Railway projects prioritisation for investment: Application of goal programming
Aoife Ahern₃, Gabrial Anandarajah

School of Architecture, Landscape and Civil Engineering, Earlsfort Terrace, University College Dublin, Dublin 2, Ireland

Abstract

This research develops a weighted integer goal-programming model for prioritising railway projects for investment. The goal of the model is to prioritise the identified projects for investment while maximising the objectives and meeting the budget limit for capital investment. The model minimises the goal deviations of the objectives. The objectives of the model include quantitative and qualitative attributes. The model is applied to prioritise the new railway projects, which have a total cost of Euro 2 billion for capital investment, identified and analysed by Department of Transport, Ireland. Even though the objective is maximising all the attributes, the investment decision is subject to financial availability. The study recommends investment options at different capital investment levels when the decision is made on the basis of economic benefits, revenue or qualitative goal scores.

Keywords: Railway; Project prioritisation; Transport policy

1.  Introduction

1.1.  Linear programming and goal programming

Optimisation models are constructed for decision-mak-ing especially in selecting an optional subset of projects that are identified for investment. These models vary widely in their degree of objectivity and reliance on data and in the format of their outputs. In the optimisation techniques, linear programming (LP) is widely used. Major limitations in LP are that it optimises only single objective and cannot include soft (flexible) constraint.  Lee (1972) and  Ignizio (1985) criticised the LP approach for its inability to deal with multiple goals and soft constraints. Ignizio (1972) states that as with any quantitative approach to the modelling and solution of real problems, LP has its blemishes, drawbacks and limitations. Of these, our interest is focused on: the inability—or at least limited ability—of LP to directly and effectively address the problems involving multiple objectives and goals, subject

₃Corresponding author. Tel.: +353 1 7167319; fax: +353 1 7167399. E-mail addresses:  aoife.ahern@ucd.ie (A. Ahern),

 gabrial.anandarajah@ucd.ie (G. Anandarajah).

to soft as well as rigid (or hard) constraints. The development of goal programming (GP) is one approach for eliminating or at least alleviating the above-mentioned limitations of the LP. GP is a linear mathematical model in which the optimum attainment of goals is achieved within the given decision environment ( Lee, 1972).

GP is an extension of LP in which one or more goals are formulated as constraints and the objective functions seek to minimise the sum of the absolute deviations from these goals. The main difference between GP and LP is that GP allows for multiple objectives to be considered simulta-neously while LP focuses on one objective ( Ignizio, 1985). For example a common LP objective function would be to minimise cost subject to constraints particular to the system such as production limitations and product demand. Goal programs on the other hand can be formulated to consider multiple objectives.

Another important difference between GP and LP is the concept of soft and rigid constraints. In a linear program the constraints are treated as rigid. That is, if production must be greater than a given value then even a small negative deviation from that value is not allowed. GP allows for both rigid and soft constraints. Soft constraints utilise deviation variables (typically both positive and negative deviation

variables) that measure the difference between the desired value (or goal) and the predicted model value.

 Romero (1991) discusses the equivalence of GP and LP formulations. Romero states that this will only occur if the GP model has been poorly formulated where one goal has been set too optimistically (outside the feasible region) while all other goals have been set too pessimistically (well within the feasible region). The solution to this goal program could be equivalent to a linear program that optimises the optimistically set goal area. Romero also states that equivalency between GP and LP has led to some researchers believing that GP is not a useful tool when in fact its flexibility of utilising multiple objectives makes it highly useful. The fact that in certain cases the two may be equivalent is not a detriment to the field of GP. In an article  Ignizio (1989) refutes previous claims that integer GP (IGP) was a questionable methodology as the computer programs can be used to formulate the integer GP model, particularly to the handling of the negative and positive deviation variables.

LP and GP formulations are not acceptable for several computational and structural reasons ( Shaffer and Fricker,  1987). The computational reasons are no longer valid given the speed of computer processors and the widespread availability of optimisation software. To avoid the scaling problems, a normalising or scale method should be applied to the goals within the model formulation ( Romero, 1991).

Another issue with respect to goal levels is that the numeric value of the deviation variables does not correspond to the actual geometric distance causing a possible bias in the problem solution.  Hannan (1985) states ‘‘to make the scales between goals equal then the deviations of equal geometric distances must yield equal numerical values’’. In order to obtain a true correspondence between the numeric values and the geometric differences the goals must be adjusted using Euclidean normalisation techniques ( Young, 2002).

