Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations

•Sample-based time-variant link travel times are adopted to capture the correlations of dynamics and randomness in transportation networks.•We transform two-stage non-linear stochastic programming models into their linear forms for finding the most reliable paths with two reliability evaluation criteria.•A Lagrangian relaxation based algorithmic framework is provided to solve different models.•Numerical experiments demonstrate the efficiency and effectiveness of the proposed approaches.

Aiming to provide a generic modeling framework for finding reliable paths in dynamic and stochastic transportation networks, this paper addresses a class of two-stage routing models through reformulation of two commonly used travel time reliability measures, namely on-time arrival probability and percentile travel time, which are much more complex to model in comparison to expected utility criteria. A sample-based representation is adopted to allow time-dependent link travel time data to be spatially and temporally correlated. A number of novel reformulation methods are introduced to establish equivalent linear integer programming models that can be easily solved. A Lagrangian decomposition approach is further developed to dualize the non-anticipatory coupling constraints across different samples and then decompose the relaxed model into a series of computationally efficient time-dependent least cost path sub-problems. Numerical experiments are implemented to demonstrate the solution quality and computational performance of the proposed approaches.