Multicriteria decision analysis (MCDA): Central Porto high-speed railway station

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European Journal of Operational Research 187 (2008) 1–18

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Case Study

Multicriteria decision analysis (MCDA): Central Portohigh-speed railway station

Ricardo Mateus a,*, J.A. Ferreira b, Joao Carreira a

a CISED Consultores, Av. Almirante Reis, 219, 2.� Esq., 1000-049 Lisbon, Portugalb CESUR–IST, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

Received 21 September 2006; accepted 3 April 2007Available online 18 April 2007

Abstract

Over recent years, Portugal has been working towards their integration in the trans-European high-speed railway net-work. While in Spain several new high-speed lines are already under construction or beginning operation, in Portugal thenecessary studies are still being carried out. One of these studies concerned the location of one of the high-speed railwaystations to be built in the city of Porto, meant to connect the second most populated metropolitan area in Portugal to thehigh-speed railway network. The goal for the study was to compare alternative siting strategies, defined by the Portuguesehigh-speed railway authority. These strategies were materialized in a set of location alternatives, which were evaluatedfrom a range of technical, economical, social and environmental criteria. This paper describes the multicriteria decisionanalysis (MCDA) approach by which the best alternative was identified from the given set of possible alternatives.� 2007 Elsevier B.V. All rights reserved.

Keywords: Multiple criteria analysis; Decision analysis; Robustness and sensitivity analysis; Transportation; Real-world application

1. The central Porto high-speed railway station

Portugal has been investing on its transportinfrastructure ever since its integration in the Euro-pean Union in the 1980’s. The integration of theIberian Peninsula in the trans-European railwaynetwork has been one of the goals of this Union-sponsored investment policy, and one of the priorityprojects defined for the trans-European transportnetwork. The general layout for a high-speed rail-way network in the Iberian Peninsula has beenagreed upon in 2003 (see Fig. 1).

0377-2217/$ - see front matter � 2007 Elsevier B.V. All rights reserved

doi:10.1016/j.ejor.2007.04.006

* Corresponding author. Tel.: +351 936265287.E-mail address: [email protected] (R. Mateus).

The High-Speed Railway Authority (HSRA)considered it necessary to have a station locatednear the centre of the Porto metropolitan area innorthern Portugal. The specific location of this sta-tion was the object of the study (henceforth referredas the Central Porto Station).

On September 2004, the authors were selected bythe HSRA to carry out a Multicriteria DecisionAnalysis (MCDA) to evaluate the relative overall

value of the location alternatives defined by theHSRA. The problem at hand was not circumscribedto the Central Porto Station itself – which wouldalready have significant impacts. Each alternativealso had to take into account the distinct specificaccess infrastructures linking the station to the

.

mailto:[email protected]

Fig. 1. Central Porto station within the Portuguese high-speed railway network.

2 R. Mateus et al. / European Journal of Operational Research 187 (2008) 1–18

high-speed railway network, both to north andsouth, as different station sites would obviouslyimply different railway paths for the rail. Manyother constraints had to be taken into considerationas well, not the least of which was that it had beenalready decided by the HSRA to have an additionalstation at the Porto region’s main airport (FranciscoSa Carneiro Airport), a few kilometres to the northof Porto. This station (Airport Station) was relevantfor the study since it was mandatory to have bothconnected.

A cost-benefit analysis (CBA) was not appliedbecause not all consequences could be expressed inmonetary terms, given the influence of exogenousor intangible criteria, or due to the imprecise orill-defined nature of many of these criteria. More-over, the criteria to be considered on this problemand its operational expression do not have a purelyobjective and neutral meaning, i.e. they are depen-dent on the values of the decision maker and noton the existence of a hypothetic consensual eco-nomic rationale. For those reasons and as suggestedby the European Commission (Florio et al., 2002),the criteria and the evaluation model were consid-ered within the methodological framework of a mul-ticriteria analysis – for a comprehensive analysis ofthe main methodological differences between CBAand MCDA see (Phillips and Stock, 2003).

Furthermore, the implications of decisionsinvolving technical, social, economic and environ-mental aspects are difficult to evaluate, because ofthe complex multitude of conflicting impacts. There-fore, such consequences should be identified,expected costs and benefits measured and properlyjustified in advance. This requires a formal andcomprehensive analysis process like MCDA.

Although a wide range of important aspectshad to be taken into consideration for the evalua-tion of the various alternatives, it was necessary toexclude, on defining the criteria: any aspect withequivalent impacts on all alternatives; every aspectof the problem not concerning the current decisioncontext (Keeney, 1992). Moreover, the evaluationcriteria and impact estimations for all alternativesare supposed to reflect the present awareness onthe problem and the technical knowledge andexperience of the project team. Furthermore, theevaluation process had to demonstrate its ratio-nale before any public, by taking the form of anopen and formal evaluation model of unquestion-ably sound scientific base. This would support thedecision process as well as provide any justifica-tions required, within the scope of the study. Itwas also necessary to analyze the sensitivity androbustness of the final recommendations, as it isimpossible to completely avoid uncertainty in

PROBLEM STRUCTURING

EVALUATION OFALTERNATIVES

ELABORATION OFRECOMMENDATIONS

Definitionof the criteria

Construction of animpact descriptorfor each criterion

Sensitivity and robustness analyses RECOMMENDATIONS

Construction of avalue function

for each criterion

Overall value of the alternatives

Calculation ofweights

for the criteria

Local/partial valueof the alternativeson each criterion

Impact estimationsof the alternativeson each criterion

Identification of the alternatives

Fig. 2. Methodological steps.

R. Mateus et al. / European Journal of Operational Research 187 (2008) 1–18 3

impact estimations and in the elicitation of valuejudgments.

The MCDA methodology adopted has followedthe three fundamental phases defined by Bana eCosta (1992). It structures the problem through asocio-technical process in which the various decisionmakers and other stakeholders participate – struc-turing phase – to produce a formal evaluation model– evaluation phase – using an interactive and recur-sive learning approach, and never adopting a norma-tive or optimizing stance. In the end, sensitivity androbustness analyses of the model’s results are funda-mental for producing recommendations – recom-mendations phase – on the relative attractiveness(preference) of the different alternatives (see Fig. 2).

In Section 2 of this paper, the different sitingalternatives given by the Portuguese HSRA will bepresented. Section 3 will be devoted to the variouscriteria identified as relevant for the evaluation ofthe alternatives and the estimation of its impactson each criterion using impact descriptors con-structed for that purpose. The additive (hierarchi-cal) aggregation model and further considerationson the various techniques, tools and decision sup-port systems used to evaluate the alternatives willbe laid out in Section 4. Sensitivity and robustnessanalyses will be addressed in Section 5, and finally,the recommendations will be presented in Section 6.

2. Siting alternatives

The set of alternatives provided by the HSRAmaterialized distinct siting strategies which theHSRA wished to have evaluated and compared:

(a) Located north of the Douro river, Boavistawas one of the site options. The new stationto be built on the Boavista site would be under-ground. Two of the alternatives consideredinvolved this site, Boavista (I) and Boavista(II). These two alternatives differed fromeach other solely because they considered twoand three station tracks, respectively (seeFig. 3a);

(b) The Devesas site was on the south side of theDouro river. This alternative considered anunderground station, underneath an alreadyexisting railway station (Fig. 3b);

(c) And finally, slightly outside the central area ofthe city of Porto, but taking advantage of theexisting main railway station, was the Cam-panha site. This site held the remaining threealternatives given by the HSRA, designatedCampanha (I), Campanha (II) and Campanha(III), which differed from each other mainlybecause they considered different railwaypaths (see Fig. 3c–e).

