Optimized two-directional phased development of a rail transit line

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, economics - subsidy, economics - fare revenue, ridership - demand, ridership - elasticity, planning, land use - planning, planning - methods


Rail transit, Optimization, Phased development, Demand elasticity, Investment planning


A model is developed for optimizing the phased development of a pre-designed rail transit line. The investment plan and extension phases of the line are optimized over continuous time and under budget constraints to maximize net present value (NPV) over a long analysis period. The budget constraints account for external subsidies and funding generated from fares. This model determines the maximal allowable train headway while considering the spatial distribution and elasticity of demand. The model is formulated for a two-directional extension problem. A genetic algorithm (GA) with customized operators is developed for optimizing the sequence and grouping of link and station completions. The model is demonstrated with a numerical case and the GA effectiveness is checked with a statistical test. The sensitivity of results to several important input parameters is analyzed. Results show that the potential demand and in-vehicle time value greatly influence the optimized NPV, while the unit construction cost and potential demand are most influential on the optimized extension plan. The effects of uncertainties in some parameters, including demand growth rates, are also analyzed.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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