A two-phase optimization model for the demand-responsive customized bus network design

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, mode - demand responsive transit, planning - methods, planning - network design, planning - travel demand management, ridership - demand, ridership - behaviour


Customized bus, Demand-responsive transit, Hierarchical decision-making problem, Dynamic insertion, Branch-and-bound algorithm


This paper proposes a new optimization model for the network design problem of the demand-responsive customized bus (CB). The proposed model consists of two phases: inserting passenger requests dynamically in an interactive manner (dynamic phase) and optimizing the service network statically based on the overall demand (static phase). In the dynamic phase, we propose a hierarchical decision-making model to describe the interactive manner between operator and passengers. The CB network design problem is formulated in a mixed-integer program with the objective of maximizing operator’s revenue. The CB passenger’s travel behavior is measured by a discrete choice model given the trip plan provided by the operator. A dynamic insertion method is developed to address the proposed model in the dynamic phase. For the network design problem in the static phase, the service network is re-optimized based on the confirmed passengers with strict time deviation constraints embedded in the static multi-vehicle pickup and delivery problem. An exact solution method is developed based on the branch-and-bound (B&B) algorithm. Numerical examples are conducted to verify the proposed models and solution algorithms.


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


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