Fig. 3. Porto metropolitan area and the six alternatives (a) Boavista (I)/(II), (b) Devesas, (c) Campanha (I), (d) Campanha (II), (e)Campanha (III).


Fig. 3 shows the general layout of the differentalternatives in its entirety, including the stationand associated railway paths – from the AirportStation site, 10 km north of the Douro river, toRibeira de Silvalde, 14 km south of the river. Com-mon infrastructures, located north of the AirportStation or south of Ribeira de Silvalde were notconsidered for analysis, as they would be exactlythe same.

Boavista (I) and (II) and Devesas alternativesshare much of its access infrastructures.

The Campanha (I) alternative would have themost inland route of all the alternatives, and wouldinvolve the construction of a new track in its entirelength and a new railway bridge over the Douroriver. This alternative could not be studied to thesame level of detail (scale) as the remaining ones,since the information made available was lessdetailed and precise. Thus, it was broken into threenew ones, which were analyzed separately (as if theywere different alternatives), designated: C(I) – B:best possible scenario, a combination of the bestimpacts across all criteria; C(I) – W: worst possiblescenario, a combination of the worst impacts acrossall criteria; C(I) – I: ‘‘intermediate’’ scenario, a com-bination of the intermediate values between the bestand worst impacts.

Campanha (II) and (III) would use much thesame corridor as Boavista and Devesas on thesouthern side of the river, and the same corridor

as Campanha (I) on the northern side (see Fig. 3).These alternatives would use the existing railwaybridge in the first 15 years of operation, and thenmove to a new one to be built. Campanha (I),Boavista (I)/(II) and Devesas would require newbridges in place from day one. Campanha (II) and(III) would differ on just a small section of the rail-way track, on the southern side of Porto. Cam-panha (III) would take advantage of the existingrailway track, in that section, while Campanha (II)would use a new underground railway track.

3. Problem structuring

This phase comprises the development of the fol-lowing tasks: (1) identifying the relevant evaluationcriteria and organizing these into a hierarchicalstructure; (2) constructing an impact descriptor foreach criterion, to make operational the evaluationof the alternatives; (3) making an impact estimationof the different alternatives on each criterion, usingthe descriptor constructed for that purpose. Thesedifferent tasks flowed in an iterative and recursiveway, and involved a decision maker which included6 members on behalf of the HSRA (1 Administra-tor; 2 Directors and 3 Project Managers from theHSRA) and external expert technical consultantsinvolved in the process (an international engineeringcompany, a Portuguese university R&D organisa-tion, and a local urban planning company). The

Table 1Hierarchical structure of the criteria

1.1 Endogenous Factors during Construction1.1.1 Construction and Expropriation Costs

1.1.2 Construction Schedules

1.1.3 Construction Risks1.1.3.1 Geological/Geotechnical1.1.3.1.1 Tunnelled Railway Line

1.1.3.1.2 Bridge over the Douro River

1.1.3.2 Location/Accessibility of the Construction Site

1.1.3.3 Affected Utilities

1.2 Endogenous Factors during Operation1.2.1 Maintenance and Operation Costs

1.2.2 Demand

1.2.3 Accessibility1.2.3.1 For Professional Purposes1.2.3.1.1 Individual

1.2.3.1.2 Collective

1.2.3.2 For Non-professional Purposes1.2.3.2.1 Individual

1.2.3.2.2 Collective

1.2.4 Travel Time

1.2.5 Customer Comfort1.2.5.1 Intermodality with the Roadway Mode1.2.5.1.1 Availability of Parking for Individual Transport1.2.5.1.1.1 Private

1.2.5.1.1.2 Public

1.2.5.1.2 Availability of Parking for Collective Transport

1.2.5.2 Intermodality with the Surface Light Rail

1.2.5.3 Intermodality with the Railway Mode

1.2.5.4 Availability of Support Services

1.2.6 Operating Easiness

2.1 Exogenous Factors during Cnstruction2.1.1 Earthworks

2.1.2 Noise Impact

2.1.3 Vibration Impact

2.1.4 Impact on Traffic

2.1.5 Impact on Residential Activities

2.1.6 Impact on Economic Activities

2.2 Exogenous Factors during Operation2.2.1 Impact on Ecologically Sensitive Areas

2.2.2 Impact on Architectural/Archaeological Heritage

2.2.3 Noise Impact

2.2.4 Vibration Impact

2.2.5 Residential Relocations

2.2.6 Impact on Urban Planning

2.2.7 Impact on Traffic and Accessibility2.2.7.1 On Streets Around the Station

2.2.7.2 To the City Centre

2.2.7.3 On Streets Connecting National Roadway Network

2.2.7.4 On the National Roadway Network

2.2.7.5 On Intermodality Infrastructures


authors acted as ‘‘facilitators’’, helping the decisionmaker in this decision process. Whenever some dis-agreement occurred among the decision maker’smembers, the authors helped by asking each mem-ber to state and discuss his or her opinion until afinal consensus was reached.

3.1. Criteria

All points of view for comparing and evaluatingthe alternatives were identified and structured dur-ing this methodological step. A point of view isany aspect within a specific decision context thatat least one stakeholder considered relevant to theevaluation of alternatives, such as stated concernsor objectives of the decision makers, characteristics(or attributes) of the alternatives, or possible conse-quences of potential actions (Bana e Costa, 1992).Not all points of view are criteria since some arerelevant just because they are means to achieveother points of view (ends). One criterion reflects afundamental point of view, in the sense that itreflects what the decision maker really wants toaccomplish. It is an isolated evaluation axis whichmust verify the necessary preference independenceconditions.

This process was led by the authors through anumber of decision conferences (Phillips, 1988) withthe decision maker (HSRA members) based on avalue-focused thinking approach (Keeney, 1992)and the ‘‘Why Is That Important’’ test (Clemenand Reilly, 2001).

In order to ensure that all criteria relevant for theevaluation of the alternatives were identified, thehierarchical structure of the criteria was organized,at a first level, in four evaluation areas:

(1.1) Endogenous factors during construction: thisarea comprises all the evaluation criteriarelated to the high speed railway network(HSRN) itself, during the construction phase;

(1.2) Endogenous factors during operation: this areacomprises all the evaluation criteria relatedto the HSRN itself, during the operation;

(2.1) Exogenous factors during construction: thisarea comprises all the evaluation criteria con-cerned with the impacts of the HSRN upon itssurroundings, during the construction phase;

(2.2) Exogenous factors during operation: this areacomprises all the evaluation criteria concernedwith the impacts of the HSRN upon its sur-roundings, during operation.

Table 1 contains the complete hierarchical struc-ture of the criteria. The elementary criteria aremarked in bold.

In order to ensure the model’s intrinsic coher-ence, it was necessary to ensure that the whole fam-ily of evaluation criteria satisfied the following


properties (Keeney, 1992; Dogson et al., 2000):completeness, mutual independence preference (isol-ability), non-redundancy (no double-counting),conciseness, consensuality, measurability, operatio-nality and non-ambiguity (understandability).

3.2. Impact descriptors

Any criterion must be associated to an impactdescriptor in order to make it operational. Adescriptor is an ordered set of plausible impact lev-els (quantitative or qualitative) in terms of a crite-rion. When creating descriptors, one should keepin mind the need for establishing a close and easilyunderstandable relationship between each criterionand the method for evaluating its attractiveness(preference). Descriptors must also be easily quanti-fiable or, alternatively, the qualitative impact levelsassociated to the criterion must be easily under-standable and useable. The more direct and objec-tive (natural) a descriptor is, the more intelligibleand less ambiguous will the criterion be, and as aresult, the more easily accepted and less controver-sial the evaluation model will be.

