Assessment of large transport infrastructure projects: The CBA-DK model

Transportation Research Part A 43 (2009) 800–813

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

Assessment of large transport infrastructure projects: The CBA-DK model Kim Bang Salling a,*, David Banister b,1 a b

Department of Transport, Technical University of Denmark, Bygningstorvet 115, 2800 Kgs. Lyngby, Denmark Transport Studies Unit, Oxford University, South Parks Road, Oxford OX1 3QY, United Kingdom

a r t i c l e

i n f o

Article history: Received 10 March 2009 Received in revised form 17 August 2009 Accepted 29 August 2009

Keywords: Decision support system Cost–benefit analysis Transport project appraisal Risk analysis Optimism Bias

a b s t r a c t This paper presents a newly developed decision support model to assess transport infrastructure projects: CBA-DK. The model combines use of conventional cost–benefit analysis to produce aggregated single point estimates, with quantitative risk analysis using Monte Carlo simulation to produce interval results. The embedded uncertainties within traditional CBA such as ex-ante based investment costs and travel time savings are of particular concern. The paper investigates these two impacts in terms of the Optimism Bias principle which is used to take account of the underestimation of construction costs and the overestimation of travel time savings. The CBA-DK methodological approach has been used to apply suitable probability distribution functions on the uncertain parameters, thus resulting in feasibility risk assessment moving from point to interval results. The proposed assessment model makes use of both deterministic and stochastic based information. Decision support as illustrated in this paper aims to provide assistance in the development and ultimately the choice of action, while accounting for the uncertainties surrounding transport appraisal schemes. The modelling framework is illustrated by the use of a case study appraising airport and runway alternatives in the capital of Greenland – Nuuk. The case study has been conducted in cooperation with the Home Rule Authorities of Greenland. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The main challenge when assessing large-scale transport infrastructure projects is to find a rational and trustworthy method to compare the advantages and disadvantages of the project, and to distinguish between the alternative characteristics of the project. Traditionally, transport investment decisions are based on conventional cost–benefit analysis (CBA) converting the virtual impacts into monetary units, such as pollutants, accidents, time savings. The virtues (pros) of a project are set against the deficiencies (cons) of the project leading to a set of investment criteria that can be exploited. There is a huge literature on this well-established and debated process in transport – see, for example Pearman et al. (2003), Grant-Muller et al. (2001), and Leleur (2000). However, these deterministic single point output criteria are based upon ‘‘best guess” estimates of each input variable to the model. Thus, the CBA depicts more of a most likely (modal) value of the transport assessment scheme than the actual value. Traditionally, these modal values are assessed by sensitivities performed on each individual impact to determine how much the output might vary before the project is either accepted or rejected. This is typically achieved by selecting various combinations for each input variable, for example running the model with a worst and best case scenario. These combinations of possible values around the best guess are commonly known as ‘‘what if” scenarios. However, the assessment of transport projects increasingly requires a greater understanding of the complexity of alternatives. Hence, the number of * Corresponding author. Tel.: +45 4525 1548; fax: +45 4525 6493. E-mail addresses: [email protected] (K.B. Salling), [email protected] (D. Banister). 1 Tel.: +44 (0)1865 285066; fax: +44 (0)1865 275885. 0965-8564/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tra.2009.08.001

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‘‘what if” scenario combinations increases rapidly. Secondly, as illustrated in Mackie and Preston (1998), the greatest problem in transport project appraisal is so-called appraisal optimism. In this respect, new research has conceptualised this scheme of appraisal optimism into Optimism Bias that reflects the tendency for a project’s costs and demand forecasts to be respectively under and overestimated. The Optimism Bias is defined as the percentage difference between ex-ante (before) estimates of the appraisal and ex-post (after) values from the final outturn of the projects (Mott MacDonald, 2002; Flyvbjerg and COWI, 2004). These levels of uncertainty can be applied in ex-ante based project appraisal studies, but they are currently disregarded in transport appraisal schemes in most parts of the World. This paper applies quantitative risk analysis (QRA) and Monte Carlo simulation, which is very similar to a traditional sensitivity analysis, as it generates a number of possible scenarios. Hence, the procedure effectively accounts for the two input uncertainties of ‘‘what if” scenarios and Optimism Bias. The simulation procedure then goes one step further by generating a large set of values that each input variable can take and weighs each scenario by the probability of occurrence. Consequently, instead of receiving single point results, the decision-makers receive interval results in terms of an output probability distribution. An advantage of this approach is the possibility of incorporating expert opinions in terms of choosing the most suitable probability distributions and the determination of appropriate limits (intervals). The paper furthermore investigates whether the feasibility risk assessment adopted for evaluation of transport infrastructure projects can provide useful decision support (namely by moving from single point estimates (CBA) to interval results (QRA)). By combining the latter three methodologies of CBA, Optimism Bias and QRA, a new decision support model has been developed – the CBA-DK model that conceptualises the idea of feasibility risk assessment (Salling, 2008). The paper is structured as follows. The decision support model of CBA-DK is presented together with a case study description. The model consists of the three types of analyses as described above, resulting in feasibility risk assessment. For each method a sub-section in the paper is provided, together with detailed definitions all relating to the case study of Greenland airport options. Finally, a set of conclusions and a more general discussion of the results are presented together with a perspective for future work.

