How to optimize train lines for diverse passenger demands: A line planning approach providing matched train services for each O-D market

Line planning decides critical service contents of a passenger railway schedule. In real-world scenarios, passengers’ travel expectations or preferences on service qualities tend to be heterogeneous among different origin–destination (O-D) pairs or even in the same O-D pair, which requires railway operators to schedule train services catering to those diverse passenger demands. However, previous line planning approaches either treated passengers homogeneously or roughly divided simple passenger groups by travel purposes or service types. In this paper, we view each passenger O-D pair as an individual O-D market and propose a line planning approach where concluded train lines can deliver matched service levels of trains for each O-D market. Based on the Set Covering Problem (SCP), we establish a novel bi-objective mixed integer linear programming (MILP) model that considers the benefits of both railway operators and passengers. Multiple service qualities for each passenger O-D pair, such as travel speed, direct or transfer connection, frequency, price, etc. are seen as the objects to be “covered” by train lines, to achieve a more accurate supply–demand match. Facing the potential conflicts between diverse passenger demands and limited railway supply, we formulate a series of non-rigid constraints (NRC) to achieve a non-rigid supply–demand match i.e., each O-D pair’s demands can be either guaranteed to be satisfied or satisfied as much as possible. In this manner, railway operators can testify different marketing policies and make marketing decisions regarding which O-D markets should improve, maintain, or degrade services. A heuristic rule-based adaptive iterative searching approach (ISA) is designed to solve large-scale model structures. We take the Beijing-Shanghai high-speed railway (HSR) line as the case study background. We comparatively evaluate the operation and service performances of multiple cyclic line plan scenarios, discuss the performance difference, and state our policy implication. We also recalibrate the service levels of the real-world non-cyclic line plan. The experiment results show that our proposed approach can efficiently help design the line plans based on customized marketing policies and improve the service levels of the real-world line plan.