Zhai Shuo
Urban rail transit is a crucial part of the city's transportation system. Especially during the city's morning and evening peak hours, the surge in passenger numbers puts significant pressure on the operation of the rail system. For operators, designing a reasonable train timetable is an effective way to reduce operating costs while improving service quality.The optimization of train timetables is a classic issue in the field of urban rail transportation. Typically, this problem is addressed using linear or nonlinear programming techniques. Due to the diversity of objectives and the complexity of constraints, professional computing software is often required to complete the optimization quickly. Among many mathematical programming software options, Gurobi is favored for solving large-scale mathematical planning problems due to its simple user interface, fast computational capabilities, detailed documentation support, and a free policy for the academic community. In this study, Gurobi was chosen as the main programming tool to build a mathematical model based on detailed data provided and to complete the optimization using its Python interface, successfully solving the following two issues.First, with the assurance of meeting passenger demand, the objective is to minimize the company's operational costs and maximize service levels, leading to the formulation of a train operation plan. This specifically includes determining the number of trains for the main operational segments and the operating intervals and number of trains for the secondary segments.Train operations employ a 1:n or n:1 loop mode, with the goal of minimizing the company's operational costs (including the number of trains and the mileage) and the passengers' waiting costs (including time on the train and waiting time), converting these costs into economic costs. To achieve this, a weighted objective planning model was established, with a 0.7 weight assigned to the company's operating costs and a 0.3 weight to passengers' waiting time. This model was developed and optimized using Gurobi.To further reduce operational costs and enhance service levels, we conducted sensitivity analysis based on changes in external conditions, proposing methods to improve train operation schemes and schedules.
Rail operations; Mathematical optimization; Goal programming; Nonlinear programming