 Niemeier et al. (1995) constructed five optimisation models for selecting an optimal subset of transportation projects submitted for a statewide programming process. The five models include the following: a priority index that provides a ranking of projects but does not directly facilitate trade-offs between project costs and the rank (model 1); a model that incorporates a formal approach to making trade-offs between rank and cost (model 2); a model that explicitly includes a strict budget constraint in addition to each objective (model 3); a model that includes a strict budget constraint in addition to requiring that funded projects equal or exceed a fixed goal for each policy objective (model 4); and finally, a model that combines the relative rankings and a budgetary constraint (model 5). Even though the authors constructed five different models, the authors do not provide a definite answer to which model is best.

An investment-planning model was developed ( Petersen  and Taylor, 2001) for a new North-Central railway in Brazil. The authors say that the shippers route their traffic

over the network to minimise their costs, and the railway investor selects the sequence and timing of new links (if any) that maximise the present value of benefits to the investor. A doctoral thesis ( Young, 2002) applied the GP techniques in the multi-modal investment choice analysis project. Optimisation models results showed that the projects selected under NPV criteria at a particular financial availability level for capital investment are a special case of optimisation results ( Anandarajah and  Ahern, 2004).  Teng and Tzeng (1998) conclude in their research that under a complex social infrastructure and international environment, criterion for one single objec-tive (promotion of economic development for instance) is no longer valid. Thus, the decision obviously belongs to the dominion of multiple objective decision makings.

A social cost benefit basis is a comprehensive evaluation of a rail option, where all relevant impacts are taken into account using social benefits and cost rather than the private benefits and costs (Cole, 1998). Two situations where public funding is involved in rail are major rail infrastructure projects and loss-making rail services. The first refers to public funding for investment projects while the second one is concerned with funding support to the operation of rail services. In both situations a private perspective could imply the ‘do-nothing’ option is selected. However, if significant social benefits exist then these could justify public funding; for example, the evaluation of the social costs and benefits from rail services which are profit making and where enhancement has external benefits, e.g., congestion or reducing pollution.

1.2.  Multi-criteria analysis

Multi-criteria analysis (MCA) provides the framework and tools to estimate the opportunity costs of interest here, i.e. values imputed to selected qualitative or political objectives in terms of forgone investment ( Beuthe et al.,  2000). The multicriteria arena offers various methods for eliciting a decision maker’s preferences among projects based on the relative importance given to the various criteria. In doing so, it builds an index of preference or utility via a weighted aggregation of several criteria.  ODPM (2003) states, in the MCA manual, that:

the main role of the techniques is to deal with the difficulties that human decision-makers have been shown to have in handling large amounts of complex information in a consistent way.

Further, MCA techniques can be used to identify a single most preferred option, to rank options, to short-list a limited number of options for subsequent detailed apprai-sal, or simply to distinguish acceptable from unacceptable possibilities.  Young (1997) states that optimisation techni-ques may be considered as a subset of MCA and would represent the high end of the technical spectrum for this analysis technique.

The goal achievement matrix (GAM) is now generally accepted as a suitable process for evaluating the benefits and costs of alternative plans. The GAM process is a useful tool for the consideration of issues whose benefits and costs are not able to be quantified in dollar values and are therefore unable to be included in a conventional benefit-cost analysis. The Esk Main Road Strategy Study (GHD, 1998) used the GAM analysis to consider road project priorities. The Department of Transport, Ireland ( DOT,  2003) used the GAM technique to evaluate the qualitative goals of the identified railway projects for investment.

This study develops a weighted integer goal-program-ming (WIGP) model to prioritise the identified projects for investment while maximizing the objectives and meeting the budget limit for capital investment. To avoid a biased result in the model solution due to the differences in measurement units and in scale of magnitude between the attributes; the goal constraints in this paper are normalised using Euclidean normalising techniques. The new railway projects, which are identified and analysed by Department of Transport (DOT), Ireland, are used for the case study. This paper prioritises the railway projects for investment and analyses the combination of projects for investment. The study further recommends the investment options at different capital investment level when the decision is made on the basis of economic benefits, revenue or qualitative goal scores. This paper is organised into six sections: Section 2 states the problem, Section 3 presents the model development, Section 4 provides the data source, Section 5 discusses the optimisation model results and Section 6 provides the conclusion and recommendations.

