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We study the problem of jointly pricing and designing a smart transit system, where a transit agency (the platform) controls a fleet of demand-responsive vehicles (cars) and a fixed line service (buses). The platform offers commuters a menu of options (modes) to travel between origin and destination (e.g., direct car trip, a bus ride, or a combination of the two), and commuters make a utility-maximizing choice within this menu, given the price of each mode. The goal of the platform is to determine an optimal set of modes to display to commuters, prices for these modes, and the design of the transit network in order to maximize the social welfare of the system. In this work, we tackle the commuter choice aspect of this problem, traditionally approached via computationally intensive bilevel programming techniques. In particular, we develop a framework that efficiently decouples the pricing and network design problem: Given an efficient (approximation) algorithm for centralized network design without prices, there exists an efficient (approximation) algorithm for decentralized network design with prices and commuter choice. We demonstrate the practicality of our framework via extensive numerical experiments on a real-world data set. We moreover explore the dependence of metrics such as welfare, revenue, and mode usage on (i) transfer costs and (ii) cost of contracting with on-demand service providers and exhibit the welfare gains of a fully integrated mobility system. Funding: This work was supported by the National Science Foundation [Awards CMMI-2308750, CNS-1952011, and CMMI-2144127]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0452 . 

We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and the decision-maker must commit to an allocation for these individuals before moving on to the next round. In contrast to prior work, we consider a setting in which resources are perishable and individuals' utilities are potentially non-linear (e.g., goods exhibit complementarities). The goal is to construct a sequence of allocations that is envy-free and efficient. We design an algorithm that takes as input (i) a prediction of the perishing order, and (ii) a desired bound on envy. Given the remaining budget in each period, the algorithm uses forecasts of future demand and perishing to adaptively choose one of two carefully constructed guardrail quantities. We characterize conditions under which our algorithm achieves the optimal envy-efficiency Pareto frontier. We moreover demonstrate its strong numerical performance using data from a partnering food bank. 

We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its fleet of cars as a feeder to connect passengers to its high-capacity fleet, which operates on fixed routes. Our goal is to find the optimal set of (bus) routes and corresponding frequencies to maximize the social welfare of the system in a given time window. This generalizes the Line Planning Problem, a widely studied topic in the transportation literature, for which existing solutions are either heuristic (with no performance guarantees), or require extensive computation time (and hence are impractical for real-time use). To this end, we develop a 1-1/e-ε approximation algorithm for the Real-Time Line Planning Problem, using ideas from randomized rounding and the Generalized Assignment Problem. Our guarantee holds under two assumptions: (i) no inter-bus transfers and (ii) access to a pre-specified set of feasible bus lines. We moreover show that these two assumptions are crucial by proving that, if either assumption is relaxed, the łineplanningproblem does not admit any constant-factor approximation. Finally, we demonstrate the practicality of our algorithm via numerical experiments on real-world and synthetic datasets, in which we show that, given a fixed time budget, our algorithm outperforms Integer Linear Programming-based exact methods.