  There are many news articles reporting the obstacles confronting
poverty-stricken households in access to public transits. These barriers create
a great deal of inconveniences for these impoverished families and more
importantly, they contribute a lot of social inequalities. A typical approach
addressing the issue is to build more transport infrastructure to offer more
opportunities to access the public transits especially for those deprived
communities. Examples include adding more bus lines connecting needy residents
to railways systems and extending existing bus lines to areas with low
socioeconomic status. Recently, a new strategy is proposed, which is to harness
the ubiquitous ride-hailing services to connect disadvantaged households with
the nearest public transportations. Compared with the former
infrastructure-based solution, the ride-hailing-based strategy enjoys a few
exclusive benefits such as higher effectiveness and more flexibility.
  In this paper, we propose an optimization model to study how to integrate the
two approaches together for equity-promotion purposes. Specifically, we aim to
design a strategy of allocating a given limited budget to different candidate
programs such that the overall social equity is maximized, which is defined as
the minimum covering ratio among all pre-specified protected groups of
households (based on race, income, etc.). We have designed a linear-programming
(LP) based rounding algorithm, which proves to achieve an optimal approximation
ratio of 1-1/e. Additionally, we test our algorithm against a few baselines on
real data assembled by outsourcing multiple public datasets collected in the
city of Chicago. Experimental results confirm our theoretical predictions and
demonstrate the effectiveness of our LP-based strategy in promoting social
equity, especially when the budget is insufficient.