2. The CBA-DK decision support model In 2003, the Danish Ministry of Transport issued guidelines on how to perform socio-economic analysis in the Danish transportation sector (DMT, 2003). This Manual supports a consistent and transparent approach to performing socioeconomic analyses in situations where monetary quantifiable impacts can be allocated. This Manual has been the main reason for building a flexible and up-to-date decision support model for assessing transport infrastructure projects, and it provides the basis from which this extended analysis takes place. Socio-economic analysis, as interpreted in Denmark, is based upon conventional CBA, in which deterministic single point evaluation criteria are calculated. Uncertainties can only be handled by sensitivity tests in terms of worst and best case scenarios. The proposed modelling scheme of CBA-DK combines a deterministic calculation (CBA and Optimism Bias) with a stochastic calculation (QRA). In this way, the model supports the socio-economic analysis proposed in the Manual, but combines this with an additional stage covering the embedded uncertainties. The model is developed on a Microsoft Excel platform forming the basis of the cost–benefit approach, and the quantitative risk analysis is carried out with add-in software from Palisade named @RISK implementing a Monte Carlo simulation (Salling, 2008; Palisade, 2007). 2.1. The Greenland case study Transport to and from Greenland is both expensive and difficult. However, new infrastructure plans proposed by the Home Rule authority and municipalities within Greenland are now trying to address these problems. A new airport transport plan was needed to accommodate the phasing-out of the current Dash 7 aeroplanes. The current runways would be too short to handle newer aeroplanes such as the Dash 8. For example, the current runway length in Nuuk is 1199 m, whereas the Dash 8–400 needs at least 1600 m to land. Secondly, this case study investigates the possibility of moving the major international airport from Kangerlussuaq to the Greenland’s capital, Nuuk. Naturally, the various stakeholders are all interested in maximizing their benefits, and this has resulted in several project proposals for new infrastructure investment in Greenland. All the municipalities want to gain from tourism, which means that new and improved airports, road connections, harbour connections, etc. are of substantial importance. There are two principal areas of interest; first to attract the major international airport to the capital of Greenland, Nuuk and secondly, to decide whether or not the existing international airport in Kangerlussuaq should remain open. If the airport is moved to Nuuk, it would seem obvious to close the existing airport. However, closing the airport in Kangerlussuaq would have negative effects on the whole area as it relies heavily on the transfer traffic (a so-called hub). Fig. 1 depicts the current flight situation to and from Greenland, where Kangerlussuaq is the major international airport. It is possible to travel from the capital of Iceland, Reykjavik, to Nuuk, and this offers some competition on the route. Narsarsuaq in the south offers one international connection, through a weekly service with the Scandinavian airline service (SAS), but this route has been terminated (2008). The flight situation internationally as well as domestically in Greenland presents many obstacles for the passengers. The overall transport plan in Greenland states that all townships and cities are to be connected with the capital, which currently means serving additional 25 cities and townships (Leleur et al., 2007). All national flights must have at least one connecting flight to Nuuk, so people who want to go abroad usually have to make a stop-over in Nuuk before changing flights at

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Fig. 1. Location of main airports in Greenland.

Kangerlussuaq. This way of handling a national transport plan is extremely costly, as all the remote townships have to be covered. This paper investigates the first step of the transport plan in Greenland, namely the alignment of the international airport in Nuuk. Three case alternatives are presented, with two upgrade scenarios replacing the existing runway in Nuuk, by increasing the current runway length from 1199 m (Do nothing) to either 1799 m (Option 1) or 2200 m (Option 2), and a closure of the existing airport in Nuuk, and the construction of a brand new airport in the south with a 3000 m runway (Option 3) (Leleur et al., 2007; Salling and Leleur, 2007). The analysis carried through in the following sections assumes that the International Airport in Kangerlussuaq is closed and only open for national flights. Fig. 2 illustrates the existing runway in Nuuk, which is situated very close to the town centre. The proposal will extend this in Option 1 or 2, with Option 3 being located to the south of the city. It is clear, that the two smaller runway alternatives are the easiest to build with substantially lower construction costs than Option 3 (Table 1). But Option 3 is the one with the best future prospects, even though the construction costs are particularly high, since the airport needs a new road stretch (black line) and a tunnel (the dotted line) in addition to the longer runway. Given the three runway options, larger aeroplanes such as the Airbus 330–200 cannot operate on the shorter runways, if Option 1 or 2 are chosen. Thus, some politicians and especially the general population of Nuuk are in favour of Option 3, and they argue that selecting the two shorter runway options will increase pollution, as load factors decrease and more frequent flights are necessary. It is also argued that future increases in tourism and business trips will in turn contribute to the need of larger aeroplanes. The Home Rule of Greenland has decided to assess the three options shown above.

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Fig. 2. Map of Nuuk showing the three runway options with Options 1 and 2 situated very close to the town centre and Option 3 to the South of Nuuk (Leleur et al., 2007).

Table 1 Overview of the results from the three alternatives (Leleur et al., 2007).

Investment NPV IRR BCR

Option 1: Nuuk 1799

Option 2: Nuuk 2200

Option 3: Nuuk 3000

785 Million DKK 2847 Million DKK 22.94% 4.62

1074 Million DKK 3442 Million DKK 19.74% 4.20

2820 Million DKK 1341 Million DKK 8.02% 1.48

The major impacts to consider when assessing air transportation are the travel time savings, split into in-flight time, unscheduled waiting time, changing/connection time and scheduled waiting time (Wardman, 2004). The Greenland case is special when assessing respectively the unscheduled waiting time and the scheduled waiting time, due to the very low frequency of flights and the weather conditions. For many of the townships, flights may only depart once or twice a week, meaning that passengers can experience extremely high waiting times. Secondly, especially in the winter season, the weather conditions can often ground an aeroplane for several days, even weeks. Hence, it has been assumed that unit prices associated with the waiting time effect decreases over time, meaning that passengers are able to use their waiting time productively (e.g. sight-seeing or other activities). The scheduled waiting time is defined as the time associated with travelling by public transport with a time schedule, and it is assumed that passengers can use this particular waiting time productively. Other important impacts associated with this type of analysis are the operating costs, including the purchase of the aircraft, fuel, maintenance and other operating costs, air traffic control and landing costs. In addition, there is the ticket revenue for the airline carriers and the user benefits for the passengers resulting from the provision of the service. These factors, together with the prices paid by passengers and other subsidies for low density routes, determine the airline carriers’ profit or

