Batching and Greedy Policies: How Good Are They in Dynamic Matching?

Problem definition : We study a dynamic nonbipartite stochastic matching problem, where nodes appear following a type-specific independent distribution and wait in the system for a given sojourn time. This problem is motivated by applications in ride-sharing and freight transportation marketplaces and is related to other on-demand marketplaces. Methodology/results : We study the asymptotic properties of two widely used policies, batching and greedy, by analyzing a single-pair case and then converting to the general counterpart using a fluid relaxation and randomization. Finally, we present a computational study simulating freight transportation and ride-sharing marketplaces to assess the empirical effectiveness of the policies. We show that the batching policy is asymptotically optimal with respect to the sojourn time; similarly, although a straightforward greedy policy may not be optimal, a greedy policy with randomized modifications is asymptotically optimal. Perhaps more practically relevant, both policies converge exponentially fast to approximate optimality. We also extend our model to an impatient setting in which each unmatched node leaves at the end of each period with a type-dependent probability. We show that the results for the two policies still hold under different assumptions about the nodes’ patience; roughly speaking, the batching policy requires more patient nodes than the greedy policy to remain optimal. Managerial implications : Our results suggest that managers can achieve near-optimal performance by using simple greedy or batching policies, with only a reasonably small maximum waiting time guarantee, and even in the presence of potentially impatient nodes.