2.  GP model formulation issues

Typical model formulations for capital budgeting problems include a zero–one integer model and a continuous linear model. The integer model does not allow for partial funding of projects, while the continuous model does. Allowing for the partial funding of projects ensures that the entire budget amount is utilised since the final project selected will be funded until the budget constraint is met. In addition to fully utilising the budget, the continuous formulation has the added advantage of notably faster computing times due to the reduced complexity of the solution algorithm. This becomes more important as the number of projects being considered increases. Since the number of projects considered in this research study is less and partial funding is not possible, integer GP is used for the model formulation.

The terminology used in GP varies widely in the literature.  Ignizio (1985), more precisely defined the terminology associated with GP.

Structural variables: The structural variables are those problem variables over which one can exercise some control. Consequently, they are also known as control or decision variables.

Objective: An objective is a function that we seek to optimise via changes in the structural variables. The two most common forms of objectives are ‘‘maximise’’ or ‘‘minimise’’ their respective values.

Goal: The goal functions appear as objective functions in conjunction with the right-hand side. This right-hand side is the ‘‘target value’’ or ‘‘aspiration level’’ associated with the goal.

The GP model formulation terminology used in this study is defined below. As the terminology varies greatly in the literature any other common names will be listed in parentheses after each item along with the mathematical term used in the formulae.

Decision variables–(Xi, unknowns, solution variables, structural variables). A set of unknowns, which the problem determines.
Technical coefficients–(bij or dij, project attributes). Values that describe the contribution of each project with respect to the particular goal area.

Goal levels–(Bj, or Dj right-hand side values, target value, aspiration level). Values that the decision-maker seeks to achieve. The goal levels can also be set using arbitrary values. In order to ensure that this is not the case a sensitivity analysis of the goal level should be performed ( Schniederjans, 1995). Another way to address this issue is to set impossibly high target values. In this modelling, each goal level is set to the maximum value (sum of the project values).

Deviation variables–(dBj or dCk). Values that allow for negative and positive differences between the achieved and aspired goal levels. Deviation variables are the crucial difference between LP and GP.

3.  Problem statement

The core business of Irish Rail is passenger transport. At present, the rail service is slow and investment is required to improve the quality, reliability and safety of the railway system to attract many more passengers to use the railway services. Since rail may be more sensitive than bus to service change ( TRL, 2004), this would make people choose rail for their travel instead of car/bus for long journeys. The purpose of most of the Government’s investment in renewal and expansion of the rail services is to improve passenger transport. The DOT identified and estimated respective cost and benefits for several possible railway routes/projects for investment all over Ireland under two categories; one is the investment in existing routes to improve the rail services and the other is developing new schemes. This paper discusses only the new schemes.  Table 1 presents the identified new railway projects and the values are annual averages.

There are ten projects identified for investment under the new scheme, having a total cost of about Euro two billion for capital investment over a 20 year period between 2003 and 2022. The estimated benefits are both quantitative and qualitative. There are three quantitative and four qualitative

Table 1								
Identified projects and respective costs and benefitsa							
							
Scheme	Capital cost	Annual economic benefits	Annual revenue	Qualitative benefits			
								
				QG1	QG2	QG3	QG4	
								
Cork suburban	123.6	21.4	6.3	3	4	3	4	
Limerick jutn.–Rossalare (LDMU)	33.4	12.1	4.1	3	3	2	3	
Limerick–shannon–ennis	116.8	12.1	3.5	1	3	2	1	
Limerick–ballybrophy (LDMU)	28.9	10.4	3.5	2	3	2	2	
Galway to cork (via Limerick)	289.8	34.4	12.2	2	3	2	2	
Navan–drogheda	109.8	11.2	3.4	2	1	2	1	
Athlone–mullingar	154.2	4.9	1.8	1	3	2	0	
Derry–letterkenny	150.6	3.6	1.2	1	3	1	2	
Western corridor–sligo to cork	571.7	73.1	13.4	1	3	2	1	
Connolly st.–navan (direct)	407.5	14.4	4.3	1	2	1	1	
Total	1986	198	54	17	28	20	17	
								
Source:  DOT, 2003.								
aCost, economic benefits and revenue are in million Euros.						
Table 2								
Attributes considered in the MCA analysis							
								
Goals	Criteria							

(1) To explore the particular strength of rail to provide a high quality public transport and/or haulage services

(2)	To support land use social and economic policy at national, regional and local level 

