Operating Three-sided Marketplace: Pricing and Spatial Staffing in Food Delivery Systems

Abstract:  We study a food delivery platform’s joint pricing and staffing problem under the endogenous participation of three sides—restaurants, customers, and deliverers—each with its own incentives and heterogeneous features. With deliverer pooling and nearest matching, we represent the spatial multi-server system as a state-dependent Markovian queueing model, where the service rate depends on the imbalance of all three sides due to spatial frictions. We then analyze the system’s equilibrium behavior and limiting service regimes in heavy traffic, and solve the platform’s revenue maximization problem in large systems. Our explicit approximate solutions circumvent the tedious exact optimization by exploiting large-system asymptotics and economic implications. We show that the platform’s asymptotically optimal solutions decouple into leading terms that neglect stochastic effects, and lower-order terms that reveal a balance of server utilization and service quality by a power-of-2/3 scaling (contrasting the classic square-root scaling). The main insights gleaned from our analytical results include: both the Efficiency-Driven (ED) and Quality-Driven (QD) regimes may prevail, depending primarily on customers’ delay sensitivity; the revenue-maximizing platform still generates remarkable value to all three parties as well as social welfare, thanks to deliverer pooling and spatial matching; restaurants with intermediate profit margins join the platform, reaping demand boost and logistic savings.

Biography: Zhe Liu is an Assistant Professor in the Analytics & Operations group at Imperial College Business School, Imperial College London. His research lies in revenue management, with particular interests in the operations and design of sharing economy platforms, and supply chain management, with a focus on multi-sourcing and inventory control. He is the recipient of the Finalist in George Nicholson Student Paper Competition, 2nd Place in POMS Student Paper Competition, and 2nd Place in POMS-HK Best Student Paper Competition. Zhe currently serves as the PhD director for the Analytics & Operations group. Zhe received his PhD in Operations Management from Columbia Business School and BS in Industrial Engineering from Tsinghua University.

A Zoom link is available on request by emailing business.researchub@durham.ac.uk