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Fig. 3. Conceptualised approach concerning the CBA-DK framework model.

loss. As the airlines carry more passengers, revenues and turnover are increased, which in turn leads to an improved service and more travellers. The passengers experience a lower ticket price, as a consequence of more competition, a more frequent service and a direct connection to Nuuk. Finally, as the airport in Kangerlussuaq is abandoned, there are substantial benefits from reductions in direct operating and maintenance costs, and the freeing up of resources that are currently being used to subsidise this airport (Salling and Leleur, 2007). The following three sections outline the set of methodological approaches used within the CBA-DK model. All methodologies are well described individually in the literature, but no combined methodology has been attempted. The three methodologies consist of a deterministic calculation within a conventional cost–benefit analysis together with the Optimism Bias principle, and this is linked to the stochastic calculation that consists of a quantitative risk analysis and Monte Carlo simulation. The approach outlined in this paper combines all three methodologies through the new concept of feasibility risk assessment (Fig. 3). 2.2. Cost–benefit analysis The socio-economic analysis forming the basis for appraising the three runway options are carried out by a traditional cost–benefit analysis. This deterministic calculation produces a set of decision variables in which decision-makers can have a preliminary view of the project. Three sets of criteria are calculated, namely the net present value (NPV), the internal rate of return (IRR) and the benefit–cost ratio (BCR). The cost–benefit analysis focuses mainly on three groups or actors and their respective evaluation impacts (Fig. 4): the users where most of the benefits accrue, the authorities (in this case consisting of the Home Rule Authorities in Greenland and the Danish Government) where the infrastructure and construction costs are allocated, and the operators that provide the service. Currently there is only one operator, namely Air Greenland.2 The implementation of an overall socio-economic analysis in Greenland only considers trips made by business and resident travellers, with all tourist related trips being omitted. The argument here is that the monetary cost and/or benefits stemming from tourists accrue to their respective countries and not Greenland. Hence, the travel time savings and the user benefits are only appraised for business and resident trips. Although the user benefits from tourists may not contribute directly to the services being run, there would be a transfer payment to the operators for the costs of running the service. In addition, the tourists may bring substantial benefits to the local economy through hotel business, through the creation of new tourist related jobs and other tourist related activities. The multiplier effects are substantial, provided that the money remains in the local economy (Banister and Berechman, 2000). This is unfortunately one limitation of the CBA approach, namely that it is primarily concerned with estimating the transport costs and benefits, as reflected in the users, the airlines and airport operators, and the government, rather than the wider impacts on the local economy and the environment. The tourism effects are treated within the multi-criteria analysis, where additional effects such as regional planning, business and accessibility are also addressed (Salling et al., 2007; Banister and Berechman, 2000). A deterministic run of CBA-DK produces a result sheet embedding the principal three evaluation criteria (Table 1). The net changes are evaluated over a 50 year period and discounted to present values. This discount ratio is crucial to the analysis and it is often debated, especially since the lower rates favour projects with shorter time horizons. The Danish Ministry of Transport has together with the Home Rule authorities of Greenland decided to use the official discount ratio from Denmark set at 6% (Leleur et al., 2007). It is problematic to apply a constant discount ratio over the 50 years of evaluation as assump2 The ownership of Air Greenland is currently divided into three shares where the Home Rule of Greenland owns 37.5%, the Danish Government owns 25% and the Scandinavian Airline Services (SAS) owns 37.5%. It has been assumed in this analysis that only the benefits accruing to the society of Greenland are included, meaning that all benefits and costs associated with Air Greenland is depreciated to 37.5%.

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Fig. 4. Flowchart on the different actors and impacts applied in the CBA-DK model (adapted from Gissel, 1999).

tions are made about the productivity of the investment over the whole lifetime of the project. The UK Government has recently introduced a so-called certainty-equivalent discount ratio which can be found by taking the average of the discount factor, rather than the discount ratio itself (HEATCO, 2004, p. 31). A future perspective within the modelling framework of CBA-DK would be to apply the uncertainty principles on the discounting of a given transport project, but as no common ground has been established, the traditional discounting is applied. These point estimates from the CBA indicate three case results, with Option 3 (Nuuk 3000 m) performing worst, but with a positive NPV of nearly 1.5 Billion DKK. The other two Options perform almost identically with very high decision variables. The choice between Options 1, 2 and 3 need to be debated by policy-makers and various stakeholders. One major aspect, however, is that Option 3 is almost three times as expensive as Options 1 and 2, even though it still produces feasible decision results. The embedded uncertainty and appraisal optimism is creating variability in the model output where two transport-related impacts stand out, namely the construction costs and the user benefits, which mainly consist of travel time savings (Mackie and Preston, 1998). 2.2.1. Travel time savings By far the largest contributor of direct benefits from any given transport project is the travel time savings. Benefits originating from this category often make up about 70–90% of the overall user benefits (Mackie et al., 2001). These benefits consist of three components, which together make up the overall monetary value of the travel time savings, namely the money costs, the opportunity cost of time, and the disutility of travelling (Banister and Berechman, 2000, p. 178). The money costs are associated directly with the choice of travelling namely tolls, fares or car purchase, sometimes referred to as the outof-pocket direct travel costs. The opportunity costs refer to the alternative use of time spent on travelling, including the use of time productively to accomplish other activities such as work. The latter time value varies considerably between people, thus its value lies between 0 (time saved cannot be used productively elsewhere) and 1 (time saved can be fully utilized into other alternative use). Finally, the third component is the experience of travelling which among others can be expressed by the lack of comfort. This component makes up the inconvenience that travelling creates (Banister and Berechman, 2000). Moreover as previously illustrated, travel time savings are determined for three categories of travel, namely business, home/work and leisure trips. These categories are further split into travel related utilities such as in-vehicle time, waiting time, changing time. All these aspects are gathered in the key figure catalogue (DMT, 2006) where frequent updates are made. Banister and Berechman (2000, Table 7.2) and Leleur (2000, Table 4.6) both combine information of the substantial variation between countries of values of travel time savings by trip purposes. It is clear from these figures, that even though

