Empty Car Distribution Considering Timeliness Requirement At Chinese Railways

Due to variations in freight traffic arising in daily operations, railways need to develop a distribution plan to determine the actual movements of empty cars every day. This paper investigates the daily empty car distribution problem in the Chinese railway system, which is a scheduled railway system but one where scheduled train services in the timetable are not fixed. To make current empty car distribution more market-oriented, this paper takes the timeliness requirement of empty car demands into account. A time-space network that divides the planning horizon into multiple decision-making stages is constructed to describe the process of empty car distribution. With consideration of car types and the network capacity shared by loaded and empty cars, an integer programming model is proposed to minimize total cost in the distribution process. A Lagrangian relaxation heuristic algorithm is designed to solve this problem. The effectiveness of the proposed model and algorithm is demonstrated by numerical experiments based on realistic data from the Haoji Railway, a rail freight corridor. Finally, sensitivity analyses indicate that unit shortage costs and delay penalties can be set relatively high and that many train paths should be scheduled in the timetable to ensure that stations receive empty cars on time.