Capacitated hub location routing problem with time windows and stochastic demands for the design of intra-city express systems

This work focuses on planning an intra-city express system in a practical environment. Various operation characteristics, such as vehicle capacity, hub capacity, time windows, and stochastic demands, have been considered. Therefore, we introduce a capacitated hub location routing problem with time windows and stochastic demand and formulate it using a multi-stage recourse model. In this model, long-term decisions (hub location and client-to-hub allocation) are made first, and short-term decisions (vehicle routing) are determined after revealing stochastic variables. To solve the problem, we propose a hybrid stochastic variable neighbourhood search (HSVNS) algorithm, which integrates an adaptive large neighbourhood search (ALNS) algorithm within a stochastic variable neighbourhood search (SVNS) framework. Numerical experiments and case studies indicate that the HSVNS algorithm can provide high-quality solutions within a reasonable computation time for instances with up to 70 clients and that considering stochastic factors can efficiently reduce operation costs, especially for instances with tight vehicle capacity and loose time windows.