Shared mobility systems such as car sharing 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 types, 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 part of the optimization model that formalizes how rentals are realized depending on available vehicles and arriving customers, i.e., how supply and demand match. However, this adaption results in a simplification that does 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 crucial issue of accurate optimization model formulation for freefloating systems. 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 the integrability into existing optimization models. An extensive computational study shows that the two functions’ accuracy can be up to 20 times higher than the existing approach. In addition, in a real-world price optimization 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.