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Table 2 Applicable capital expenditure uplifts for selected percentiles applied to constant prices (adapted from Flyvbjerg and COWI, 2004). Level of acceptable Optimism Bias

50%

60%

70%

80%

90%

Road Rail (and air) Fixed links

15% 40% 23%

24% 45% 26%

27% 51% 34%

32% 57% 55%

45% 68% 83%

extensive efforts have been made on deriving valid data, variation exists between countries and there is no common approach to the calculation of travel time savings. These travel time savings are then converted into costs through the use of a range of different values of time, so that they can be incorporated into the CBA as monetary values (Mackie et al., 2001; Fosgerau, 2007). 2.2.2. Construction costs The impact with the highest overall significance on any given appraisal study in the pre-stage is the construction cost. In order for the transport authorities or government to prepare reliable financial transport infrastructure programmes, accurate estimates of future funding are vital. For example, within the construction of road infrastructure projects in Denmark, forecasting future construction costs has been achieved basically by constructing a unit rate, using Danish Kroner (DKK) per kilometer highway of a predefined road type (Lahrmann and Leleur, 1997). However, this method is considered unreliable due to local site conditions, such as topography, soil, land prices, environment, traffic loads, which all vary significantly from location to location (Wilmot and Cheng, 2003). Current studies have shown extensive underestimation of future costs resulting in budget overruns by up to 100% (Flyvbjerg et al., 2003a). Such budget overruns are not acceptable and ‘better’ construction cost estimates are needed, in order to make recommendations that are valid and that provide trustworthy decision support. The travel time savings and the construction costs have proved to be very difficult to derive accurately through modelling. Flyvbjerg et al. (2003a) actually concludes that in the case of large-scale bridge and tunnel projects, on average, construction costs were 50–100% undervalued whereas the travel time savings effect, based on traffic forecasts, were about 60% overestimated (compared with the opening year traffic situation). The majority of proposed transport systems cost on average 50% more than their ex-ante estimates, while the ex-post demand within travel savings are about 50% below the estimated demand. This has resulted in an established maxime for transport CBA, suggesting that in order to derive actual benefit and cost values of an infrastructure project, one should normally halve the predicted benefits and double its estimated costs (Banister and Berechman, 2000, p. 187). These more or less consistent overestimations of benefits and underestimations of costs within transport infrastructure appraisals have been named Optimism Bias. Decision-makers and analysts tend to be overly optimistic with respect to construction costs and future traffic demands. Thus, a new guideline has been developed for the British Department for Transport in which parameter values have been determined in order to cope with some of these appraisal shortcomings (Mott MacDonald, 2002; Flyvbjerg and COWI, 2004). 2.3. Optimism Bias The Optimism Bias approach is dealt with by the use of a well-established technique named Reference Class Forecasting (RCF). The theoretical background to RCF originates in prospect theory3 developed by Kahneman and Tversky4 (Kahneman and Tversky, 1979). A reference class denotes a pool of past projects similar to the one being appraised. A systematic collection of differences between forecast and actual values is gathered for a range of similar projects, the deficiencies in the forecast process (for costs and demand) are compared, and this evidence is then used to improve current decisions. Experience from past projects is then collected, compared and used so that ‘‘planning fallacy” can be avoided (Buehler et al., 1994; Koole and Spijker, 2000). A substantial number of reference class projects have been identified, for example in Flyvbjerg et al. (2003a) where budget overruns and demand forecasts for several road, rail and fixed link projects were examined. The pattern of results showed that rail projects were subject to cost underestimations with an average of 45%, road projects with an average of 20% and fixed links with an average of 34% (Flyvbjerg et al., 2003a, pp. 15–16). The resulting outcome from the reference classes are determined by the Optimism Bias uplifts, which are then related to the preliminary construction cost predictions. The uplifts should be applied to the estimated budget costs at the time of the decision to build. Thus, uplifts are referred to as the cost overruns calculated in fixed prices. Table 2 shows some of the uplifts applicable within transport infrastructure projects, for different levels of certainty ranging from 50–90% (Flyvbjerg and COWI, 2004). The three main categories of road, rail and fixed link are covering a huge variety of different projects, i.e. road projects are for example divided into difference reference classes depicting motorways, trunk roads, local roads, bus lane schemes, etc. Rail projects have been divided into Metro projects, light rail projects, high speed rail projects, etc. whilst the fixed link also covers bridges and tunnels. 3 Prospect theory describes decisions between alternatives that involve risk. There are several alternatives where the general outcome is uncertain but the associated probabilities are known. 4 Daniel Kahneman received the Nobel prize in Economics in 2002 for his work in collaboration with Amos Tversky (1937–1996).

