Optimize train capacity allocation for the high-speed railway mixed transportation of passenger and freight

• We study the train capacity allocation problem for mixed transportation in high-speed rail systems. • Develop two optimization models with deterministic and stochastic demand to improve total revenue and expected revenue, respectively. • Propose approximate linearization techniques to solve the probabilistic non-linear programming model. • Provide numerical experiments with different scales to illustrate the proposed approach. The collaborative transportation strategy of passengers and freights can improve the efficiency and revenue of the high-speed railway (HSR) system. This paper focuses on the train capacity allocation problem for the mixed transportation pattern of passenger and freight in HSR systems, in which rail operators introduce revenue management to determine the optimal train capacity allocation plan for each train service. We first propose a general train capacity allocation model which addresses passenger priority and freight loading/unloading capacity, and then the deterministic and stochastic demand scenarios are considered respectively. With the deterministic demand, the train capacity allocation model is linear programming with the objective of maximizing the revenue of the HSR system. While a non-linear programming model is built for the stochastic demand to maximize the expected revenue. For solving the problem with stochastic demand, the non-linear programming model is transformed into a mixed integer linear programming model, which can be easily solved by the existing solver to obtain the optimal solution. Two different-sized numerical experiments are conducted to demonstrate the efficiency and effectiveness of the proposed methods.