Beijing’s metro system could soon carry express parcels alongside commuters during quiet periods, according to a new operational blueprint published in Engineering. Researchers from Beijing Jiaotong University and East China Jiaotong University have designed a joint optimization model that simultaneously plans train timetables, rolling-stock circulation, and cargo loading while allowing trains to skip stations with low demand. The approach, tested on the Yizhuang Line, cut operating costs by up to 25% compared with conventional fixed-composition, all-stop services.

The study addresses the rapid rise in urban freight volumes—already 15 million parcels a day in Beijing—by repurposing surplus metro capacity outside peak hours. Instead of building costly underground logistics tunnels, the team treats the existing passenger network as a shared infrastructure where freight containers ride in dedicated carriages that can be coupled or uncoupled at terminal depots. Five train configurations are available, ranging from all-passenger to all-freight formations, each with a known operating cost and capacity.

A mixed-integer nonlinear programming (MINLP) model minimizes a weighted sum of train operating costs, passenger waiting penalties, and cargo delays. It enforces strict first-in-first-out rules for cargo groups, ensures that no passenger waits more than two trains, and guarantees that rolling-stock counts at each depot never drop below one. Skip-stop decisions are integrated directly into the timetable: a train omits a station only when both passenger and freight stopping modes allow it, shortening running times and reducing energy use.

To solve the large-scale problem, the researchers developed a variable neighborhood search (VNS) algorithm that alternates between shaking the timetable headways and refining skip-stop patterns. Numerical experiments on a six-station synthetic line and on the 14-station Yizhuang Line show that the VNS algorithm finds near-optimal solutions in minutes, whereas the commercial solver GUROBI struggles with gaps above 30% once more than 32 trains are scheduled.

During off-peak hours (11:00 a.m.–4:00 p.m.), the flexible composition plan deployed 16 small-passenger, eight mixed, and four small-freight trains, cutting total costs by reducing operating expenses by 19.9%. Only four passengers were briefly detained, and cargo delays averaged 10 minutes. When the same logic was applied across a full day with 150 trains per direction, morning-peak cargo groups experienced longer waits, but most of parcels still arrived within 40 minutes of their desired time.

The paper notes that skip-stop strategies must be calibrated to passenger flow: skipping stations with fewer than 100 arrivals during off-peak periods avoided mass detentions, whereas careless skipping could strand hundreds. They also note that legislation in some jurisdictions still prohibits mixed passenger-freight carriages, so the decoupled composition approach offers a legally viable compromise.

Future work will explore uncertainty in demand and dwell times, extend the model to entire metro networks, and incorporate passenger attitudes toward sharing space with freight. For now, the study demonstrates that with careful scheduling, today’s metro lines can quietly carry tomorrow’s parcels without adding a single new tunnel.

The paper “Joint Optimization of Train Timetable and Rolling Stock Circulation Plan with Flexible Composition and Skip-Stop Strategies for Co-Transportation of Passenger and Freight,” is authored by Jianian He, Jianguo Qi, Lixing Yang, Zhen Di, Housheng Zhou, Chuntian Zhang. Full text of the open access paper: https://doi.org/10.1016/j.eng.2025.07.005. For more information about Engineering, visit the website at https://www.sciencedirect.com/journal/engineering.