There are three types of descriptors (Keeney,1992): natural: whenever its impact levels reflectthe effects directly; proxy: whenever its impact levelsmainly reflect the causes rather than its effects; andconstructed: whenever its impact levels are definedas a finite combination of reference levels.

The definition of descriptors is one of the crucialactivities in structuring the evaluation model. Thisprocess was conducted by the authors in a seriesof decision conferences with both the HSRA andselected members from the external expert technicalconsultants. This time, focus was in feasibility, thatis: are the consultants able to do the necessary anal-yses and impact estimations in the allotted time withthe available resources? This process often led tonew insights and uncovering hidden criteria (Kee-ney, 1992), in which cases, the initial set of evalua-tion criteria had to be redefined. In fact, and asmentioned previously, structuring is a cyclic learn-ing process.

Table 2 lists the final impact descriptors definedfor each elementary criterion as well as the typeof descriptor selected: (N)atural; (P)roxy; or(C)onstructed. For instance, criteria 1.1.1 and1.2.1 were made operational using natural descrip-tors while criteria 2.1.2 and 2.1.3 were made opera-tional using proxy descriptors, since a natural onewas not economically and technically feasible.

Whenever a criterion combined several elemen-tary points of view that were preference dependent,a constructed descriptor was used. For example, cri-terion 2.2.6 (urban planning) combined 6 character-istics from (a) urban landscape to f) land useplanning. Each one of these was described usingan ordered scale of six qualitative impact levels:(+++): resulting in highly desirable consequences;(++): wanted consequences; (+): ordinary conse-quences; (0): indifferent (without consequences);(-): unwanted consequences; (–): highly undesirableconsequences.

3.3. Impacts of the alternatives

The impact of each alternative on each criterionwas estimated by the expert technical consultantsusing the defined impact descriptors. The R&Dinstitute estimated impacts on criteria 1.2.2, 1.2.3,2.1.5, 2.1.6 and 2.2.5, the urban planning companyon criteria 2.2.6 and on subcriteria from 2.2.7. Otherimpacts were estimated by the international engi-neering company. Results were subsequently vali-dated by the HSRA. The final output of theseactivities was compiled into an Impact Matrix,depicted in Table 3, which presented the results ina table format, with the alternatives presented inthe rows and the criteria (defined at its most elemen-tary level) in the columns.

It was estimated that for criteria 1.2.2, 1.2.5.1.1.1,1.2.5.1.1.2, 1.2.5.1.2, 1.2.5.2, and 1.2.5.4, all alterna-tives presented the same impact (see Table 3), andtherefore these were removed from the subsequentphases of the evaluation process.

4. Evaluation of alternatives

Some important questions remained unsolved atthe beginning of this phase: (1) how can impactson different criteria, which are measured in differentunits (euros, days, meters, inhabitants and evenqualitative judgments), be aggregated for an overallevaluation of the various alternatives? (2) How canthe attractiveness (value) of each alternative be mea-sured on each criterion? (3) And finally, how muchshould each criterion affect the overall value of thevarious alternatives?

The three major tasks to be carried out duringthe evaluation phase, corresponding to the ques-tions presented above, were: (1) construction of avalue function for each criterion; (2) evaluation of

Table 2Impact descriptors

Criterion Descriptor Type

1.1.1 Present value of construction and expropriation costs N1.1.2 Construction schedule: (a) between Ribeira de Silvalde and the Central Porto Station; (b) between Ribeira de

Silvalde and the Airport StationC

1.1.3.1.1 Length of tunnelled track crossing geologically or geotechnically unfavourable soil P1.1.3.1.2 Bridge-supporting elements placed on geologically or geotechnically unfavourable soil C1.1.3.2 Location and accessibility of the construction site: (a) availability of public land for setting up the site; (b)

existence of traffic congestion near the siteC

1.1.3.3 Length of surface track crossing the roadway in urban areas P1.2.1 Present value of annual maintenance and operation costs N1.2.2 Increase of potential demand over the high speed service P1.2.3.1.1 Reduction of average travel time to the station, on individual transport, for professional purposes P1.2.3.1.2 Reduction of average travel time to the station, on collective transport, for professional purposes P1.2.3.2.1 Reduction of average travel time to the station, on individual transport, for other purposes P1.2.3.2.2 Reduction of average travel time to the station, on collective transport, for other purposes P1.2.4 Journey time: (a) between Aveiro Station and the Central Porto Station; (b) between Aveiro Station and the

Airport StationC

1.2.5.1.1.1 Availability of parking space for individual private vehicles on the station C1.2.5.1.1.2 Availability of parking space for taxi vehicles on the station C1.2.5.1.2 Availability of parking space for collective transport vehicles on the station C1.2.5.2 Intermodality between the station and the surface light rail C1.2.5.3 Intermodality between the station and the national rail network: (a) influence area (population living in

municipalities of northern Portugal with a railway line directly connected to the station); (b) frequency (averagenumber of trains per day on working days)

C

1.2.5.4 Availability of space for support services on the station C1.2.6 Railway tracks on the station P2.1.1 Volume of earthworks to be carried out P2.1.2 Length of surface railway track P2.1.3 Length of tunnelled railway track crossing urban areas P2.1.4 Area of primary roadways in urban areas crossed by surface railway track P2.1.5 Population living in city blocks crossed by surface railway track P2.1.6 Employees of companies located on the city blocks crossed by surface railway track P2.2.1 Area of national ecological or agricultural park crossed by surface railway track P2.2.2 Historical and cultural heritage: (a) architectural items within 50 m of the right-of-way; (b) archaeological items

within 50 m of the right-of-wayC

2.2.3 Length of surface railway track P2.2.4 Length of tunnelled railway track crossing urban areas P2.2.5 Population to be relocated N2.2.6 Urban impacts on: (a) urban landscape; (b) functional zoning; (c) urban regeneration; (d) planned public urban

projects; (e) changes in land value; (f) land use planningC

2.2.7.1 Traffic/accessibility impacts on the streets surrounding the station: (a) present conditions; (b) current designsand works; (c) planned projects

C

2.2.7.2 Traffic/accessibility impacts on the city centre: (a) present conditions; (b) current designs and works; (c) plannedprojects

C

2.2.7.3 Traffic/accessibility impacts on streets linking to the national roadway network: (a) present conditions; (b)current designs and works; (c) planned projects

C

2.2.7.4 Traffic/accessibility impacts on the national roadway network: (a) present conditions; (b) current designs andworks; (c) planned projects

C

2.2.7.5 Public transport infrastructures and intermodality impacts C


the value of the alternatives on each criterion and;(3) calculation of weights for each of the criteria.

4.1. Value functions

The evaluation phase began with the constructionof value functions for converting the impact units

(euros, meters, inhabitants, etc.) of the different cri-teria into a numeric scale, which measures the rela-tive attractiveness (value) of each impact level.

