, we obtain a matrix of ratios between each of the alternatives in a series of pairwise comparisons (Table 1). For the criterion under consideration, alternative 1 weighs twice as much as alternative 3; alternative 2 weighs three times as much as alternative 1; alternative 2 weighs six times as much as alternative 2.
We must now infer from this table the relative weights of the three alternatives, according to the criterion considered here.
Criterion X 
Alternative 1 
Alternative 2 
Alternative 3 
Alternative 1 
1 
1/3 
2 
Alternative 2 
3 
1 
6 
Alternative 3 
1/2 
1/6 
1 
Table 1: The matrix of pairwise comparisons
If we normalise the columns we obtain the following values:
Criterion X 
Alternative 1 
Alternative 2 
Alternative 3 
Alternative 1 
0.222 
0.222 
0.222 
Alternative 2 
0.667 
0.667 
0.667 
Alternative 3 
0.111 
0.111 
0.111 
Table 2: The columns normalised to one
We therefore get the following relative weights for the three alternatives:
Criterion X 
Sums 
Alternative 1 
0.222 
Alternative 2 
0.667 
Alternative 3 
0.111 
Table 3: Relative weights
Now we have obtained three weights which represent the relative importance of the three alternatives, according to the criterion under consideration.
You can easily check that the weights shown in Table 3 are fully compatible with the ratios of Table 1. This shows that we have been perfectly consistent in our pairwise comparisons. It is difficult to be totally consistent when comparing many pairs of alternatives. In the following example, we show how to deal with limited consistency. For example, we could have obtained the following ratios:
Criterion X 
Alternative 1 
Alternative 2 
Alternative 3 
Alternative 1 
1 
1/3 
2 
Alternative 2 
3 
1 
4 
Alternative 3 
1/2 
1/4 
1 
Table 4: Another matrix of pairwise comparisons
In that case we normalize each column and sum over the columns to get the following:
Criterion X 
Alternative 1 
Alternative 2 
Alternative 3 
Alternative 1 
0.222 
0.211 
0.286 
Alternative 2 
0.667 
0.632 
0.571 
Alternative 3 
0.111 
0.158 
0.143 
Table 5: The normalised columns
These normalised columns are not identical. Averaging over the columns we obtain the relative weights of the alternatives.
Criterion X 
Sums 
Alternative 1 
0.239 
Alternative 2 
0.623 
Alternative 3 
0.137 
Table 6: The relative weights
In our Excel version of an AHP model that we use for this lecture, we systematically use this averaging technique to produce the relative weights at different levels of the hierarchy. We shall describe this averaging process shortly.
The criteria hierarchy
The Figure 6 shows the set of criteria used in the site selection decision. The alternatives are the five potential sites that have been identified in Lecture 1.1.1. The thick arrow on the right means that each subcriterion, for example ‘Investment’ or ‘Bulk Transportation’, is connected to each of the alternatives.
The criteria hierarchy is built by the decision maker (DM). It represents the DMs appreciation of what is taken into consideration in the decision process. Here the DM has identified three groups of criteria: economy, environment and political acceptence. The group of criteria Economy is composed of Investment and Transport cost. The group Environment is composed of three subcriteria: NO_{2} exposure, Transport nuisance and (possibility) Bulk transportation. The group SocioPolitical acceptability is composed of Neighborhood and NIMBY (Not In My Backyard syndrom).
The construction of the criteria hierarchy is the most important step in the AHP procedure. In complex problems one may have up to seven levels in the hierarchy, and up to 9 subcriteria within group.
This completes the first phase in implementing the AHP.
The weighing process
Table 7 contains the results of the successive weighings, obtained at each level of the hierarchy, through a systematic set of pairwise comparisons. The method for achieving this weighing process will be described in Lecture 1.4.1. For the moment, it suffices to understand that these weights have been identified by the DM as a representation of his own preferences.
If you download the Excel file site_criteria.xls you will obtain all the details on how to obtain these weights. As you saw in the previous example, the process is based on a series of pairwise comparisons of alternatives according each criterion, which is located one level above in the hierarchy. From the complete set of pairwise comparisons, one deduces a relative weight for the different elements evaluated through a given criterion. A global weight, called a ‘score’ is finally obtained for the alternatives, by combining the different weights calculated at different levels of the hierarchy.
Note that the sum of the weights under the criterion Investment equals one (up to some rounding error). This is the same for all secondlevel criteria. So for this decision maker, when it comes to comparing the different alternatives in terms of Investment cost, the resulting weights for the five potential sites are 0.29 for ZIMEYZA, 0.11 for BOISDEBAY, 0.05 for VELODROME, 0.12 for LES RUPIERES, and 0.45 for LES CHENEVIERS.
You will also notice that the two subcriteria within the group Economy have weightsequal to 0.67 for Investment and 0.33 for Transportation costs. Similarly, in the Environment group, the three subcriteria have the following weights: 0.32 for NO_{2} exposure, 0.54 for Transportation nuisance, and 0.14 for Bulk transportation. In the Politics group the two subcriteria are weighed 0.67 for NIMBY and 0.33 for Neighbourhood.
The weights for the three groups of criteria are as follows: 0.61 for Economy, 0.29 for Environment, and 0.10 for Politics.
0.61 
0.61 
0.29 
0.29 
0.29 
0.10 
0.10 

