Joint travel problem (JTP) is an extension of the classic shortest path problem
and relevant to shared mobility. A pioneering endeavor via supernetwork framework has
been put forward to model two-person JTP. However, it was only addressed in the static
context and with the assumption of zero waiting disutility, which resulted in no or weak
synchronization among the travelers. This paper proposes a space–time multi-state
supernetwork framework to address JTP for conducting one joint activity in the timedependent
context. Space–time synchronization and various choice facets related to joint
travel are captured systematically. Two-person JTP is first discussed in a uni-modal
transport network, and further extended to incorporate multi-modal and multi-person
respectively. Stage-wise recursive formulations are proposed to find the optimal joint
paths. It is found that JTP is a variant of Steiner tree problem by reduction and the number
of meeting/departing points has no impact on the run-time complexity in space–time multistate
supernetworks.

• Joint travel problem in space–time multi-state supernetworks