Since the goal of this study was to make a relativeevaluation among the different alternatives, for eachelementary criterion, a local value of ‘‘100’’ was setfor the best (most attractive) impact level on its

Table 3Impact matrix

Alternatives 1.1.1 1.1.2.a 1.1.2.b 1.1.3.1.1 1.1.3.1.2 1.1.3.2.a 1.1.3.2.b 1.1.3.3 1.2.1 1.2.2 1.2.3.1.1

B(I) 555.4 1011 1065 6351 2/- Restricted V.High 782.0 20.15 0% 12.2

B(II) 594.7 1106 1137 6351 2/- Restricted V.High 782.0 22.14 0% 12.2

D 488.3 853 1070 4829 2/- Yes Normal 170.0 16.75 0% 4.2

C(I) – W 536.7 784 814 894 6/- Yes High 211.0 17.26 0% 10.0

C(I) – I 528.1 784 814 894 6/- Yes V.High 205.5 16.83 0% 10.0

C(I) – B 519.4 784 814 894 6/- Yes Normal 200.0 16.40 0% 10.0

C(II) 528.9 608 814 4585 0/6 Yes Normal 217.0 17.05 0% 10.0

C(III) 506.5 608 814 3579 0/6 Yes Normal 302.0 15.96 0% 10.0

Unit M € Days Days Metres Elements Metres M €/y % Minutes

1.2.3.1.2 1.2.3.2.1 1.2.3.2.2 1.2.4.a 1.2.4.b 1.2.5.1.1.1 1.2.5.1.1.2 1.2.5.1.2 1.2.5.2 1.2.5.3.a 1.2.5.3.b

B(I) 8.9 7.1 6.9 16.28 24.05 Yes Yes Yes Yes 0 0

B(II) 8.9 7.1 6.9 16.28 24.05 Yes Yes Yes Yes 0 0

D 3.8 5.3 4.3 15.40 24.62 Yes Yes Yes Yes 0.956 29

C(I) – W 11.2 7.5 10.4 16.92 26.29 Yes Yes Yes Yes 3.170 140

C(I) – I 11.2 7.5 10.4 16.31 25.68 Yes Yes Yes Yes 3.170 140

C(I) – B 11.2 7.5 10.4 15.69 25.06 Yes Yes Yes Yes 3.170 140

C(II) 11.2 7.5 10.4 17.66 27.07 Yes Yes Yes Yes 3.170 140

C(III) 11.2 7.5 10.4 17.98 27.36 Yes Yes Yes Yes 3.170 140

Unit Minutes Minutes Minutes Minutes Minutes M Inhabitants Trains/day

1.2.5.4 1.2.6 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.2.1 2.2.2.a 2.2.2.b

B(I) Yes 2 0.932 11.567 12.335 2548 6459 1784 175162 a, b, c, d, e I

B(II) Yes 3 0.993 11.567 12.335 2548 6459 1784 175162 a, b, c, d, e I

D Yes 4 0.947 11.427 12.359 2380 6105 554 177828 a, b, c, d, e I

C(I) – W Yes 4 1.027 14.321 6.267 2743 7041 519 130205 a, b, f –

C(I) – I Yes 4 1.007 14.071 6.110 2675 7041 519 126950 a, b, f –

C(I) – B Yes 4 0.986 13.821 5.954 2606 7041 519 123695 a, b, f –

C(II) Yes 4 1.302 15.940 8.034 2968 7712 774 127657 a, b/f I/–

C(III) Yes 4 1.308 17.994 6.541 3745 7712 774 127657 a, b/f I, II, III/–

Unit Lines M m3 km km m2 Inhabitants Employees m2 Items Items

2.2.3 2.2.4 2.2.5 2.2.6.a 2.2.6.b 2.2.6.c 2.2.6.d 2.2.6.e) 2.2.6.f) 2.2.7.1.a 2.2.7.1.b

B(I) 11.567 12.335 795 - + +++ 0 ++ - 0 ++

B(II) 11.567 12.335 795 - + +++ 0 ++ – 0 ++

D 11.427 12.359 786 + +++ + + +++ +++ +++ +

C(I) – W 14.321 6.267 1075 0 ++ ++ 0 0 0 + +++

C(I) – I 14.071 6.110 1075 0 ++ ++ 0 0 0 + +++

C(I) – B 13.821 5.954 1075 0 ++ ++ 0 0 0 + +++

C(II) 15.940 8.034 1177 0 ++ + 0 0 ++ + +++

C(III) 17.994 6.541 1177 0 ++ + 0 0 ++ + +++

Unit km km Inhabitants

2.2.7.1.c 2.2.7.2.a 2.2.7.2.b 2.2.7.2.c 2.2.7.3.a 2.2.7.3.b 2.2.7.3.c 2.2.7.4.a 2.2.7.4.b 2.2.7.4.c 2.2.7.5

B(I) + - 0 - 0 0 +++ - 0 ++ ++

B(II) + - 0 - 0 0 +++ - 0 ++ ++

D + 0 0 0 0 ++ 0 ++ +++ + ++

C(I) – W 0 - 0 + - +++ 0 - 0 + +++

C(I) – I 0 - 0 + - +++ 0 - 0 + +++

C(I) – B 0 - 0 + - +++ 0 - 0 + +++

C(II) 0 - 0 + - +++ 0 - 0 + +++

C(III) 0 - 0 + - +++ 0 - 0 + +++

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descriptor, and ‘‘0’’ for the worst (least attractive)impact level.

On the one hand, for all criteria (except 1.2.6)made operational using natural or proxy descriptors,a linear value function has been defined. These func-tions were validated by the decision maker, by ask-ing about the differences in attractiveness betweenthe least attractive impact level and the intermediateimpact level (within the impact range of the descrip-tor), and between this intermediate impact level andthe most attractive one. For a value function to beconsidered linear, the decision maker had to deter-mine that both swings are identically preferred.

On the other hand, for all criteria made opera-tional using constructed descriptors, or wheneverthe linearity property mentioned earlier could notbe ensured (as for criterion 1.2.6), the value functionwas defined using the MACBETH approach (seewww.m-macbeth.com).

4.2. Local value of the alternatives on each

elementary criterion

For linear value functions, determining the localvalues vjðaÞ for each alternative a on each elemen-tary criterion j was a simple matter, using the fol-lowing expressions:

(a) for decreasing linear value functions:vjðaÞ ¼ 100� Mj�IjðaÞ

Mj�mj,

(b) for increasing linear value functions:vjðaÞ ¼ 100� IjðaÞ�mj

Mj�mj,

a) b) c) d) e) f)

B(I), B(II) D C(I) C(II), C(III)

+++

++

+

0

–

– –

b

Características D B(I), B(II) C(I) C(II), C(III)a) 1 -1 0 0b) 3 1 2 2c) 1 3 2 1d) 1 0 0 0e) 3 2 0 0f) 3 -1 0 2

ALTERNATIVA

Fig. 4. Determining the local values of alternatives on criterion 2.2.6difference of attractiveness between alternatives.

where, I jðaÞ is the impact level for alternative a on cri-terion j; Mj is the maximum impact level for all alter-natives on criterion j; and, mj is the minimum impactlevel for all alternatives on criterion j.

As mentioned earlier, non-linear value functionswere constructed using the MACBETH approach(see Bana e Costa and Vansnick, 1997, 1999). Thisprocedure was conducted in a series of decision con-ferences with the decision maker which will be illus-trated, as example, for criterion 2.2.6. The authorsstarted by asking the decision maker to rank allalternatives, on this criterion, by descending orderof attractiveness (preference), based on their impactprofiles (Fig. 4a).

