Online-to-offline on the railway: Optimization of on-demand meal ordering on high-speed railway*

On-demand meal ordering on high-speed railway is an emerging on-demand service that is becoming increasingly popular. One key challenge about this service is how to design the ordering system to maximize profits while guaranteeing timely delivery. However, few related studies have been done for this new business. In this paper, we first develop a mathematical model to optimize the existing ordering procedure, which sets a deadline for order placement. Furthermore, we propose a pre-ordering policy which cancels the order deadline but ensures timely delivery via stocking up. Considering the ambiguity in demand distributions and uncertainty in delivery time, we develop distributionally robust stochastic optimization models for both the existing and the pre-ordering procedures. Cutting-plane algorithms are developed to solve the proposed models. Computational studies on a real-world high-speed railway line in China show that our proposed new policy could simultaneously increase service availability, improve the profit, and reduce delay rate.