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.