Planning for modular-vehicle transit service system: Model formulation and solution methods

Document Type

Journal Article

Publication Date


Subject Area

place - asia, place - urban, mode - other, economics - operating costs, ridership - demand, infrastructure - station, infrastructure - vehicle, operations - capacity, operations - performance, planning - methods


Modular-vehicle transit service, Location, Vehicle formation, MILP reformulation, Surrogate optimization


This paper studies the optimal planning of public transit services with modular vehicles. In the modular service operation, the vehicle is comprised of smaller modular units/pods, which can be assembled/dissembled at some specially designed transit stations. The planning decisions are to determine the locations of the specially constructed stations enabling station-wise assembling/dissembling of modular units. Meanwhile, the capacity of these stations, i.e., the maximum number of modular units that can be accommodated, will also be determined. The optimal vehicle formation at these stations will be considered for the multi-period passenger demand to evaluate the system performance. Aiming to minimize the total cost of the operator and passengers, we formulate this problem into a mixed-integer nonlinear program (MINLP). Two solution methods are proposed to solve the problem. One is to transform the formulated MINLP into a mixed-integer linear program (MILP) using various linearization reformulation techniques, which can be solved by using many existing solution methods for MILP. Despite that this method ensures exact solutions, its solution efficiency is compromised. To solve a practical large-size problem, we propose another solution method applying surrogate model-based optimization approaches. A case study in the context of a proposed Singapore dynamic autonomous road transit (DART) line is conducted. Numerical experiments have been carried out to test the validity of the model formulation and the solution performance of the proposed solution methods. The advantage of the modular-vehicle transit service in significantly reducing the operating cost and passengers’ travel time costs has been demonstrated as well. This study offers the public transportation planners a useful tool for determining optimal operation strategies for the future transit service system with modular vehicles.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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