## 3 Methodology
### Model Basis and Assumption  
This section will construct an optimization model for a non-splittable high-speed rail express transportation scheme, taking into account the loss of passenger transport capacity. The model is based on the scheduled passenger trains and considers the selection of transport modes for each train and the potential operation of dedicated freight trains. The objective is to maximize operational revenue, minimize operational costs, and minimize the loss of passenger transport capacity. This coordinated optimization integer programming model will determine the transport mode for each train and the transportation scheme for high-speed rail express goods, facilitating model construction and solution. In this paper, transport modes are defined as the confirmation train mode, passenger train piggyback mode, reserved mode, and dedicated train mode (see Figure 2):  
1. The high-speed rail confirmation train mode involves Electric Multiple Units (EMUs) used by railway departments to check line safety. In express transportation, it is used for point-to-point cargo transport without carrying passengers, utilizing idle capacity with low investment costs. However, this mode faces limitations such as a limited number of operations, insufficient automation equipment, restricted cargo space, and one-directional transport, limiting its market potential. From January 2024, the pilot work of mass transport of confirmed trains on the high-speed railway between Zhengzhou and Chongqing has been officially launched, and two confirmed trains on the high-speed railway will be arranged to run bidirectional from Zhengzhou Airport Station and Chongqing North Station each day, effectively improving the transport efficiency between Zhengzhou and Chongqing. 2. Passenger train piggyback mode utilizes the remaining space in passenger trains for express items, offering low cost, high frequency, and flexible timing, making it suitable for urgent small batch cargo. However, it faces insufficient loading schedules and limited volume and is affected by passenger peak times, which restricts its development potential. 3. The reserved mode designates specific carriages in passenger EMUs for express delivery, reducing interference with passenger transport and accommodating larger volumes. However, it reduces passenger transport capacity and is suitable for transitional periods with increased express volume, constrained by passenger transport needs. 4. The dedicated train mode is ideal for the mature stage of high-speed rail freight transport, offering high reliability, large carrying capacity, and precise timing, providing high-quality service. However, it requires significant investment, long-term cargo sources, and station modifications, making it suitable for direct transport between stations with large cargo volumes where it can demonstrate significant advantages. The cargo capacity and its impact on passenger transport capacity vary under different transport modes, as do the associated costs. Therefore, the selection of transport modes must consider the passenger capacity already occupied by the train and develop train travel modes that meet high-speed rail express transportation needs. This includes determining  
Figure 2: Schematic diagram of high-speed rail express transportation mode. the transport modes selected by each train and the number of dedicated high-speed rail express freight trains to be operated. The core of the high-speed rail express transportation scheme involves considering the costs and benefits and efficiently allocating express cargo flows to appropriate loading and unloading stations, transfer stations, and high-speed rail schedules. Essentially, it focuses on selecting transport paths for different OD express cargo flows. The optimization problem discussed in this paper involves several key operational processes: loading operations, high-speed rail transportation, transfer storage, and unloading operations.