Stochastic Scheduled Service Network Design: The Value of Deterministic Solutions

We study the value and quality of deterministic solutions to scheduled stochastic capacitated multi-commodity service network design problems. We study both the fixed and variable (integer and continuous) capacity cases, and investigate models with and without asset-balance constraints. For the deterministic cases, we replace the random variables in the stochastic model with the 50 th and the 75 th percentiles from the demand distributions, confirming the better quality of solutions from the latter case in all situations. We also investigate what makes the optimal stochastic solution better in the stochastic environment than other feasible solutions, particularly those obtained by addressing the deterministic versions of the problem. We do this by quantitatively analyzing the structures of different solutions. A measurement scheme is proposed to evaluate the level of potentially beneficial structural properties (multi-path usage and path-sharing) in different solutions. We show that these structural properties are important and correlated with the performance of a solution in the stochastic environment.