Railway projects prioritisation for investment: Application of goal programming

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.

Introduction

Optimisation models are constructed for decision-making 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 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 simultaneously 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 objective (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.

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 appraisal, or simply to distinguish acceptable from unacceptable possibilities. Young (1997) states that optimisation techniques 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-programming (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.