Plan Your System and Price for Free: Fast Algorithms for Multimodal Transit Operations

Abstract

We study the problem of jointly pricing and designing a smart transit system, where the 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 to travel between origin and destination (e.g., a direct car trip, a bus ride, or a hybrid combination of the two), and commuters make the utility-maximizing choice within this menu, given the price of each trip option. The goal of the platform is to determine the optimal set of trip options (modes) to display to commuters, the 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 bi-level 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) for decentralized network design with prices and commuter choice. We demonstrate the practicality of our framework via extensive numerical experiments on a real-world dataset, in which we show the efficiency of pricing algorithm. We moreover explore the dependence of system welfare, revenue, and demand on transfer costs, as well as the cost of contracting with the on-demand service provider, and exhibit the welfare gains from a fully integrated mobility system.

Keywords: smart transit, pricing, network design