Matching functions for free-floating shared mobility system optimization to capture maximum walking distances

Abstract

Shared mobility systems have become a frequently used inner-city mobility option. In particular, free-floating shared mobility systems are experiencing strong growth compared to station-based systems. For both, many approaches have been proposed to optimize operations, e.g., through pricing and vehicle relocation. To date, however, optimization models for free-floating shared mobility systems have simply adopted key assumptions from station-based models. This refers, in particular, to the models’ part that formalizes how rentals realize depending on available vehicles and arriving customers, i.e., how supply and demand match. However, this adoption results in simplifications that do not adequately account for the unique characteristics of free-floating systems, leading to overestimated rentals, suboptimal decisions, and lost profits.In this paper, we address the issue of accurate optimization model formulation for free-floating systems. Thereby, we build on the state-of-the-art concept of considering a spatial discretization of the operating area into zones. We formally derive two novel analytical matching functions specifically suited for free-floating system optimization, incorporating additional parameters besides supply and demand, such as customers’ maximum walking distance and zone sizes. We investigate their properties, like their linearizability and integrability into existing optimization models. Our computational study shows that the two functions’ accuracy can be up to 20 times higher than the existing approach. In addition, in a pricing case study based on data of Share Now, Europe’s largest free-floating car sharing provider, we demonstrate that more profitable pricing decisions are made. Most importantly, our work enables the adaptation of station-based optimization models to free-floating systems.