(3)	To improve environmental quality and health 

(4)	To promote sound project selection 

By operating within or between major population centres

By operating on routes with a competitive advantage over car

By modernising rolling stock, stations and other infrastructure to comfortable accessible standards By overcoming the backlog of asset renewals

By implementing a maintenance regime

By line speed improvements, increased line capacity, increased frequency and/or regular time tabling By providing long term (20 year) public transport/overall transportation capacity

By integrating in complementary fashion with rail services and other modes

By ensuring compliance with National Spatial Strategy, or other guidance on balanced regional development and sustainability

By improving rail services in areas identified for development under socio-economic initiatives By ensuring compatibility with relevant local and regional land use plans

By locating stations, and station access, within existing or proposed development to maximise catchments and minimise access times

By promoting partnership and co-operation in order to maximise benefits and efficiencies

By identifying if scheme impinges on area of known environmental sensitivity or with existing environmental problem

By reducing the air and noise pollution impacts of transport By enhancing the built and natural environment

By reducing the number of road accidents

By ensuring fundamental constraints are not breached (i. relevant scoping and feasibility studies, ii. safety, accessibility and other standards met, and iii. on-going and documented formal consultation with public and statutory bodies).

Source:  DOT, 2003.

attributes to be considered in the prioritisation process. The quantitative attributes include user benefits, safety and accident benefits, environmental benefits, car resource cost savings and estimated annual revenue due to the projects. Total economic benefit is here defined as the summation of user benefits, safety and accident benefits, environmental benefits and car resource cost savings. The costs benefits analyses were conducted based on the discount rate of 5%

( DOT, 2003). The DOT included a number of capital cost components when estimating the capital investment cost of the projects such as land costs, equipment costs, construc-tion costs, rolling stocks costs, decommissioning costs, dislocation cost, etc. Land costs include acquisition, demolition, clearance and site preparation. The values were based on the market price or opportunity costs. In quantifying the operating costs; labour costs, maintenance

costs, energy/fuel consumable costs, and utility services costs are considered. A range of user costs were considered; generalised cost values and penalties (waiting time penalties, travel time penalties, interchange penalties, access and egress costs and fare), modal shift penalties and accident costs.

The DOT used MCA techniques to analyse the qualitative attributes. The form of MCA technique adopted was known as the GAM method. The primary focuses of the GAM method was on selected socio-economic objectives as opposed to the effects on commu-nity groups.  Table 2 presents the qualitative attributes and the respective criteria. In the MCA analysis, scores are given to the projects from 0 to 4; 0 ¼ no/negative effect, 1 ¼ remotely meets, 2 ¼ partially meets, 3 ¼ substantially meets, 4 ¼ best/fully meets. The MCA analysis scores are presented in  Table 1. In this research study, the authors formulate a GP model to prioritise the identified railway projects for investment.

4.  Model development

This is a WIGP model with strictly zero or one variable being developed to apply for prioritising identified intercity railway projects for investment in Ireland. The objective of the model is to minimise the goal deviation variables. Only the negative deviations are considered in the objective function, as shown in Eq. (1). The GP formulation has been written using the LINGO software.  Fig. 1 presents the flowchart of the methodology.

Variables

Xi The decision variable, which is used for the selection of the projects, i.e., it is one when the project i is selected and zero when the projected i is not selected

d₃Bj negative deviation variable of the goal j dþBj positive deviation variable of the goal j

	Qualitative					
	Attributes					
								
				Identified		Weights		
								
Multi-Criteria			Projects				

Analysis					
Quantitative

Attributes
GP MODEL	
Analysed	Related	
Externally	Costs	
Optimal Project	
	Mix	
Total Costs	Total Benefits	

Fig. 1.  Flowchart of the methodology.

Parameters

bij numerical outcome of the ith project with respect to the jth attribute (this represents the value of the attributes j for the project i).
Bj	jth attribute considered in the decision

C total finance available for capital investment ci capital cost of the project i

dij Euclidean normalised numerical outcome of the ith project with respect to the jth attribute

Dj target for the jth attribute considered in the decision

m	number of goal attributes considered 

n	number of projects considered 
WBj	user assigned weight for the attribute j

Model

The objective of the model is to minimise weighted negative goal deviations. The minimization of deviations implies that all the objectives are minimised simulta-neously.

	m			
Objective :	Min Xj¼1	W Bj dBj₃,	(1)	
W Bj is the user-assigned weight to the attributes, in order to take into account of the importance of the attributes in
project selection. The sum of user assigned weights to the
₃ P ₃ attributes is equal to one j W Bj ¼ 1 .
Subject to the following constraints:

The model includes five quantitative and four qualitative attributes for soft constraint in addition to rigid budget constraint.

