Optimizing block configuration and operation protocol for extra-long metro trains

In many densely populated mega-cities around the world, metro systems are becoming overly saturated by the ever-increasing travel demand, which results in overcrowded stations, excessive delay, and unsafe anxieties among riders. The concept of extra-long trains (i.e., trains longer than station platforms) was recently proposed in the literature as a promising way to increase a metro line's capacity without additional infrastructure construction. This paper develops a general modeling framework to optimize train block configuration and operation protocols of a metro line so that extra-long trains can be used under varying demand distribution and infrastructure setting. The design problem is formulated as the integration of two coupled vehicle routing problems which simultaneously optimizes the train block configuration plan, door opening strategy, stop skipping strategy, and train dispatch schedule. This paper proposes two customized solution methods, including an adapted savings heuristic and a destroy-and-repair algorithm. A series of hypothetical examples are tested to demonstrate how the proposed solution approaches outperform an existing commercial solver even for small to moderate problem instances. Moreover, two real-world case studies, with very different demand patterns from two continents, are presented to test the effectiveness of using extra-long trains. Our results show that a metro line with extra-long train operations is capable of serving up to 20%–30% more passenger demand as compared to that with only regular trains, while at the same time producing a similar or lower passenger average travel time.