How Meituan Uses Gaussian Mixture Models to Optimize Food Delivery: New Research from Tsinghua University

Research Background: The Challenge of Uncertainty in Food Delivery

In today’s rapidly evolving on-demand delivery industry, food delivery platforms face massive order scheduling decisions every day. Platforms like Meituan, Deliveroo, and DoorDash must complete the entire process from order acceptance to dispatch and delivery within minutes. However, the real world is full of uncertainties—fluctuations in restaurant preparation times, changes in rider traffic conditions, and customer reception delays all make delivery optimization exceptionally complex.

Among these variables, service time (the duration from a rider’s arrival at the restaurant to pickup and departure) is a critical yet difficult-to-predict factor. Traditional methods often estimate service time using fixed values or simple statistics, but this ignores its inherent randomness and multi-modal distribution characteristics. A research team from Tsinghua University’s Department of Automation, in collaboration with Meituan, has proposed a Gaussian Mixture Model-based approach to service time modeling, offering a new solution to this problem.

Methodology: How Gaussian Mixture Models Capture Service Time Complexity

A Gaussian Mixture Model (GMM) is a probabilistic model that assumes data is composed of multiple Gaussian distributions (normal distributions) combined together. Think of it this way: food delivery service times may exhibit different distribution patterns under different scenarios—weekday lunch peaks follow one pattern, weekend dinners another, and rainy days yet another. GMM can automatically identify these hidden patterns and assign a weight to each one.

The research team transformed the service time distribution estimation problem into a clustering problem. Specifically, they learned the GMM parameters by determining the probability that each data point belongs to each component (i.e., each cluster). The advantage of this approach is that it doesn’t require pre-assuming that service time follows a specific distribution; instead, it lets the data “speak for itself” and automatically discovers the most suitable distribution form.

Core Algorithm: Four Innovations of the Hybrid Estimation of Distribution Algorithm

To efficiently solve for GMM parameters, the research team proposed a Hybrid Estimation of Distribution Algorithm (HEDA). This algorithm incorporates four key innovations: