Farbod Ekbatani

Farbod Ekbatani, Rad Niazadeh, Mehdi Golari et al.

Ride-hailing platforms increasingly rely on non-exclusive notifications-broadcasting a single request to multiple drivers simultaneously-to mitigate inefficiencies caused by uncertain driver acceptance. In this paper, the first in a two-part collaboration with Lyft, we formally model the 'Notification Set Selection Problem' for a single decision cycle, where the platform determines the optimal subset of drivers to notify for each incoming ride request. We analyze this combinatorial optimization problem under two contention-resolution protocols: 'First Acceptance (FA)', which prioritizes speed by assigning the ride to the first responder, and 'Best Acceptance (BA)', which prioritizes match quality by selecting the highest-valued accepting driver. We show that welfare maximization under both mechanisms is strongly NP-hard, ruling out a Fully Polynomial Time Approximation Scheme (FPTAS). Despite this, we derive several positive algorithmic results. For FA, we present a Polynomial Time Approximation Scheme (PTAS) for the single-rider case and a constant-factor approximation (factor 4) for the general matching setting. We highlight that the FA valuation function can be viewed as a novel discrete choice model with theoretical properties of independent interest. For BA, we prove that the objective is monotone and submodular, admitting a standard $(1 - 1/e)$-approximation. Moreover, using a polynomial-time demand oracle that we design for this problem, we show it is possible to surpass the $(1 - 1/e)$ barrier. Finally, in the special case of homogeneous acceptance probabilities, we show that the BA problem can be solved exactly in polynomial time via a linear programming formulation. We validate the empirical performance our algorithms through numerical experiments on synthetic data and on instances calibrated using real ride-sharing data from Lyft.

Farbod Ekbatani, Rad Niazadeh, Mehdi Golari et al.

Ride-hailing platforms increasingly face uncertain driver acceptance, which makes traditional one-to-one 'exclusive dispatch (ED)' less efficient: rejections and timeouts force sequential retries and lengthen rider wait times, which in turn creates friction in the marketplace. 'Non-exclusive dispatch (NED)' mitigates this friction by broadcasting a request to multiple drivers in parallel. While NED can reduce latency, it introduces new design challenges -- most notably, how to choose notification sets and how to resolve driver contention (when multiple drivers accept the same ride). In this paper -- the second in a two-part collaboration with Lyft -- we develop a theoretically grounded framework to evaluate the long-run performance and marketplace effects of transitioning from ED to NED. We bridge theory and practice by combining (i) an optimization model that formulates NED as a constrained welfare maximization problem with (ii) large-scale discrete-event simulations on proprietary Lyft traces and (iii) a stylized macroscopic equilibrium model. Across simulation and equilibrium analysis, we find that NED improves key fulfillment metrics relative to ED: it reduces match time (and hence rider reneging) while increasing both the number and the average quality of completed matches. We also quantify the speed--quality trade-off between two common contention resolution rules, 'First-Accept' and 'Best-Accept': First-Accept maximizes speed and throughput, whereas Best-Accept is required to maximize per-match quality. Finally, we show that slightly conservative notification heuristics can improve long-run efficiency by avoiding excessive locking of high-value drivers and preserving future availability.