(1)	Rigid budget constraint: the total capital investment cost of the selected projects should be below the financial availability for capital investment. The goal-programming model is run at different budget level for 

capital investment; starting from h 100 million, it goes up to h 2000 million with steps of h 100 million.

n	ciX ipC.			
Xi¼1		(2)		
(2) Soft constraints for different goals: There are five quantitative and four qualitative attributes to be considered in this soft constraint.

n						
Xi¼1	bij X i  þ dB₃j	₃ dBþj	¼ Bj	8j ,	(3)	
Eq. (3) shall be improved for the following reason: The differences in measurement units and in scale of magnitude between the attributes leads to a biased result in the model solution; the goal constraints are normalised using Euclidean normalising techniques to offset the units and the magnitude differences.

Revenue and user benefits are in million euros and qualitative goals are in numbers. To overcome the
(8) problem with scale and units, the values are normalised using Euclidean normalising techniques. The first step in

The matrix form of goal attributes B can be presented as in Eq. (4). There are m projects and n attributes, which make up the following matrix:

2 b11       b12:::::           bij :::::           b1n  3

(3)	Nonnegative constraint. The goal deviation variables should be positive. 

₃	þ	X	0		.	(9)		
dBj	; dBj			8j				

		6 b:21	b22::::::	b2j::::::	b:2n  7	
		6	:	:	:	:	7	
		6					7	
B		6					7	
	¼	6	bi1	bi2:::::	bij :::::	bin	7	
		6					7	
		6	:	:	:	:	7	
		6					7	
		6					7	
		6	:	:	:	:	7	
		6					7	
		6	bm1	bm2:::::	bmj :::::	bmn	7	
		6					7	
		4					5	

(4)	Bounding decision variable. The physical interpretation of Xi is such that a 0–1 integer solution indicates whether a project is not-funded or funded (called as 

(4)	binary variable) 

	0pX ip1    8i.	(10)	
5.	Illustrative example		

Using Euclidean normalising technique, an element of the Euclidean normalised decision matrix dij can be calculated as in Eq. (5), ( Hwang and Yoon, 1981;

 Niemeier et al., 1995).
,s
Xm
dij  ¼ bij	b2ij .				(5)	
				i¼1					
	The  matrix  form  of  the  Euclidean  normalised  goal	
attributes D is presented in Eq. (6).		
		2	dd2111	dd2212::::::::::	dd2ijj::::::::::	dd21nn	3		
		6	:	:	:	:	7		
		6	:	:	:	:	7		
		6					7		
D		6					7.	(6)	
	¼	6	di1	di2:::::	dij :::::	din	7		
		6					7		
		6	:	:	:	:	7		
		6					7		
		6					7		
		6	:	:	:	:	7		
		6					7		
		6	dm1	dm2:::::	dmj :::::	dmn	7		
		6					7		
		4					5		

From Eqs. (3) and (5), the Euclidean normalised form of the soft constraint can be presented as shown in Eq. (7).
Xm
₃	þ			.	(7)	
dij X i  þ dBj	₃ dBj	¼ Dj	8j			
i¼1

The goal level Dj for each attribute is set as in Eq. (8).

That is to have maximum values.

m			
Dj  ¼ Xi¼1	dij	8j .	
Table 3

To illustrate this GP approach steps, let us consider the following example with four projects and four attributes (objectives) as presented in  Table 3. Weights for the attributes are: Revenue ¼ 0.249, User benefits ¼ 0.287, Qualitative goal 1 ¼ 0.256, qualitative goal 2 ¼ 0.208.

The objective function for the problem according to Eq. (1) is presented in Eq. (11).
Obj	Min	0 249	₃	0 287	₃	0 256	₃	0 208	₃ .	
		:	dB1	þ  :	dB2	þ  :	dB3	þ  :	dB4	
									(11)	

The hard constraint for capital cost according to Eq. (2) is presented in Eq. (11). Finance available for capital investment is assumed to be 200 million Euro.

123:64X 1 þ 33:44X 2 þ 109:87X 3 þ 28:94X 4p200	(12)

Soft constraints for the four attributes according to Eq. (3) are presented in Eq. (12).

