Optimal capacity allocation for high-speed railway express delivery

This study investigates the potential of implementing express delivery services within specified time windows on the high-speed railway (HSR) and optimizes the train capacity allocation scheme for HSR express delivery (HSReD). We first propose an integer linear programming (ILP) model for the deterministic demand case to maximize the profit of the HSReD operation (revenue minus transportation cost, loading/unloading costs, and the penalty incurred due to schedule delays). Then, a two-stage stochastic programming model is developed to account for the stochastic demand case, with the objective of maximizing the expected profit. To facilitate the solution process, the two-stage stochastic programming model is transformed into an equivalent nonlinear model, which is further reformulated into an equivalent integer linear programming (EILP) model that can be solved by commercial solvers. Finally, the proposed method is applied on a small toy network, Nanjing-Hangzhou HSR network and Beijing-Shanghai HSR network to illustrate its efficacy.