Dynamic Type Matching

96 Pages Posted: 11 Apr 2015 Last revised: 10 Sep 2020

See all articles by Ming Hu

Ming Hu

University of Toronto - Rotman School of Management

Yun Zhou

McMaster University - Michael G. DeGroote School of Business

Date Written: September 9, 2020

Abstract

Problem definition: We consider an intermediary’s problem of dynamically matching demand and supply of heterogeneous types in a periodic-review fashion. Specifically, there are two disjoint sets of demand and supply types, and a reward for each possible matching of a demand type and a supply type. In each period, demand and supply of various types arrive in random quantities. The platform decides on the optimal matching policy to maximize the total discounted rewards, given that unmatched demand and supply may incur waiting or holding costs, and will be fully or partially carried over to the next period.
Academic/Practical relevance: The problem is crucial to many intermediaries who manage matchings centrally in a sharing economy.
Methodology: We formulate the problem as a dynamic program. We explore the structural properties of the optimal policy and propose heuristic policies. Results: We provide sufficient conditions on matching rewards such that the optimal matching policy follows a priority hierarchy among possible matching pairs. We show that those conditions are satisfied by vertically and unidirectionally horizontally differentiated types, for which quality and distance determine priority, respectively.
Managerial implications: The priority property simplifies the matching decision within a period, and the trade-off reduces to a choice between matching in the current period and that in the future. Then the optimal matching policy has a match-down-to thresholds(s) structure when considering a specific pair of demand and supply types in the priority hierarchy.

Keywords: dynamic matching, two-sided market, sharing economy, match-down-to policy, top-down matching, horizontally differentiated types, vertically differentiated types

JEL Classification: C61, D8, D9, L8, L9, O31, R4

Suggested Citation

Hu, Ming and Zhou, Yun, Dynamic Type Matching (September 9, 2020). Rotman School of Management Working Paper No. 2592622, Available at SSRN: https://ssrn.com/abstract=2592622 or http://dx.doi.org/10.2139/ssrn.2592622

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

Yun Zhou

McMaster University - Michael G. DeGroote School of Business ( email )

1280 Main Street West
Hamilton, Ontario L8S 4M4
Canada

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