After that, the authors asked the decision makerto verbally judge the difference of attractiveness(preference) between each pair of alternatives, bychoosing one of the following semantic categories:no (indifference); very weak; weak; moderate;strong; very strong; extreme. During this process,in a visual interactive and learning process, theauthors filled in a matrix with the elicited judgments(see Fig. 4b). Based on this information, the MAC-BETH approach verifies whether it is possible toassociate local values vðanÞ for all alternatives an

which satisfy the following conditions: (1) if a1 ismore attractive than a2, then vða1Þ > vða2Þ; (2) if a1

is as attractive as a2, then vða1Þ ¼ vða2Þ; (3) if the dif-ference of attractiveness between a1 and a2 is greaterthan the difference of attractiveness between a3

and a4, then vða1Þ � vða2Þ > vða3Þ� vða4Þ, e.g. thedifference of attractiveness between alternatives D

using MACBETH: (a) impact profiles of the alternatives and (b)

http://www.m-macbeth.com

Table 4Local values matrix

Alternatives 1.1.1 1.1.2 1.1.3.1.1 1.1.3.1.2 1.1.3.2 1.1.3.3 1.2.1 1.2.3.1.1 1.2.3.1.2 1.2.3.2.1 1.2.3.2.2

B(I) 36.98 15.38 0.00 33.33 0.00 0.00 32.24 100.00 68.92 81.82 42.62B(II) 0.00 0.00 0.00 33.33 0.00 0.00 0.00 100.00 68.92 81.82 42.62D 100.00 46.15 27.89 33.33 100.00 100.00 87.26 0.00 0.00 0.00 0.00C(I) – W 54.51 69.23 100.00 0.00 66.67 93.30 79.00 72.50 100.00 100.00 100.00C(I) – I 62.63 69.23 100.00 0.00 83.34 94.20 85.99 72.50 100.00 100.00 100.00C(I) – B 70.75 69.23 100.00 0.00 100.00 95.10 92.98 72.50 100.00 100.00 100.00C(II) 61.80 100.00 32.36 100.00 100.00 92.32 82.35 72.50 100.00 100.00 100.00C(III) 82.87 100.00 50.80 100.00 100.00 78.43 100.00 72.50 100.00 100.00 100.00

1.2.4 1.2.5.3 1.2.6 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.2.1 2.2.2 2.2.3

B(I) 100.00 0.00 0.00 100.00 97.87 0.37 87.69 71.63 0.00 4.92 0.00 97.87B(II) 100.00 0.00 71.43 83.66 97.87 0.37 87.69 71.63 0.00 4.92 0.00 97.87D 100.00 60.00 100.00 96.11 100.00 0.00 100.00 100.00 97.23 0.00 0.00 100.00C(I) – W 50.00 100.00 100.00 74.70 55.93 95.11 73.41 46.79 100.00 87.97 100.00 55.93C(I) – I 75.00 100.00 100.00 80.16 59.74 97.55 78.42 46.79 100.00 93.99 100.00 59.74C(I) – B 100.00 100.00 100.00 85.63 63.54 100.00 83.44 46.79 100.00 100.00 100.00 63.54C(II) 12.50 100.00 100.00 1.68 31.28 67.52 56.92 0.00 79.84 92.68 75.00 31.28C(III) 0.00 100.00 100.00 0.00 0.00 90.83 0.00 0.00 79.84 92.68 62.50 0.00

2.2.4 2.2.5 2.2.6 2.2.7.1 2.2.7.2 2.2.7.3 2.2.7.4 2.2.7.5

B(I) 0.37 97.70 33.33 0.00 0.00 100.00 20.00 25.00B(II) 0.37 97.70 33.33 0.00 0.00 100.00 20.00 25.00D 0.00 100.00 100.00 100.00 100.00 71.00 100.00 0.00C(I) – W 95.11 26.09 0.00 67.00 57.00 0.00 0.00 100.00C(I) – I 97.55 26.09 0.00 67.00 57.00 0.00 0.00 100.00C(I) – B 100.00 26.09 0.00 67.00 57.00 0.00 0.00 100.00

Line missing


and B(I) is greater than the difference of attractive-ness between B(I) and C(I), then 100 –33.33 > 33.33 – 0. Under these conditions, and fur-ther imposing that the most and least attractivealternatives must be transformed into ‘‘100’’ and‘‘0’’, respectively, through a direct linear conversion,MACBETH suggests a compatible 0–100 numericscale indicative of the local value of each alternative(see last column in Fig. 4b). This process was onlyfinished after discussion of the meaning of the sug-gested local values and their validation with the deci-sion maker.

In the end of this process, all value functionstranslate the impacts measured in the various unitsinto a numerical scale, which measures its attrac-tiveness (preference), transforming the ImpactMatrix presented in Table 3 into a Local ValuesMatrix (see Table 4).

4.3. Weights and partial value of the alternatives on

each criterion

Having determined the local values of each alter-native, on all criteria, the next step was to calculate

the weights for the criteria, in order to aggregatethem in an overall value for each alternative.

In order to reduce the number of criteria, theprocedure started by using a hierarchical additivemodel for aggregating the local values on the vari-ous elementary criteria up to the criteria immedi-ately below each evaluation area (bottom-upapproach). The additive hierarchical model is acomposition of simple additive models, adapted toa hierarchical criteria structure.

The framework for simple additive models can berepresented through the following expression:

V iðaÞ ¼Xn

j¼1

kj � vjðaÞ; withXn

j¼1

kj ¼ 1 and

0 < kj < 1; 8jwhere, V iðaÞ is the partial value of alternative a oncriterion i; j is each sub-criterion under criterion i;n is the number of sub-criteria under criterion i;vjðaÞ is the local (or partial) value of alternative a

on sub-criterion j, with the best impact correspond-ing to a value equal to 100 and the worst impact cor-responding to a value equal to 0; and kj is the weightfor sub-criterion j.

Fig. 5. Within weights for criteria 1.1.3.1.1 and 1.1.3.1.2.

Table 6Within weights and partial values for each alternative on criterion1.1.3.1

Alternatives 1.1.3.1.1 1.1.3.1.2 1.1.3.1

B(I) 0.00 33.33 4.77 0.00


In the framework of the aforementioned additivemodel, weights are scaling constants used merely toharmonize the different 0–100 value scales. They aresubstitution rates reflecting how much one is willingto trade-off impact improvements on a criterion vis-a-vis worsening impacts on other criteria. Weightsdo not translate any intrinsic importance of the cri-teria. They are only meaningful in the context of theparticular impact levels determined in the study.The inobservance of this assumption on the weight-ing procedure is ‘‘the most common critical mis-take’’ (Keeney, 1992), resulting in completelyarbitrary weights which do not translate the deci-sion makers’ value judgments.

Therefore, scientifically sound weighting proce-dures use the answers given by the decision makeron questions which require them to compare pairsof plausible fictitious alternatives based on two ref-erence impact levels, such as the ‘‘best’’ and ‘‘worst’’impact levels determined for the criteria.

Initially, the MACBETH procedure (Bana eCosta and Vansnick, 1999) was selected for calculat-ing the criteria weights. As previously mentioned, ata first stage, this weighting procedure was carriedout until the partial values for each alternative, onthe criteria immediately below each evaluation area,and the resultant (within) weights were attained (seelast row in Table 8).

This procedure will be illustrated for elementarycriteria 1.1.3.1.1 and 1.1.3.1.2:

(1) First, two fictitious reference alternatives (A1and A2) were created, as many as the criteria,each one with the best impact on one criterionand the worst impact on the other one. Then,an additional fictitious reference alternative(W), with the worst impact on both criteriawas also added (Table 5).

(2) The decision maker was asked to rank thesethree fictitious reference alternatives bydecreasing level of its overall attractiveness(see last column in Table 5).

