Two-stage Stochastic Matching with Application to Ride Hailing

We study a two-stage stochastic matching problem motivated in part by applications in online marketplaces used for ride hailing. Using a randomized primal-dual algorithm applied to a family of “balancing” convex programs, we obtain the optimal 3/4 competitive ratio against the optimum offline benchmark. These balancing convex programs offer a natural generalization of the matching skeleton by Goel et al. (2012) and may be of independent interest. Switching to the more precise benchmark of optimum online, we exploit connections to submodular optimization and use a factor-revealing program to improve the 3/4 ratio to (1 – 1/e + 1/e2) ≈ 0.767 for the unweighted and 0.761 for the weighted case. We also show it is NP-hard to obtain an FPTAS with respect to this benchmark.