Pricing and Optimization in Shared Vehicle Systems: Queuing Models and Approximation Algorithms



Daniel Freund

Monday, March 6th, 2017
4:00pm 122 Gates Hall




Designing and operating shared vehicle systems (bike-sharing/car-sharing/ride-sharing) is more challenging compared to other resource allocation settings due to complex network externalities: in such systems, altering prices in any location affects future supply throughout the system within very short timescales. Such externalities are well captured by steady-state Markov chain models, and hence these are widely used for shared vehicle systems in academic research and industry. 
However, using such models to design pricing policies is computationally difficult since the resulting optimization problem is high-dimensional and non-convex. 

We develop a general framework for designing pricing policies in such systems, based on a novel convex relaxation which we term elevated flow relaxation. Our approach provides the first efficient algorithms with rigorous approximation guarantees for a wide range of objective functions (throughput, revenue, welfare).

For any shared vehicle system with n stations and m vehicles, we show that a simple pricing policy with an approximation ratio of 1+(n-1)/m can be efficiently computed via our relaxation. This guarantee is particularly meaningful when m/n, the average number of vehicles per station is large, as is often the case in practice.

The simplicity of our approach also allows us to extend it to more complex settings. Apart from pricing, shared vehicle systems enable other control levers for modulating demand and supply: rebalancing empty vehicles, redirecting riders to nearby vehicles, etc. Our approach yields efficient algorithms with the same approximation guarantees for all these problems, and in the process, obtains as special cases several existing heuristics and asymptotic guarantees. We also extend our approach to obtain bi-criterion guarantees in multi-objective settings; we illustrate this with the example of Ramsey pricing.

Joint work with Sid Banerjee and Thodoris Lykouris