  The potential of integrating public transit with ridesharing includes shorter
travel time for commuters and higher occupancy rate of personal vehicles and
public transit ridership. In this paper, we describe a centralized transit
system that integrates public transit and ridesharing to reduce travel time for
commuters. In the system, a set of ridesharing providers (drivers) and a set of
public transit riders are received. The optimization goal of the system is to
assign riders to drivers by arranging public transit and ridesharing combined
routes subject to shorter commuting time for as many riders as possible. We
give an exact algorithm, which is an ILP formulation based on a hypergraph
representation of the problem. By using the ILP and the hypergraph, we give
approximation algorithms based on LP-rounding and hypergraph matching/weighted
set packing, respectively. As a case study, we conduct an extensive
computational study based on real-world public transit dataset and ridesharing
dataset in Chicago city. To evaluate the effectiveness of the transit system
and our algorithms, we generate data instances from the datasets. The
experimental results show that more than 60% of riders are assigned to drivers
on average, riders' commuting time is reduced by 23% and vehicle occupancy rate
is improved to almost 3. Our proposed algorithms are efficient for practical
scenarios.
