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.

Equity Promotion in Public Transportation


We consider the allocation of limited resources to heterogeneous customers who arrive in an online fashion. We would like to allocate the resources “fairly”, so that no group of customers is marginalized in terms of their overall service rate. We study whether this is possible to do so in an online fashion, and if so, what a good online allocation policy is.
We model this problem using online bipartite matching under stationary arrivals, a fundamental model in the literature typically studied under the objective of maximizing the total number of customers served. We instead study the objective of maximizing the minimum service rate across all groups, and propose two notions of fairness: long-run and short-run.
For these fairness objectives, we analyze how competitive online algorithms can be, in comparison to offline algorithms which know the sequence of demands in advance. For long-run fairness, we propose two online heuristics (Sampling and Pooling) which establish asymptotic optimality in different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand). By contrast, outside all of these regimes, we show that the competitive ratio of online algorithms is between 0.632 and 0.732. For short-run fairness, we show for complete bipartite graphs that the competitive ratio of online algorithms is between 0.863 and 0.942; we also derive a probabilistic rejection algorithm which is asymptotically optimal in the total demand.
Depending on the overall scarcity of resources, either our Sampling or Pooling heuristics could be desirable. The most difficult situation for online allocation occurs when the total supply is just enough to serve the total demand, in which case an organization could try to make allocations offline instead. 
We simulate our algorithms on a public ride-hailing dataset, which both demonstrates the efficacy of our heuristics and validates our managerial insights.

Group-level Fairness Maximization in Online Bipartite Matching

We consider online resource allocation under a typical non-profit setting, where limited or even scarce resources are administered by a not-for-profit organization like a government. We focus on the internal-equity by assuming that arriving requesters are homogeneous in terms of their external factors like demands but heterogeneous for their internal attributes like demographics. Specifically, we associate each arriving requester with one or several groups based on their demographics (i.e., race, gender, and age), and we aim to design an equitable distributing strategy such that every group of requesters can receive a fair share of resources proportional to a preset target ratio. 
 We present two LP-based sampling algorithms and investigate them both theoretically (in terms of competitive-ratio analysis) and experimentally based on real COVID-19 vaccination data maintained by the Minnesota Department of Health. Both theoretical and numerical results show that our LP-based sampling strategies can effectively promote equity, especially when the arrival population is disproportionately represented, as observed in the early stage of the COVID-19 vaccine rollout.

Equity Promotion in Online Resource Allocation

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Yifan Xu

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Equity Promotion in Public Transportation

Group-level Fairness Maximization in Online Bipartite Matching

Equity Promotion in Online Resource Allocation

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