Revenue															
6 29		4 06		3 38	3 50			þ		₃		17 22,		
:		X 1 þ  :		X 2 þ  :        X 3 þ  :	X 4 þ dB1	₃ dB1	¼		:			
Userbenefit															
8 34		3 68	4 13	3 14			þ		₃		19 28,	
	:		X 1 þ  :	X 2 þ  :	X 3 þ  :		X 4 þ dB2	₃ dB2	¼		:		
Qualitative	goal1													
3			3		2	2	þ		₃		10,							
	X 1 þ  X 2 þ  X 3 þ  X 4 þ dB3	₃ dB3	¼								
Qualitative	goal2													
4			3		1	3	þ		₃		11,					13		
	X 1 þ  X 2 þ  X 3 þ  X 4 þ dB4	₃ dB4	¼					ð		Þ	

Estimated values for the projects (million Euro)

Projects	Revenue	User benefits	Qualitative goal 1	Qualitative goal 2	Capital cost	
			(numbers)	(numbers)		
						
P1	6.29	8.34	3	4	123.64	
P2	4.06	3.68	3	3	33.44	
P3	3.38	4.13	2	1	109.87	
P4	3.50	3.14	2	3	28.94	

	

normalisation is dividing each coefficient by the square root of the sum of the squares of each coefficient as explained in Eq. (5).

Revenue												
6:29	4:06		3:38							
p793:65:50X 1Xþ p79dþ:65 Xd2₃þ p7917:65:22X,3							
Userbenefitþp79:65    4 þ   B1  ₃   B1   ¼ p79:65							
8:34		3:68		4:13							
p1093::9914X 1Xþ p109dþ:99	dX₃2 þ p10919:28:99	X,	3					
Qualitativeþp109:99goal14þ   B2  ₃   B2   ¼ p109:99							
3	3	2		2		þ	₃	10	,			
Qualitativep26X1þ pgoal226X 2 þ p26	X 3 þ p26	X 4 þ dB3	₃ dB3	¼ p26				
4	3	1		3		þ	₃	10  .			
p35 X 1 þ p35 X 2 þ p35	X 3 þ p35	X 4 þ dB4	₃ dB4	¼ p35	ð14Þ	
This reduces to											
Revenue												
0:705X 1 þ 0:455X 2 þ 0:378X 3								
0 392	þ	₃		1 930,							
þ  :	X 4 þ dB1	₃ dB1	¼  :								
Userbenefit											
0:795X 1 þ 0:350X 2 þ 0:394X 3								
0 299	þ	₃		1 839,							
þ  :	X 4 þ dB2	₃ dB2	¼  :								
Qualitative    goal1											
0:588X 1 þ 0:588X 2 þ 0:392X 3								
0 392	þ	₃		1 961,							
þ  :	X 4 þ dB3	₃ dB3	¼  :								
Qualitative    goal2											
0:767X 1 þ 0:507X 2 þ 0:169X 3								
0 507	þ	₃		1 859.					15		
þ  :	X 4 þ dB4	₃ dB4	¼  :					ð		Þ	
X1, X2, X3, X4, are integer variables.

By solving Eqs. (10), (11) and (14), the projects selected for investment are P1, P2 and P4. The capital investment necessary for the selected projects is 186 million euros. Total Benefits due to the project selected and the objective values are presented in  Fig. 2. Revenue and user benefits are in million euros and the qualitative goals are in numbers.

6.  Data source

As the model uses the new railway projects identified by DOT, the data related to capital costs, user benefits, safety and accident benefits, environmental benefits, annual revenue and qualitative analysis have been taken from the D OT publication, DOT (2003).

	120					
	100			Model Results		
				Objective values		
						
Benefits	80					
	60					
	40					
						
	20					
	0					
	Revenue	User benefits	QG1	QG2		
		Attribute				

Fig. 2.  Benefits due to the projects selected for investment.

Table 4

User assigned weight to the goal attributes

Attributes	Weight	
		
User benefit	0.131	
Safety and accident benefits	0.128	
Environmental benefits	0.111	
Car resource cost savings	0.105	
Revenue	0.095	
Qualitative goal 1	0.114	
Qualitative goal 2	0.117	
Qualitative goal 3	0.111	
Qualitative goal 4	0.088	

The degree of importance (weights to the attributes) of the factors/goals in prioritising railway project for invest-ment has been taken from  Anandarajah et al. (2004). The questionnaire was sent by email to transport professionals, academics and transport researchers. A hard copy of the questionnaire was distributed to postgraduate researchers in the transport field. A copy of the questionnaire also was sent to university transport study group (UTSG), an Internet discussion group based in United Kingdom, by email. The respondents to the questionnaire included transport professionals, including people from Irish Rail, academics and researchers in the transport field. Twenty seven people responded to the questionnaire.

