A three-sided network equilibrium model for on-demand food delivery services

The on-demand food delivery (OFD) industry has experienced significant growth in recent years; however, this rapid expansion has also presented numerous operational challenges for OFD platforms. While existing studies on the operational design for OFD platforms offer valuable managerial insights, few of them have considered spatial heterogeneity which greatly impacts the OFD market because many drivers deliver orders as bundles, i.e., delivering multiple orders in a trip. This work develops a network equilibrium model to capture the complex interactions among the market’s three major players, namely, customers, drivers, and merchants. We consider a game-theoretical framework in the Stackelberg leader-follower structure. As the leader, the OFD platform aims to achieve its desired objectives by leveraging two major operations: (1) the batch-matching between delivery drivers and orders, and (2) the bundling delivery dispatching which optimizes the drivers’ routes in delivering multiple orders per ride. Three market players are regarded as followers, with their behaviors depicted by utility-based discrete choice models, and their interactions on a network scope captured by the three-sided network equilibrium model. We formulate the matching and delivering problem as a mathematical program with equilibrium constraints, and develop a coordinate descent–based algorithm to solve it efficiently. Through extensive numerical studies on real-world data, we showcase the efficacy of our proposed model in evaluating the performance of various operational strategies for OFD platforms. Our analysis offers insights into the impacts of platform operations on market players from a stationary equilibrium perspective. The proposed model can be utilized as an analytical tool to assist OFD platforms and the government in high-level planning that enhances efficiency and sustainability.