Near-Optimal Pricing and Resource Allocation in a Large-Scale Service System

We study dynamic pricing and resource allocation in large-scale service systems where multiple service units serve customers who are both price and delay sensitive. Customers are segmented into classes characterized by class-specific service rates and demand functions shaped by posted prices and estimated delays. To jointly optimize revenue and delay performance, we propose a family of state-dependent greedy heuristics that (i) assign dedicated service capacities to each customer class, and (ii) dynamically set prices by solving a tractable one-step optimization problem. Despite their simplicity, these heuristics achieve a relative optimality gap of $O(n^{-2/3}\log n)$ in large-market regimes where demand scales with the number of servers n. We further establish that replacing the dedicated-capacity rule with any work-conserving allocation preserves the same order of optimality. Numerical experiments confirm the efficacy and robustness of our approach and offer additional insights, including the counterintuitive finding that congestion-based pricing can be nonmonotonic in system congestion when customers observe queue-based wait-time estimates.

Funding: This research was supported by the National Natural Science Foundation of China [Grants 72371161 and 71972133].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1073.