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The Optimism Bias uplifts shown above are classified according to the risk aversion of decision-makers in terms of cost overruns. If a group of decision-makers decides that the risk of a cost overrun must be less than 20% for a road type project, the construction cost estimate must be uplifted by 32%. Thus, if the initial budget estimate was 100 million DKK the final budget taking into account the Optimism Bias at an 80% probability level would be 132 million DKK. Flyvbjerg and COWI (2004) suggest only shifting between the 50 percentile (lower) and the 80 percentile (upper), so that the upper percentile denotes investors with a high degree of certainty that cost overruns will not occur. This is typically present when no additional funds are available. The lower percentile should only be applied if decision-makers are willing to take a high risk that cost overruns can occur. Table 2 presents clear empirical guidelines for practitioners and analysts within the field of transport project appraisal, but care must be taken in using the uplifts as presented in the table. A vital part of deriving the set of uplift parameters is the setting of the reference class projects obtained and used as comparators. Stakeholders and decision-makers should be involved early in the evaluation process to select the level of acceptable Optimism Bias. Recalculating the three case alternatives from Nuuk incorporating the Optimism Bias uplift in respective 50% and 80% acceptance level, the following decision variables are determined (Table 3). It has been assumed that the empirical results from rail projects can be transferred directly to airport infrastructure projects. In the original database, there was not a separate section on airport infrastructure projects, and by taking rail as the exemplar here may be over emphasising the problem as the worse case. The introduction of the Optimism Bias uplifts provides a preliminary robustness analysis. Options 1 and 2 still produce very high returns. Option 3 becomes marginal with both sets of Optimism Bias used. The set of ‘‘alternative” investment costs produces decision criteria in which the uncertainty of cost overruns is embedded. Decision-makers are presented with a more cautious set of values on which to make their decisions, with the investment costs being substantially increased and the benefits remaining the same. Although the overall BCRs are lowered, the relative positions of the three Options against each other remain unchanged. The only possibility of change is where one Option has a substantially higher or lower risk attached to it. Hence the Optimism Bias can be seen as a scaling effect unless the different Options have different levels of uncertainty associated with them. As noted before, a large section of the population and politicians in Greenland are in favour of Option 3 due to its future possibilities. The preliminary deterministic results (Table 2) make Option 3 a relatively attractive alternative, but after introducing Optimism Bias (Table 3), the feasibility becomes negative. The following analysis builds solely upon Option 3 in which an investigation of the overall feasibility risk of choosing this case alternative is performed. The main interest is in determining whether this option is feasible and how robust the alternative is, after a risk analysis. It is proposed to introduce probability distributions and Monte Carlo simulation to assess the embedded uncertainty of this particular alternative. The method uses combinatorial evaluations to perform uncertainty analysis on the travel time savings and construction costs. The simulation approach differs to the Optimism Bias that is heavily dependent on detailed empirical analyses to determine the values to be used. Options 1 and 2 are extremely attractive given the input as shown in Tables 2 and 3, hence, it is assumed that a QRA does not contribute to any variation between the selection and attractiveness of these two runway alternatives. 2.4. Quantitative risk analysis Even though a key advantage of using cost–benefit analysis is the transparency, this may also be considered a weakness. The method relies on single result values, where all the considerations and calculations are reduced to just a single aggregated value. The quantification of ‘‘non-market” effects such as accidents saved, air pollution and other externalities present a practical measurement problem. Thus, the uncertainty embedded within the different pricing strategies is problematic. To set a price mark on an accident, the time saved in a vehicle or the emission of one tonne of CO2 is highly uncertain (Leleur, 2000). Consequently, two sets of uncertainties are identified in the assessment of transport infrastructure projects. Firstly, there is the underlying model uncertainties embedded within any traffic or impact model and secondly, there are the uncertainties in any CBA pricing strategy. By adding to the conventional CBA through the adoption of a quantitative risk analysis, the probabilities of occurrence of particular risk factors can be incorporated, and decision-makers and analysts can make use of their expertise, conceptualised as the level-of-knowledge (LoK). The technique used is Monte Carlo simulation which involves a random sampling method concerning each different probability distribution selected for the actual model set-up (Rubinstein, 1981; Law and Kelton, 2000). The selection of the most Table 3 Resulting criteria when applying Optimism Bias.

