Erratum: “Dynamic Pricing and Matching for Two-Sided Queues”

In Varma et al. (2023) [Dynamic pricing and matching for two-sided queues. Operations Research 2023;71(1):83–100], Theorem 2 may not hold under the max-weight matching policy. In particular, the proof of Lemma 2 is incorrect. Specifically, the original proof did not carefully bound the Lagrange multipliers of the fluid problem. We propose a modified version of the max-weight matching policy and provide proof of Lemma 2 and Theorem 2 under this policy. When the complete resource pooling (CRP) condition (Varma et al. 2023, Condition 2) is satisfied, the modified max-weight matching policy is the same as the max-weight matching policy, and therefore, the conclusion of Varma et al. (2023, Theorem 2) continues to hold under the max-weight matching policy. When the CRP condition is not satisfied, we conduct simulations to show that the conclusion of Varma et al. (2023, Theorem 2) may not hold under the max-weight matching policy but continues to hold under the modified max-weight matching policy. We further provide clarifications for several technical caveats that were glossed over.

Funding: This work was supported by the National Science Foundation [Grants EPCN-2144316 and CMMI-2140534].