Dynamic and Stochastic Rematching for Ridesharing Systems: Formulations and Reductions

Two‐stage stochastic one‐to‐many driver matching for ridesharing

“…$$ This problem is commonly referred to as the expected value problem (EVP) [7]. Similarly to [15], the EVP has binary variables on the left‐hand side and may have fractional coefficients on the right‐hand side of Constraints (12). This may render the formulation too restrictive or even infeasible, which therefore requires us to also relax the integrality constraints of the $$$ y $$$ variables.…”

“…When ridesharing, we assume that riders are willing to accept travel times up to $$$ 30\% $$$ longer than individual travel times, that is, their earliest departure time is computed based on $$$ {\tau}_{\mathrm{R}}=1.3 $$$. As in [16], we estimate the true routing distance between two points with the aid of a regression model trained with OSRM routing data [21], resulting in the following formula: $$$$ d\left({u}_i,{v}_i\right)=1.57+81.91\cdotp \overline{d}\left({u}_i,{v}_i\right), $$$$ where $$$ \overline{d}\left({u}_i,{v}_i\right) $$$ is the Manhattan distance between $$$ {u}_i $$$ and $$$ {v}_i $$$.…”

“…Myopic approaches are likely to underperform approaches that explicitly acknowledge uncertainty. To the best of our knowledge, [15,16] are the only studies that address demand uncertainty in a dynamic context. [15] introduce a two-stage matching model with rematches and stochastic rider requests for ridesharing, while [16] evaluate this model within a rolling horizon framework.…”

“…To the best of our knowledge, [15,16] are the only studies that address demand uncertainty in a dynamic context. [15] introduce a two-stage matching model with rematches and stochastic rider requests for ridesharing, while [16] evaluate this model within a rolling horizon framework. Our work is inspired by these works in the sense that we consider stochastic rider requests.…”

“…We address this gap in the literature by allowing for different types of driver booking, which may be associated with different booking fees and penalties, and impact the profitability and feasibility of potential rideshares. Finally, previous studies have suggested penalties based on the response time, that is, the time of occurrence of requests and the time the match is generated (e.g., [15,29]), or penalties for riders that were not serviced [17]. However, to the best of our knowledge, no attention was given to studying penalties associated with the failure to provide a rideshare to drivers once an agreement (i.e., a booking) between the system and the drivers is established.…”