Investment, 40% Investment, 57% BCR, 40% BCR, 57%

Option 1: Nuuk 1799

Option 2: Nuuk 2200

Option 3: Nuuk 3000

1100 Million DKK 1233 Million DKK 3.29 2.93

1504 Million DKK 1687 Million DKK 2.99 2.66

3947 Million DKK 4427 Million DKK 1.04 0.92

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appropriate probability distribution has been a major task of the research where several distributions have been tested in terms of their suitability (Salling, 2008). A common mistake within quantitative risk analysis is to apply unsuitable or inadequate probability distributions. Thus, a separation of actual data fit and ‘‘expert opinion” is necessary (Vose, 2002, p. 273). This distinction has lead to the conceptual interpretation in terms of LoK on the uncertain variables. If the uncertain variables are well defined in literature or by data, parametric distributions should be applied e.g. Normal, Gamma or Beta (high LoK). On the other hand, if the variables rely on experts to judge the uncertainty, then non-parametric distributions should be assigned, such as Beta-PERT, triangular or uniform (low LoK) (Vose, 2002, p. 273). Salling (2008) proposes five types of distributions suitable in transport evaluation schemes ranging from low via middle to high LoK (Table 4). Table 4 depicts the two types of distributions applicable within CBA-DK, parametric and non-parametric distributions together with their LoK, the transport impacts, and where they can be usefully applied. The following section describes findings and applications of the two impacts addressed in this paper, namely travel time savings and construction costs. 2.4.1. Assigning probability distributions The available data on transport infrastructure projects is extremely sparse, and often subject to copyright and other limitations. The following two sub-sections make use of graphical represented data from one reasonably sized database on large-scale transport projects (Flyvbjerg et al., 2003a). The data has been gathered through a 4 year study period (1997– 2001) comprising projects located in 20 nations with 181 projects in Europe, 61 in North America and 16 from South America, Australia and Asia (Flyvbjerg et al., 2003b). All projects were completed between 1927 and 1998 where the selection process was based upon available data. The convention used in the database sample was defined as the difference between actual and estimated costs and demands in percentage terms. Thus, the ex-post values are referring to the real accounted cost or demands determined at the time of completing the project, whilst the ex-ante values are found within the budgeted costs or estimated demands at the time of decision to build (Flyvbjerg, 2005, p. 524). The cases used are all taken from rail (58 classified projects), road (167 classified projects) or fixed link (33 classified projects), which mean that air transport demands and construction costs are not explicitly treated. The key point here is to establish whether the range of projects covered is suitable to appraise air transport investment decisions. Even though rail and air transport projects are not directly comparable, the issues of over estimation of demand forecasts and under estimation of construction costs have similarities, as both types of projects are large-scale investments, they are often publicly funded, and users are travelling longer distances than by car and bus. In addition, as illustrated in Fig. 4, a direct comparison between actors as well as relevant transport impacts can be drawn between air and rail projects (Gissel, 1999, p. 57), indicating that a similar flow can be made for rail transport assessment. 2.4.2. User benefits due to lower airfares As a consequence of the new airport investment that relocates the central hub to the capital Nuuk, passengers will experience lower airfares through more direct routing and increased competition, and travel time savings. Currently, passengers must transfer in Kangerlussuaq to alternate routes creating higher ticket prices and longer travel times. Traditionally, when predicting future traffic flows, various techniques can be used if historical performance data and current traffic flows are accessible. This could be accomplished using methods such as exponential smoothing, regression analysis and curve fitting (Vose, 2002). The historical data in the Greenland case, however, creates a major challenge because of low and fluctuating traffic in the present and the past. The net changes of passengers after the construction of a new airport should be applied to the induced traffic, and this may mean that historical data will be of less value. Inputs for the CBA-DK model are being calculated by traffic and demand models, trying to cope with some of the difficulties in assessing before and after studies in relation to future traffic flows (Nielsen et al., 2007). However, uncertainty within the future passenger flows must be expected, and it is suggested that probability distributions should be applied to the overall travel time savings effect. It could be argued that the same type of uncertainty is carried through from the inaccuracies within traffic demand models. Therefore, attempts are made in separating so-called epistemic and ontological uncertainties commonly referred to as the ‘‘lack of knowledge” and the ‘‘inherent randomness of the system” (Vose, 2002; Walker et al., 2003). Vose (2002) and Walker et al. (2003) claim that separating variability and uncertainty enables the stakeholders and decision-makers to view exactly where further modelling can be of relevance, and where future financing can contribute in the enhancement of the associated risks (Fig. 5).

Table 4 List of applied probability distributions and their level-of-knowledge (Salling, 2008). Distribution

Category

LoK

Impact

Source

Uniform Triangular Beta (PERT)

Non-parametric Non-parametric (Non)-parametric

Low Low Medium and high

Normal Gamma (Erlang)

Parametric Parametric

High High

Non-monetary Accident savings Maintenance costs and travel time savings Travel time savings Construction costs

Multi-criteria analysis Pricing strategies Pricing strategies and model uncertainties Model uncertainties Model uncertainties

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Fig. 5. The nature of uncertainty: Inherent variability or lack of knowledge (adapted figure from Vose (2002), Walker et al. (2003)).

The points made here contribute to the build up stages of any decision support model. However, the practical implementation seems rather confused and difficult to interpret. Vose (2002) makes explicit recommendations for splitting the two types of variability (ontological) and uncertainty (epistemic). This is operationalised by calculating the uncertainty through empirical formulas, and then simulating the variability, or vice versa. However, as Vose (2002) later concludes: ‘‘. . .it is extremely unwieldy, if not impossible, to use explicit calculation models, and simulation is the only feasible approach” (Vose, 2002, p. 27). Hence, a single simulation model is preferable rather than separating the uncertainty into an empirical calculation and then a simulation. Even though Vose (2002, pp. 203–209) advocates the separation of the two terminologies, he also states that depending on the circumstances, more uncertainty can be added to the model if the calculation and simulation procedure is not performed appropriately. The uncertainty modelling in this paper, therefore, makes simulations on the two impacts suggested (travel time savings and construction costs) by combining the total uncertainty. To perform an empirical analysis on either of the two impacts (by separating out the two types of uncertainty) is not currently possible due to the lack of suitable data. Returning to the database illustrated in Flyvbjerg et al. (2003a), inaccuracies within traffic demand forecasts are showing huge variation between ex-ante and ex-post results. By comparing 27 rail projects the inaccuracy for traffic demand forecasts was on average 39% lower than predicted with a standard deviation of 52% (Flyvbjerg et al., 2003a, p. 26). The reason for only applying 27 rail projects concerning the demand forecasts and not 58 projects as explained previously is due to data collection deficiencies. The approximated range of demand forecast bias is set between 92% and 144% (Fig. 6). The overestimation of demand forecast occurs in 85% of the cases. Furthermore, nearly one third of the projects lie within 70% and 30% of overestimations. The data derived from this review of large infrastructure projects is made from rough calculations, but it does give an indication about which probability distribution best fits the data set. The CBA-DK model is able to produce a fitted distribution as illustrated in Fig. 6 (Palisade, 2007, pp. 171–192). Even though the distribution is skewed to the right, most emphasis must be placed on the central probability mass. David Vose and David Kelton both propose the use of a beta-PERT distribution for cases with a relatively high degree of skewness (Personal communications at the 2nd European Palisade User Conference (2007), London, UK and the 40th Winter Simulation Conference (2007), Washington DC respectively). The Program Evaluation and Review Technique (PERT) distribution is derived from the Beta distribution which mathematically is fairly simple and furthermore covers a huge variety of types of skewness (Lichtenberg, 2000). From Fig. 6 it is clear that the data fit from a PERT distribution is valid. This type of distribution requires min and max limits in addition to the modal value, which acts as input from the CBA. This distribution, given the extra emphasis on the mode, makes it ideal for modelling expert opinions for a variable (Vose, 2002).

