The Restaurant Meal Delivery Problem: Dynamic Pickup and Delivery with Deadlines and Random Ready Times

We consider a stochastic dynamic pickup and delivery problem in which a fleet of drivers delivers food from a set of restaurants to ordering customers. The objective is to dynamically control a fleet of drivers in a way that avoids delays with respect to customers’ deadlines. There are two sources of uncertainty in the problem. First, the customers are unknown until they place an order. Second, the time at which the food is ready at the restaurant is unknown. To address these challenges, we present an anticipatory customer assignment (ACA) policy. To account for the stochasticity in the problem, ACA postpones the assignment decisions for selected customers, allowing more flexibility in assignments. In addition, ACA introduces a time buffer to reduce making decisions that are likely to result in delays. We also consider bundling, which is the practice of assigning multiple orders at a time to a driver. Based on real-world data, we show how ACA is able to improve service significantly for all stakeholders compared with current practice.