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

Abstract

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.

Assessing the Effects of Limited Curbside Pickup Capacity in Meal Delivery Operations for Increased Safety during a Pandemic

“…The meal delivery problem as a problem class is rather new with the first publications dedicated to this topic coming as recently as 2018 (4)(5)(6)(7)(8)(9). These studies provide problem formulations and develop operational strategies for order assignment, order bundling, and driver shift scheduling, among other areas, with an aim of improving delivery efficiency and, therefore, company revenues.…”

“…Estimated distributions and key parameters for these distributions were set as follows. Pickup handling, dropoff handling, delivery job acceptance, and travel times follow uniformly distributions: ;U [1,8], ;U [1,4], ;U[0,2], and ;U[ 0:9t, 1:2t ], respectively. Delivery job acceptance probability was set to 0.9 and order preparation times were fit to a normal distribution, ;N( m = d r , s = d r 5 ): The problem, thus, is to serve all incoming orders with the aim of minimizing the weighted sum of travel times and early or late arrival times of drivers to restaurants for pickup, while meeting curbside space restriction constraints in an environment in which customer orders arrive dynamically and drivers can check in and out of work from any location in the delivery region at will.…”

“…Reviews of literature addressing classical pickup-and-delivery problems and dynamic extensions are given in Parragh et al and Berbeglia et al, respectively ( 2 , 3 ). Newer studies are included in Ulmer et al ( 4 ).…”

Hybrid evolutionary optimization for takeaway order selection and delivery path planning utilizing habit data

“…Shan et al [29] proposed a deep reinforcement learning approach combined with Dijkstra's algorithm for food delivery route planning, which can provide accurate navigation when road network information is unknown. Ulmer et al [39] studied a stochastic PDPTW for delivering food from a set of restaurants to ordering customers. They presented an anticipatory customer assignment policy, which is able to improve service significantly for all stakeholders.…”

An effective matching algorithm with adaptive tie-breaking strategy for online food delivery problem

“…The authors formulated this problem into several MILP models solved by Gurobi [7] and proposed a dynamic programming algorithm [8]. Ulmer et al [33] presented an anticipatory customer assignment policy to deal with the stochasticity from the arrival time of new orders and the ready time of restaurants. Yu et al [40] derived the lower bounds of online pickup and delivery problem and proposed two online dispatching algorithms.…”