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Fig. 6. Inaccuracy of traffic forecasts from 27 different rail projects (Salling, 2008).

2.4.3. Construction costs Transport infrastructure assessment needs to make a thorough investigation of the construction cost of the project, so that reliable estimates can be made of the total investment costs. The determination of construction costs ex-ante tends to be underestimated, and these can be explained by technical problems, delays, and increases in labour and material costs. Other common explanations of general underestimations are the dynamic way an infrastructure project is developed over time. In the analysis, one normally tends only to consider the traditional impacts of building a new road or airport runways. However, during the project, it is common that new and better choices are made, for instance to address environmental concerns such as noise or the most suitable alignment for the runway. These costs cannot be taken into consideration in advance, and can only be added at a later stage. The decision-makers also tend to change their preferences during the construction of the project, and this is particularly apparent in large-scale projects. The mega project database (Flyvbjerg et al., 2003a) illustrates that extensive underestimation of future costs sometimes amounts up to 100% or more. Such budget overruns are not to be encouraged, and so ‘‘better” construction cost estimations are needed in order to make decision support analysis more robust. Fig. 7 presents data collected before and after completion of all together 58 rail projects. Almost 88% of the probability mass lies above zero which means that only 12% of the rail projects have been below the preliminary budget. Another Danish study has elaborated on the various features of risks and uncertainties by applying the ‘‘successive principle” in ex-ante based construction costs. This principle is based on group decision-making allowing for extreme measures in finding respectively lower and upper thresholds. The ‘‘successive principle” is then transformed into a triple estimation approach in which a mean is derived (Lichtenberg, 2000, p. 125). This approach, as in the PERT distribution (Fig. 6), places more emphasis on the mode values, as compared with traditional worst/best case scenarios. A comparison of the mean () values for respectively a Triangular, PERT and successive principle is shown in (1):

lTriang ¼

min þ mode þ max ; 3

lPERT ¼

min þ 4  mode þ max ; 6

lsucc: ¼

min þ 2:9  mode þ max 4:6

ð1Þ

The mean in the PERT distribution has four times the weighting on the mode whereas the mean from the successive principle has 2.9 on the mode. Thus, in real-life problems we are usually capable of giving a more confident guess of the mode rather than of the extreme values, hence the PERT distribution and the successive principle brings a much smoother description of the tales of the impacts to be considered compared to the triangular distribution (Vose, 2002; Lichtenberg, 2000). In order to describe the uncertainty in terms of probabilities, the successive principle makes use of an Erlang distribution. The data from Flyvbjerg et al. (2003a) are combined with the Erlang distribution found in Lichtenberg (2000). From Fig. 7, the fitted Erlang distribution is determined with a relatively high shape parameter, k = 23. A k value of 1 relates to the exponential distribution whereas a k value of 5 relates to a lognormal distribution and higher values (e.g. k > 20) resemble the normal distribution. The k parameter is often referred to as the skewness parameter in which lower values corresponds to a higher degree of skewness and vice versa. The second parameter (0.075) denotes the scale parameter, commonly known as h in which the shift of the distribution is defined (Lichtenberg, 2000).

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Fig. 7. Inaccuracy of construction cost estimates from 58 various rail projects (Salling, 2008).

Additional parameters within the deterministic framework could undergo a risk analysis as presented for the travel time savings and the construction costs (Table 4). However, there is no indication given in the literature on the range of inputs to the distribution functions presented in Table 4, and increasing the number of variables would also require further work on interdependencies and correlations between impacts (Vose, 2002). 2.5. Feasibility risk assessment The quantitative risk analysis of CBA-DK enables the analyst to enhance the deterministic results from the cost–benefit analysis into probabilistic outputs. The main scope has been to incorporate risk and uncertainty within transport appraisal in a straight-forward and comprehensive manner. Currently, the BCR is treated as the uncertain output parameter subjected to Monte Carlo simulation. The default settings are 2000 iterations by the use of the Latin Hypercube sampling method (Vose, 2002, p. 59). Latin Hypercube sampling recreates the input distribution through a stratified sampling without replacement method. Stratification of a sampling area [0; 1] means dividing the input probability distribution into intervals on the cumulative curve. A Latin square is defined where the sample only consists of one value for each row and column hence Latin Hypercube sampling ensures per definition variation of sampling where the ensemble of random numbers from the input distribution is a ‘‘valid” representation. The sampling procedure is then forced to represent the values in each interval, and it recreates the input distribution. One of the main advantages of using the Latin Hypercube sampling approach is that it reduces the number of iterations used within the Monte Carlo simulation, and this in turn speeds up the process compared to other sampling methods (McKay et al., 1979). The travel time savings and construction costs are implemented in the analysis in which a PERT and Erlang distribution is applied to Option 3. The limits and distribution functions are schematically illustrated in Table 5. The feasibility risk assessment is based upon the original input parameters where the deterministic point results have been presented in Table 2. The information regarding Optimism Bias uplifts and the associated results presented in Table 3 act as screening variables, where the two shorter Nuuk runway alternatives Options 1 and 2 are preferred over Option 3. However, choosing between the three options is open for the decision-makers to debate. It is important to bear in mind that the CBA-DK model is designed to help decision-makers arrive at the best possible decision. Ultimately, the risk associated with the analysis has to be interpreted by various decision-makers. The same results given to different individuals