(3) In order to determine the strength of prefer-ence from one criterion to the next, the deci-sion maker was then asked to choose one of

Table 5Fictious reference alternatives for criteria 1.1.3.1.1 and 1.1.3.1.2

Alternatives 1.1.3.1.1 1.1.3.1.2 Ranking

A1 0.894 km 6/- elem. 1stA2 6.351 km 0/6 elem. 2ndW 6.351 km 6/- elem. 3rd

the aforementioned MACBETH semantic cat-egories to judge the difference in attractivenessbetween any pair of fictitious reference alter-natives. A matrix with these judgments wasconstructed (Fig. 5), with the support of theMACBETH software. Based on this informa-tion, through a similar process as previouslydescribed but this time imposing that alterna-tive W must come to ‘‘0’’ and the remainingmust normalized sum to 1, MACBETH sug-gested compatible (within) weights for criteria1.1.3.1.1 and 1.1.3.1.2 (see last column inFig. 5).

Using these (within) weights, calculating the par-tial values for each alternative on criterion 1.1.3.1 isa straightforward procedure using the aforemen-tioned additive model. For instance, the partialvalue for alternative D on this criterion is:

V 1131ðDÞ ¼ k11311 � v11311ðDÞ þ k11312 � v11312ðDÞ¼ 85:71%� 27:89þ 14:29%� 33:33

¼ 28:67

Finally, the partial values for each alternative oncriterion 1.1.3.1 were then normalized, so that thebest alternative (highest partial value on the crite-rion) was transformed into a partial value of 100and the worst alternative (lowest partial value) intoa partial value of 0 (see last column in Table 6).

B(II) 0.00 33.33 4.77 0.00D 27.89 33.33 28.67 29.53C(I) – W 100.00 0.00 85.70 100.00C(I) – I 100.00 0.00 85.70 100.00C(I) – B 100.00 0.00 85.70 100.00C(II) 32.36 100.00 42.03 46.05C(III) 50.80 100.00 57.83 65.57W. weights (%) 85.71 14.29

Table 7Within weights and partial values for each alternative on criterion1.1.3

Alternatives 1.1.3.1 1.1.3.2 1.1.3.3 1.1.3

B(I) 0.00 0.00 0.00 0.00 0.00B(II) 0.00 0.00 0.00 0.00 0.00D 29.53 100.00 100.00 50.67 51.18C(I) – W 100.00 66.67 93.30 95.33 96.27C(I) – I 100.00 83.34 94.20 97.17 98.14C(I) – B 100.00 100.00 95.10 99.02 100.00C(II) 46.05 100.00 92.32 60.70 61.30C(III) 65.57 100.00 78.43 71.58 72.29W. weights (%) 70 10 20


By means of the bottom-up approach previouslyreferred, a similar process was followed to calculatethe partial values of the alternatives on criterion1.1.3 (see Table 7).

In order to determine the (within) weights andthe partial values for each alternative on the criteriaunder evaluation area 1.1 and the remaining evalu-ation areas (1.2, 2.1, and 2.2), again, a bottom-upapproach using MACBETH was used, similar tothe process presented above.

At this point, the partial values for each alterna-tive and the (within) weights, on the criteria undereach evaluation area, were determined and vali-dated by the decision maker (see Table 8).

Table 8Within weights and partial values for the alternatives on the criteria

Alternatives 1.1.1 1.1.2 1.1.3 1.2.1 1.2.3

B(I) 36.98 15.38 0.00 32.24 72.40B(II) 0.00 0.00 0.00 0.00 72.40D 100.00 46.15 51.18 87.26 0.00C(I) – W 54.51 69.23 96.27 79.00 100.00C(I) – I 62.63 69.23 98.14 85.99 100.00C(I) – B 70.75 69.23 100.00 92.98 100.00C(II) 61.80 100.00 61.30 82.35 100.00C(III) 82.87 100.00 72.29 100.00 100.00W. weights (%) 35.29 52.95 11.76 15.38 30.77

2.1.4 2.1.5 2.1.6 2.2.1 2.

B(I) 87.69 71.63 0.00 4.92B(II) 87.69 71.63 0.00 4.92D 100.00 100.00 97.23 0.00C(I) – W 73.41 46.79 100.00 87.97 10C(I) – I 78.42 46.79 100.00 93.99 10C(I) – B 83.44 46.79 100.00 100.00 10C(II) 56.92 0.00 79.84 92.68 7C(III) 0.00 0.00 79.84 92.68 6W. weights (%) 21.13 9.86 32.39 1.22

4.4. Final weights

Having determined the partial values for eachalternative and the (within) weights, on all criteriaunder each evaluation area, it was necessary todetermine the corresponding final weights for allthese criteria in order to calculate the overall valueof the alternatives. To do that, those final weightswere determined so that all criteria weights (undereach evaluation area) sum to 1.

Hence, at first, the decision maker was con-fronted with the corresponding economic trade-offsresulting from the (within) weights previously deter-mined for the criteria under evaluation area 1.1. Theessence of this ‘‘trade-off procedure’’ (Keeney andRaiffa, 1976) is to determine the marginal rate ofsubstitution between one particular criterion (in thiscase criterion 1.1.1) and any other one. For exam-ple, the (within) weight for criterion 1.1.2 implythat, for the decision maker, a decrease in construc-tion schedule from both 1106 days (up to the Cen-tral Porto Station) and 1137 days (up to theAirport Station) to 608 days and 814 days, respec-tively, are worth an increase in construction andexpropriation costs (criterion 1.1.1) of 159.6 M€,that is: (52.95%/35.29%) · 106.4 M€ (see Table 9).

These economic trade-offs must reflect how muchthe HSRA, represented by the decision maker,

1.2.4 1.2.5 1.2.6 2.1.1 2.1.2 2.1.3

100.00 0.00 0.00 100.00 97.87 0.37100.00 0.00 71.43 83.66 97.87 0.37100.00 60.00 100.00 96.11 100.00 0.0050.00 100.00 100.00 74.70 55.93 95.1175.00 100.00 100.00 80.16 59.74 97.55

100.00 100.00 100.00 85.63 63.54 100.0012.50 100.00 100.00 1.68 31.28 67.520.00 100.00 100.00 0.00 0.00 90.83

11.54 38.46 3.85 28.17 7.04 1.41

2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7

0.00 97.87 0.37 97.70 33.33 0.000.00 97.87 0.37 97.70 33.33 0.000.00 100.00 0.00 100.00 100.00 81.050.00 55.93 95.11 26.09 0.00 100.000.00 59.74 97.55 26.09 0.00 100.000.00 63.54 100.00 26.09 0.00 100.005.00 31.28 67.52 0.00 33.33 100.002.50 0.00 90.83 0.00 33.33 100.003.66 8.54 2.44 13.41 42.68 28.05

Table 9Trade-offs for the criteria under evaluation area 1.1

Criterion W. weight (%) Trade-off (D) (M€)

1.1.1 35.29 106.41.1.2 52.95 159.61.1.3 11.76 35.5

Table 11Trade-offs for the criteria under evaluation area 1.2

Criterion W. weight (%) Trade-off (D) (M€)

1.2.1 15.38 230.71.2.3 30.77 461.61.2.4 11.54 173.11.2.5 38.46 576.91.2.6 3.85 57.8


would be willing to pay additionally (in construc-tion and expropriation costs) to move, on each cri-terion, from the worst impact level (least preferred)to the best one (most preferred). Therefore, the deci-sion maker was asked to validate these preliminaryeconomic trade-offs (see last column in Table 9).Questioning the decision maker on these figuressometimes led to the revision of the initial economictrade-offs, in an interactive and learning process.