economy 
economy 
environment 
environment 
environment 
Politics 
Politics 

0.67 
0.33 
0.32 
0.54 
0.14 
0.67 
0.33 

Invest 
Transp_cost 
NO2_expo 
Transp_nuis 
Bulk_transp 
Nimby 
Neighborhood 

ZIMEYZA 
0.29 
0.36 
0.41 
0.35 
0.21 
0.29 
0.36 
BOISDEBAY 
0.11 
0.08 
0.26 
0.08 
0.05 
0.11 
0.08 
VELODROME 
0.05 
0.31 
0.04 
0.30 
0.21 
0.05 
0.31 
LES RUPIERES 
0.12 
0.19 
0.08 
0.18 
0.05 
0.12 
0.19 
LES CHENEVIERS 
0.45 
0.04 
0.21 
0.04 
0.47 
0.45 
0.04 
Table 7: The weights at each level of the hierarchy
Now, to obtain the scores of the different alternatives in the preference of the decision maker, one combines these weights together. This will maintain the normalisation (i.e., the sum of the weights is still equal to 1).
The result is shown below, first in Table 8, where the composite weights are shown for each subcriterion, and then in Table 9, where the composite scores are shown for the different alternatives.
Invest 
Transp_cost 
NO2_expo 
Transp_nuis 
Bulk_transp 
Nimby 
Neighborhood 

ZIMEYZA 
0.12 
0.07 
0.04 
0.05 
0.01 
0.02 
0.01 
BOISDEBAY 
0.04 
0.02 
0.02 
0.01 
0.00 
0.01 
0.00 
VELODROME 
0.02 
0.06 
0.00 
0.05 
0.01 
0.00 
0.01 
LES RUPIERES 
0.05 
0.04 
0.01 
0.03 
0.00 
0.01 
0.01 
LES CHENEVIERS 
0.18 
0.01 
0.02 
0.01 
0.02 
0.03 
0.00 
Table 8: The composite weights
Finally, from these composite weights one obtains, through summation, the global scores for the five possible sites.
Global scores 

ZIMEYZA 
0.32 
BOISDEBAY 
0.11 
VELODROME 
0.15 
LES RUPIERES 
0.14 
LES CHENEVIERS 
0.27 
Table 9: The global scores
The result show that the location ZIMEYZA is ranked first (score 0.32), followed by LES CHENEVIERS (score 0.27). BoisdeBay was ranked the lowest (score 0.11).
By combining GIS operations to evaluate each criterion with an MCDA technique, we have arrived at a ranking of the five possible alternatives. The GIS approach has been integrated in a decision support system.
Quiz 2
The AHP method is particularly helpful because
 it gives weights that are normalised to sum to 1.
 it permits to combine together qualitative and quantitative criteria through a simple sequence of pairwise comparisons.
 it corresponds to the psychology of most decision makers.
Answer: 2
Integration of the DSS with a GIS
The data treatment to extract valuable information concerning the waste incinerator siting problem has been done with ArcView. The AHP was implemented using Excel. There are possibilities to connect a GIS and a DSS in a common environment.
Below, we show a map that has been constructed in Excel and which represents the result of an AHP. The size of each pie is proportional to the score of the location; the different components corresponding to each criterion are shown in different colours. This summarises nicely the analysis.
Figure 7: The map showing the scores of the different sites according to an AHP
Exercise 2
Use the Excel file site_criteria.xls to define your own preferences regarding the proposed criteria. Compare the weights and the scores obtained with the ones indicated above. Download the Hands on Exercise for this Lecture (Hands_On_Lect1_1_2.doc) to learn how to work with Microsoft Map in Excel.
What have we learned?
We used the multicriterion decision analysis technique, AHP, to score five potential locations for a waste incinerator. The AHP method for multicriterion decision analysis has shown the possible integration of a GIS and a DSS, where the data is prepared in a GIS, an analysis is performed with the help of a systematic evaluation method and the result of the analysis is displayed in the GIS again.
Further readings
Keisler JM and Sundell RC. 1997. Combining MultiAttribute Utility and Geographic Information for Boundary Decisions: An Application to Park Planning. Journal of Geographic Information and Decision Analysis 1(2).
Roy B. 1991. The outranking approach and the foundation of ELECTRE methods. Theory and Decision 31:4973.
Saaty TL. 1980. The Analytic Hierarchy Process. New York: McGraw Hill.
Tkach RJ and Simonovic SP. 1997. A New Approach to Multicriteria Decision Making in Water Resources. Journal of Geographic Information and Decision Analysis 1(1):2543.
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Nice work. Thanks.