Table 5 Budget expenditure uplifts in constant prices (Salling, 2008). Impact

Distribution

Lower (%)

Upper (%)

Travel time savings Construction costs

Beta-PERT Erlang

92 40

144 180

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Fig. 8. Resulting accumulated descending graph showing the probability on the y-axis and the BCR on the x-axis.

may be interpreted differently and lead to different courses of action. A large portion of the population in Nuuk and the rest of Greenland supports the longer runway alternative presented in Option 3, even though the CBA and the CBA-DK both support Options 1 and 2. The final feasibility risk assessment from CBA-DK is presented through an accumulated descending graph. This graph depicts the likelihood of achieving a BCR as shown on the vertical axis or a BCR that exceeds that value. Higher degrees of certainty correspond to a lower BCR and vice versa (Fig. 8). The threshold of a BCR = 1.00 denotes the cut-off limit for ‘‘feasibility” in which lower values depicts infeasibility in terms of socio-economic viability. Fig. 8 presents the decision-makers risk aversion of a given assessment task, hence the vertical line illustrating a BCR equals to 1.00 depict a boundary threshold. Furthermore, CBA-DK present empirical results that denote the new decision support foundation where the BCR is illustrated for the 90% confidence level, i.e. Option 3 [0.66; 2.80]. For the selection scheme appraising either of the three runway options, Option 3 produces feasible results towards society in approximately 60% of the simulation runs. The stakeholders and politicians in Nuuk and Greenland need to debate whether they can accept the feasibility analysis. However, if wider economic impacts such as accessibility, regional planning and tourism are taken into account, the attractiveness of Option 3 will probably be further enhanced as compared to Options 1 and 2. The deterministic CBA calculation together with Optimism Bias uplifts produces a set of decision variables where Options 1 and 2 are preferable. Decision-makers with high economic preferences are likely to support one of these Options, and Option 2 has been selected for implementation by the Greenlandic Home Rule authorities (Kristensen, 2007). 3. Conclusion and perspectives This paper has focused on the treatment of uncertainty as it relates to assessment of transport projects, particularly concerning a case study involving air transport. In this way a major concern has been to determine how the conventional cost– benefit analysis could be extended to include risk analysis, while at the same time maintaining its purpose of providing decision support in a straight-forward manner. The CBA-DK model has been developed to address the issue of risk assessment. This model has demonstrated that a combination of conventional cost–benefit analysis and quantitative risk analysis examination can increase the decision-makers opportunities to make more informed decisions. The underlying modelling technique of quantitative risk analysis provides comprehensive interval results for the project alternatives, so that single value results can be replaced, with a range of benefit–cost ratios (i.e. in the 90% confidence level). The two ways of handling uncertainties have been shown to complement each other. The Optimism Bias approach provides uplift estimates with a 50% and 80% threshold, and the quantitative risk analysis has been applied with a Program Evaluation and Review Technique (PERT) and an Erlang distribution to create a mean in which the underlying uncertainty has been addressed. Modelling feasibility risk by identifying uncertain parameters or variables is developed as a tool that can assist decisionmakers in addressing the key issue of risk aversion in an explicit way, and this has been illustrated by descending

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accumulated probability graphs (Fig. 8). Care must be taken in drawing rigorous conclusions, especially if more than one probability graph is illustrated. Therefore, the CBA-DK model should be seen as a useful tool that allows consideration of uncertainty in the appraisal of infrastructure projects, but at the same time accepting the limitation that the results can never be better than the extent of the validity of the modelling assumptions used. Further research needs to be undertaken, including the determination of non-monetary impacts, which are vital in the appraisal of the tourism effect and accessibility effect in Greenland. Moreover, the inclusion of wider and long-range impacts and strategic impacts should be considered in order to investigate all issues within the assessment scheme, including the impacts of tourism (and its potential) on the overall regional economy (Banister and Berechman, 2000, p. 168–170). A composite uncertainty distribution has been used here, but possible division into ontological and epistemic uncertainty also needs further investigation. Consequently, the model outlined here is being further developed (in a project for the Danish Strategic Research Council) to address the key issues of non-monetary aspects as well as the separation of uncertainties. The issues of risk and uncertainty are central in all types of project analysis, as substantial sums of public (and private) capital are being committed to transport projects, and once decisions are made to proceed and construction starts, it is difficult to reverse the decision. It is essential that better and more flexible approaches are developed so that evidence from similar previous decisions can be used to improve current decisions. In this way, major decisions on transport investment priorities can be made with increasing confidence and less uncertainty. References Banister, D., Berechman, J., 2000. 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