Subsequently, regarding evaluation area 1.2, anequivalent procedure was used, this time using crite-rion 1.1.1 (construction and expropriation cost)against criterion 1.2.1 (maintenance and operationcosts), as shown next:

(1) First, two fictitious reference alternatives werecreated. Each with the best impact level on onecriterion and the worst impact level on theother one (see Table 10).

(2) These fictitious reference alternatives werethen ranked by the decision maker (last col-umn in Table 10).

(3) The decision maker was then asked to assesshow much the HSRA would be willing topay additionally (in construction and expro-priation costs) to decrease maintenance andoperation costs from 22.14 million €/year(worst impact level) to 15.96 million €/year(best impact level). The elicited economictrade-off was about 230.7 million €, whichimplies that the HSRA would be willing topay about 37 € in investment costs to decrease1 €/year in maintenance and operation costs.This economic trade-off reflects the presentvalue of maintenance and operation coststhroughout the project life cycle, as well asthe investment costs actually supported by

Table 10Fictious reference alternatives for criteria 1.1.1 and 1.2.1

Alternatives 1.1.1 1.2.1 Ranking

A1 488.3 M€ 22.14 M€/y 2ndA2 594.7 M€ 15.96 M€/y 1st

the HSRA, considering that these investmentcosts would be co-financed by the EU.

Having determined the trade-off for criterion1.2.1, calculating the trade-offs for the remainingcriteria under this evaluation area was a straightfor-ward task as previously explained (see Table 11).

For evaluation areas 2.1 and 2.2, a similarapproach was developed to determine the economictrade-offs using criteria 2.1.6 (impact on economic

activities) and 2.2.3 (noise impact), respectively.It should be stressed that the authors explicitly

started with the MACBETH weighting procedurefollowed by the trade-off procedure, because theywere convinced that it would be easier for the deci-sion maker to be first confronted with an initialworking figure to help him reach a consensus ona final economic trade-off. This procedure oftenled to the revision of the initial judgments elicitedwith MACBETH, in an interactive and learningprocess.

Having determined and validated the final eco-nomic trade-offs for all criteria under all evaluationareas (see Table 12), how could these be translatedinto appropriate final weights? Essentially, the deci-sion maker said that the HSRA would be indifferentbetween: (a) the worst impact level, on a given crite-rion j (51.1.1); and (b) paying an extra constructionand expropriation cost equal to the associated eco-nomic trade-off D for the best impact level on thesame criterion j. This is mathematically equivalentto: V ðaÞ ¼ V ðbÞ () k1:1:1 � v1:1:1ðaÞ þ kj � vjðaÞ ¼k1:1:1 � v1:1:1ðbÞ þ kj � vjðbÞ. Using the previousdefined decreasing linear function for v1:1:1ðaÞ andv1:1:1ðbÞ, this equation can be simplified: k1:1:1�100� ðD=106:4Þ ¼ kj � 100. Constructing n � 1similar equations, for all criteria j (51.1.1), withthe weights k as unknowns and including an extracondition that the weights must sum to 1, thenumerical values of the weights k can be determinedby solving this set of equations.

Table 12Trade-offs and final weights for all the criteria

Criterion Trade-off (D) (M€) Weight (%)

1.1.1 106.4 5.741.1.2 159.6 8.611.1.3 35.5 1.911.2.1 230.7 12.451.2.3 461.6 24.901.2.4 173.1 9.341.2.5 576.9 31.121.2.6 57.8 3.122.1.1 1.7 0.092.1.2 0.4 0.022.1.3 0.1 0.002.1.4 1.2 0.072.1.5 0.6 0.032.1.6 1.9 0.102.2.1 0.6 0.032.2.2 1.7 0.092.2.3 3.9 0.212.2.4 1.1 0.062.2.5 6.2 0.332.2.6 19.7 1.062.2.7 12.9 0.70


4.5. Overall value of the alternatives

Finally, the overall value for each alternative wascalculated using the aforementioned additive model:

V ðaÞ ¼Xn

j¼1

kj � vjðaÞ; withXn

j¼1

kj ¼ 1 and

0 < kj < 1; 8j;

where, V ðaÞ is the overall value of alternative a; j

represents each criterion under all evaluation areas;n is the number of criteria under all evaluationareas; vjðaÞ is the local (or partial) value of alterna-tive a on criterion j (see Table 8); and kj is the finalweight for criterion j (see Table 12).

Table 13 presents the calculated overall values ofeach alternative, which reflect its overall attractive-ness (preference). The most attractive are the three

Table 13Overall values and ranking for the alternatives

Alternatives Value Ranking

Boavista (I) 35.91 7thBoavista (II) 30.66 8thDevesas 55.17 6thCampanha (I) – W 85.91 4thCampanha (I) – I 89.63 2ndCampanha (I) – B 93.36 1stCampanha (II) 85.28 5thCampanha (III) 87.62 3rd

Campanha alternatives. The Devesas alternativehas an intermediate overall value, closer to theCampanha alternatives than to Boavista (I) and(II), which are clearly the least attractive. Basedon these results, the decision maker formed an ini-tial idea of what its recommendation concerningthe site selection would be. These results were thensubmitted to sensitivity and robustness analyses.Throughout the entire evaluation process, everystep was continually reassessed, as awareness andnew insights were integrated, until a requisite model(Phillips, 1984) was obtained, in order to create thebest possible mirror of the decision maker’s pointsof views and preferences.

5. Sensitivity and robustness analyses

In this methodological phase, sensitivity androbustness analyses were carried out in order to val-idate the preliminary recommendations on the over-all ranking of the alternatives.

As initially stated, uncertainty on the impact esti-mations was particularly relevant for Campanha (I).Although sensitivity analyses could be carried outon the impact estimations, the HSRA chose tomodel that uncertainty explicitly using pessimistic,intermediate and optimistic impact levels.

The sensitivity and robustness analyses focusedon criteria weights’ variation, since the decisionmaker felt confident about the estimated impacts,but felt especially uncertain on the elicited weights.Hence, both isolated variations (sensitivity) andmultiple simultaneous variations (robustness) werecarried out on the weights, using the specific soft-ware PROBE (Lourenco, 2002).

5.1. Sensitivity analyses

The sensitivity analyses carried out consisted ofanalyzing the modifications that occur on the over-all ranking of the alternatives when the weight for agiven criterion was changed, maintaining the pro-portions among the remaining weights unchanged.

At first, sensitivity analyses were performed foreach evaluation area. Fig. 6 depicts the snapshotstaken from PROBE for these sensitivity analyses,where the vertical axis represents the overall valueof the alternatives and the horizontal axis representsthe variation scale of the weight – from zero to one -for each evaluation area. The dotted vertical line rep-resents the current value of the weight for each eval-uation area. As for the sloping lines, they represent

Fig. 6. Sensitivity analyses on the weights for evaluation areas 1.1, 1.2, 2.1, and 2.2.


the overall value of the alternatives, as the weight foreach evaluation area varies between zero and one.

From the analysis of the results shown in Fig. 6,it was concluded that the alternatives involvingCampanha would be the best alternatives regardlessof the weight given to evaluation area 1.1. The alter-natives involving Campanha would remain the bestalternatives until the weight for evaluation area 1.2becomes less than 10.9%. In order to attain thisweight, the decision maker would have to be willingto pay only 6.6 M€, instead of the previously stated230.7 M€ (see Section 4.4), to reduce maintenanceand operation costs from 22.14 M€/year (worstimpact) to 15.96 M€/year (best impact). The deci-sion maker confronted with this economic trade-off, consider it unfeasible.