The study estimated the degree of importance of the attributes through a questionnaire survey. The scale of 1–5 had been used to rate the importance such that 1 ¼ not important and 5 ¼ very important in the questionnaire. The results of the questionnaire were then analysed in spreadsheet form.  Table 4 presents the user assigned weights given to the model.

7.  Results and discussion

The WIGP model determines the optimal mix of projects for investment at different budget levels while maximising the goal attributes (selected project at different budget level is presented in Appendix A).  Fig. 3 shows the benefits of quantitative attributes; user benefits, safety and accident

benefits, environmental benefits, car resource cost savings and estimated annual revenue at different capital invest-ment levels. Figures with the data label show the total investment cost of the projects. As the model maximises the goal attributes, generally the benefits are expected to increase with increasing investment level. But in this, even though the benefits are increasing on average, according to the WIGP model results, the economic benefits (economic benefits includes user benefits, safety and accident benefits, environmental benefits and car resource cost savings ( DOT, 2003)) and the revenue are lower at one investment level each; the economic benefits decrease when the capital investment cost is increased from h 984 million to h 1007 million, and the revenue decreases when the capital investment cost is increased from h 857 million to h 984 million. This does not mean that the benefits are not maximised. As the objective of the model is to maximise the benefits, which included quantitative and qualitative, at

the investment level of h 1007 million, the benefits are maximised. But the contribution by the qualitative attributes is high, as shown in  Fig. 5, the share of economic benefits decreased from 40% to 30% when additional h 100 million is added to the budget.  Fig. 4 also shows the total benefits of the selected projects at different investment levels. Total benefit at different investment levels is the difference between the weighted sum of the goal targets (Dj) and objective value (weighted goal deviations) at the corresponding investment level.

 Fig. 5 presents the variation of qualitative goal scores of the optimal mix of projects at different investment levels. Unlike the quantitative attributes, economic benefits and revenue, the qualitative goals decrease with the increasing capital investment cost at several investment levels. There are two sharp decreases in goal scores with increasing capital investment costs at the investment level of h 984 million and h 1164 million. Even though the model

	100													
		User Benefits								1986		
									1579	1832			
		Safety and Accident Benefits					1425					
						1274						
												
	80	Environmental Benefits			1164							
		Car Resource Cost Savings										
€)		Revenue				984							

(million	60													
				703	853	1007							
													
Benefits														
	40			593										
			476										

			303											
	20		296											
		186												
		62												
	0													
	0		500			1000	1500		2000		
				Investment Cost (million €)							
			Fig. 3.  Benefits at different investment level (million h).					
	80%			Economic Benefits				3.0			
				Revenue									
													
		62		Total Qualitative GoalScores							
				Total benefits (weighted)				2.5			
		186	296303								

	60%		476	593  703	853	1007							
											2.0			
						984			1579	1832		benefits		
							1164 1274	1425			1986			
Share														
	40%										1.5			
												Total		
											1.0			
														
	20%													
											0.5			
	0%										0.0			
	0		500		1000		1500		2000			
				Investment Cost (million Euro)							

Fig. 4.  Share of attributes on total benefits.

	30						1986		
									
	25					1579	1832		
									
					1007	1425			
	20				853	1274			
Score					1164				
				703	984				
	15		593						
Goal									
		303	476						

	10	296							
		186							
		62				Qualitative Goal 1			
	5					Qualitative Goal 2			
									
						Qualitative Goal 3			
						Qualitative Goal 4			
	0								
	0		500		1000	1500	2000		
			Investment Cost (million Euro)				
		Fig. 5.	Qualitative goal scores at different investment level.			

Economic Benefits Capital Cost Ratio	

0.40						0.15			
	62				Economic Benefits Capital Cost Ratio			
									
					Revenue Capital Cost Ratio				
0.30	A						Ratio		
									
						0.10			
							Cost		
	186								
									
0.20	296303			B			Capital		
									
	476	593			1164				
			703	984			Revenue		
					1274   1425	0.05			
									
				853	1579	1832			
0.10				1007				
					1986			

				C					
0.00						0.00			
0	500			1000	1500	2000			
	Capital Investment Level (Million Euro)				

Fig. 6.  Economic benefit/cost and annual revenue/cost at different investment level.

