Keywords: fuzzy sets theory, present worth, future worth, benefit-cost ratio, plausible range.

In the current turbulent economic climate, economic analysis emerges to be one of the most dominant contributors to a well established business case for rail infrastructure projects worldwide. This paper questions whether the key reason behind such dominance relates to the option selection stage as a systemic process, which heavily relies on estimating defined economic measures, and assists organisations in selecting the best cost-effectively option. The economic analysis to these measures usually depends on previous studies, future estimations and expert opinions. As a result, various levels of errors and uncertainties are inherited in this analysis. Hence these errors and uncertainties are the result of a combination of randomness and fuzziness, the preferred option is always questioned and doubted [1].

This paper, therefore, interrogates the effectiveness of the traditional methods in testing the robustness of selected options against changes in estimated capital expenditure and returns for rail infrastructure projects. It, therefore, proposes the use of a new mathematical model to support decision makers in selecting the preferred option for their projects.

The model suggests the use of fuzzy set theory to deliver a sound economic analysis for rail infrastructure projects. By transforming project cost expenditure and returns into triangular fuzzy numbers, the non-linear project present and future worth and the benefit-cost ratio to all proposed options is estimated and evaluated. A plausible range is then generated for each option, where the robustness of the preferred option is tested against all other options to inform the decision makers; as demonstrated in the numerical applications in this paper.

The novelty of this research is in the way it overcomes the problem of subjectivity in the decisions made; as the proposed model offers a robust method for quantifying uncertainties without bias by using the plausible range. It also establishes a firm basis to facilitate the drawing of evidence-based conclusions to inform stakeholders and decision makers.

This work is in concurrence with research conducted by Network Rail [2], which highlighted that 'Option Selection Report' must conclude with the justification for the preferred option, supported by relevant and sufficient backup material, through critical evaluation during the optioneering stage process. Industrial practitioners are urgently in need of such a basis for making informed judgements; without this a direct economic cost basis provides the fallback for decision making, and neither society nor the planet can really afford for this to continue.

1

M. ElCheikh, "Risk Quantitative Analysis Using Fuzzy Sets Theory", PhD Thesis, Birmingham University, UK, May 2009.

2

"Project Cost Management Services, Guidance on Estimated Final Cost, Guide to Railway Investment Projects", Network Rail, UK, 2(03), 2010.

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