Fig. 6 also shows the results from the sensitivityanalyses carried out for evaluation areas 2.1 and2.2. Again, the decision maker considered thetrade-offs resulting from these analyses unfeasible.

The decision maker was further confronted withsimilar sensitivity analyses on all criteria under eachevaluation area. These analyses showed that thealternatives involving Campanha consistentlyremained the best ones over any reasonable rangeof weights (i.e., economic trade-offs).

5.2. Robustness analyses

In addition to the sensitivity analyses, robustnessanalyses (as defined by Roy and Bouyssou, 1993)of the model’s outputs were also performed, by

Overall

1.2 1.1 2.2 2.1

1.2.5

1.2.3

1.2.1

1.2.4

1.2.6

1.1.2

1.1.1

1.1.3

2.2.6

2.2.7

2.2.5

2.2.3

2.2.2

2.2.4

2.2.1

2.1.6

2.1.1

2.1.4

2.1.5

2.1.2

2.1.3

Fig. 7. Ranking of the weights among the criteria (first step analysis).


changing various weights at the same time, regard-ing some predefined constraints on weights, suchas their ranking.

Robustness analysis is based on the concept ofadditive dominance (Bana e Costa and Vincke,1995): alternative X additively dominates alternativeY, for a given set of constraints defined among theweights (e.g., the weights ranking), if the differencebetween the overall value of X and Y is always posi-tive, for any set of weights respecting the constraintsdefined among them. As expected, the classic con-cept of absolute dominance – where X dominates Y

if and only if X is not worst than Y in any criterionand is better than Y in at least one criterion – incor-porates the additive dominance.

At a first step, a robustness analysis was carriedout on the overall value of the alternatives, byallowing simultaneous variations on the weightsrespecting the ranking of the weights among allevaluation areas ðk1:2 P k1:1 P k2:2 P k2:1Þ and theranking of the within weights among its sub-criteria

Fig. 8. Robustness analyses: (a) imposing rank constraints on

(see Fig. 7), as previously elicited by the decisionmaker (see Section 4.3).

At a second step, a similar analysis was per-formed, this time respecting the ranking of theweights among all elementary criteria ðk1:2:5 Pk1:2:3 P k1:2:1 P � � �P k2:2:1 P k2:1:2 P k2:1:3Þ, as deter-mined by the final economic trade-offs (weights)elicited by the decision maker (see Table 12).

Fig. 8a shows the dominance table resulting fromthe two aforementioned analyses, which happenedto be exactly the same. A triangle (n) representsabsolute dominance of the alternative in line overthe alternative in column. A plus sign (+) representsadditive dominance, that is, dominance imposing thepreviously defined constraints among the criteriaweights and under the conditions of the additive(hierarchical) model.

On the one hand, the Boavista alternatives – B(I)and B(II) – are dominated by the Campanha alter-natives – C(I), C(II) and C(III). On the other hand,the Devesas alternative – D – is not dominated by

weights and (b) imposing bound constraints on weights.


any other, and therefore, according to these analy-ses, the results are inconclusive.

For that reason, another robustness analysis wasperformed, this time considering that the weightscould only vary within certain variation intervals.

Uncertainty came from the elicited economictrade-offs by the decision maker, not the weights(Table 12). Thus, different uncertainty levels wereconsidered using successively increasing variationintervals on the trade-offs for each criterion, so thatthese could only vary within specific bounds. Atfirst, upper (DU

i ) and lower (DLi ) bounds were calcu-

lated for each criterion (i), as a percentage (p) of theinitial economic trade-offs (Di), using the expres-sions: DU

i ¼ ð1þ pÞ � Di and DLi ¼ ð1� pÞ � Di.

Subsequently, and since criterion 1.1.1 was madeoperational through a linear value function, calcu-lating upper (W U

i ) and lower (W Li ) bounds within

which the weights could vary, for each criterion(i), is straightforward using the expressions:

W Ui ¼

DUi

DUi þP

j 6¼iDL

jand W L

i ¼DL

i

DLi þP

j 6¼iDU

j.

This procedure will be illustrated by startingfrom an uncertainty level (p) of 10%. First, upperand lower bounds on the economic trade-offs forall criteria were calculated. The results are presentedin Table 14. From these, upper and lower boundson the weights were calculated for all criteria (seetwo last columns in Table 14).

Table 14Bounds for an uncertainty level of 10%

Criterion DLi (M€) DU

i (M€) W Li (%) W U

i (%)

1.1.1 95.787 117.073 4.75 6.931.1.2 143.721 175.659 7.16 10.331.1.3 31.920 39.013 1.57 2.331.2.1 207.638 253.779 10.42 14.801.2.3 415.410 507.724 21.34 28.841.2.4 155.796 190.417 7.77 11.181.2.5 519.229 634.613 26.99 35.581.2.6 51.977 63.527 2.56 3.782.1.1 1.485 1.815 0.07 0.112.1.2 0.371 0.454 0.02 0.032.1.3 0.074 0.091 0.00 0.012.1.4 1.114 1.362 0.05 0.082.1.5 0.520 0.635 0.03 0.042.1.6 1.708 2.087 0.08 0.132.2.1 0.507 0.619 0.02 0.042.2.2 1.520 1.857 0.07 0.112.2.3 3.546 4.334 0.17 0.262.2.4 1.013 1.238 0.05 0.072.2.5 5.568 6.805 0.27 0.412.2.6 17.722 21.660 0.87 1.302.2.7 11.647 14.235 0.57 0.85

Again, the PROBE software supported this anal-ysis. Fig. 8b shows the dominance table resultingfrom the aforementioned robustness analysis (foran uncertainty level of 10%), that is, within the pre-viously defined upper and lower bound constraintson the criteria weights and under the conditions ofthe additive (hierarchical) model. Campanha alter-natives dominate all others.

Subsequently, a similar approach was carriedout, successively increasing the uncertainty level(p). Only at an uncertainty level of 35%, the Cam-panha (II) alternative no longer dominated theDevesas alternative and, finally, at an uncertaintylevel of 40%, both the Campanha (I) – W and Cam-panha (III) alternatives no longer dominated theDevesas alternative. The decision maker consideredthat these upper and lower bounds of the economictrade-offs were sufficiently large to support the deci-sion that the Campanha alternatives dominate theDevesas alternative. Since a wide range of variationis possible without affecting this decision, it can besaid to be a robust decision.

6. Recommendations

On March 2005, having considered the overallattractiveness of the alternatives, its ranking andthe sensitivity and robustness analyses carried out,the decision maker reached the following recom-mendations:

• Campanha alternatives dominate the Boavistaalternatives;

• it is robust to decide that the Campanha alterna-tives dominate the Devesas alternative;

• it is not robust to decide that any of the Cam-panha alternatives dominates any one of theothers;

• selection of Campanha Station as the site for thenew Central Porto High-Speed Railway Stationis a robust decision.

It was further recommended that the choiceamong one of the three Campanha alternatives –(I), (II) or (III) – be based upon a more comprehen-sive and detailed analysis of these alternatives.

7. Follow up

On October 28th 2006, the HSRA formallyannounced that the location of the Central Porto


station would be in Campanha. The final solutionwas based upon the Campanha alternatives.

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Multicriteria decision analysis (MCDA): Central Porto high-speed railway station

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