		70					1986		
									
scores		60					1579		
							1832		
						1007			
		50					1425		
									
	ratio				853		1274		
goal									
									
		40		703		984	1164		
	cost								
qualitative				593					
									
				476					
	Capital		303						
		30	296						
		20	186						
									
Total									
			62						
		10							
		0							
0	500	1000	1500	2000	
		Capital Investment Level (Million Euro)			
Fig. 7.	Total qualitative goal scores/cost at different investment level.		

determines the optimal mix of projects at different investment levels while maximizing goal attributes, it is hard to make a decision as the qualitative attributes give relatively low scores at some investment levels, while the quantitative attributes give relatively high scores.

 Fig. 6 shows the calculated economic benefit cost ratio and revenue cost ratio for different investment levels. The economic benefit cost ratio at different investment levels is estimated by dividing the total economic benefits (sum of user benefits, safety and accident benefits, environmental benefits, and car resource cost savings) by the total capital investment cost. Similarly, revenue cost ratio is calculated by dividing the revenue by capital investment cost. As can be seen in the  Fig.  6, the optimal mix of projects in zone A would be the first best area for investment if the decision is taken solely based on economic benefits provided that the financial availability for capital investment is flexible. Zone B is the second best area for investment. In spite of the fact that option C (at the investment level of h 1007 million) has a lower capital investment cost than that of the few sets of projects in zone B, it is not in the second best area for investment, since its economic benefit cost ratio is relatively low. Option C would not be the worst one if the investment decision was made mainly based on the revenue, as the revenue cost ratio is not lower than that of some of the options in zone B.

Since the qualitative scores for option C are relatively high (shown in  Fig. 5), it is one of the best solutions when decisions are made considering qualitative goals especially qualitative goal 2; supporting land use, social and economic policy at national, regional and local level. At option C, the total score of each and every qualitative attribute meets more than 80% of the goal levels or target with a capital investment cost of h 1007 million. It is about half of the total capital investment cost of all the projects identified by DOT. Further, total qualitative goal scores/cost are also relatively high ( Fig. 7). Therefore, if the investment decision is made solely based on qualitative goal scores, then the recom-mended investment area would be option C.

8.	Conclusions and recommendations 

A	WIGP model is developed to prioritise the railway projects for investment with the objective of maximising the benefits including qualitative attributes. The optimal set of projects has been identified under different financial availability for capital investment. Even though the objective is maximising all the attributes, in this approach, the investment decision depends upon decision makers’ considerations and whether it is mainly based on the economic benefits, revenue or qualitative goal scores. Further, the decision is subject to financial availability for capital investment. 

When a decision is made mainly on the basis of economic benefits (quantifiable factors), then zone A is recommended as the first best solution and zone B is recommended as second best solution. In the case of considering revenue, option C also would be considered as one of the second best solutions alongside zone B. Furthermore, if the decision was made mainly based on the qualitative scores, then the investment should go to the level of h 1007 million (option C), which obtains very high scores (more than 80% of the goal level) for qualitative attributes with half of the capital investment cost to achieve 100% goal levels.

Acknowledgements

This is a part of Ph.D. research carried out with the scholarship provided by Higher Education Authority, Ireland.

Appendix A

 Table A.1.

Table A.1

Project selected at different budget level

Scheme	Budget level for capital investment (million h)									
																	
	100	200	300	400	500	600	800	900	1000	1100	1200	1300	1500	1600	1900	2000	
																	
Cork Suburban		O	O	O	O	O	O	O	O	O	O	O	O	O	O	O	
Limerick jutn.–Rossalare (light DMU)	O	O	O	O	O	O	O	O	O	O	O	O	O	O	O	O	
Limerick–Shannon–Ennis				O		O	O	O	O	O	O	O	O	O	O	O	
Limerick–Ballybrophy (light DMU)	O	O	O	O	O	O	O	O	O	O	O	O	O	O	O	O	
Galway to Cork (via Limerick)					O	O	O	O		O	O	O	O	O	O	O	
Navan–Drogheda			O				O	O		O		O	O	O	O	O	
Athlone–Mullingar								O		O			O	O	O	O	
Derry-Letterkenny										O				O		O	
Western Corridor–Sligo to Cork									O		O	O	O	O	O	O	
Connolly st.–Navan (direct)															O	O	
Number of projects selected	2	3	4	4	4	5	6	7	6	8	6	7	8	9	9	10	

	

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