SF / Food Delivery

   This article introduces a framework for estimating the minimum fleet size of online food delivery demand using historical records of eat24.com in SF. The algorithm shows that 63 delivery vehicles can serve 1611 delivery orders on April 28, 2017. On average, one vehicle can handle 25 delivery orders. Considering the Grubhub's driver payment calculation (4$ tip for each trip), each driver would earn about $22 an hour.

   The following link shows the optimized vehicle dispatching results for each day and scenario:

  (Link) Dispatching result by vehicle

Why the minimum fleet size matters?

   As the company grows and the delivery demand increases, delivery companies are recruiting more service providers (drivers) to handle the increasing demand. Like food delivery and ridesourcing service, the gig work that provides transportation services is an attractive job for those who want a side job because of low entry barriers and flexible working hours. However, the supply of excessively more drivers than demand can cause side effects. From the driver’s perspective, the hourly income can decrease as sharing the limited orders with more drivers. Indeed, as the low wage of transportation gig workers became an issue, there has been a debate over whether gig workers as independent contractors should be reclassified as employees. That means a company is obligated to guarantee minimum wages and other benefits for drivers as employees. This pressure can create a substantial financial burden for company management as long as they have more drivers than they need. Besides that, the companies have spent plenty of incentive on recruiting drivers and keeping them. The excessive supply will also lead to an increase in out-of-service vehicles, which will adversely affect the community due to road congestion and air pollution.

Data

   This study used the historical delivery records of Eat24.com partner restaurants in San Franciso for two weeks between April 17 and April 30 in 2017. Eat24.com was a web-based food and delivery service established in the San Francisco Bay area in 2008. It was one of the major online food delivery companies in San Francisco, accounting for 22.2% of the market share as of 2017. There are 251 Eat24.com partner restaurants, and 47% (118 out of 251) of them had less than 40 deliveries for the given two weeks. It suggests that many restaurants have difficulty in operating their delivery resources. These restaurants may not have provided delivery services until the online delivery platform was introduced. Many of the partner restaurants gather together in the northwest area, from Mission to North Beach. The delivery demand through Eat24.com is more concentrated on weekends than on weekdays. On weekdays, the restaurants served more deliveries on Friday and fewer deliveries on Tuesday.

The method to estimate the minimum fleet size

   Vazifeh et al. (2018) introduce a graph theory framework to estimate the minimum fleet size of taxis using a dataset of 150 million historical taxi trips taken in the city of New York. They designed a directed acyclic graph to solve the problem of finding the number of paths in the minimum path cover with O(n^2.5) time using the Hopcroft-Karp algorithm. This study adopts the basic idea of Vazifeh et al. (2018) while applying a process and assumptions that appropriate for logistics in the food delivery market.

   The object of this study is to estimate the optimal fleet size of the online food deliveries during a day by finding the minimum number of vehicles needed to serve all the delivery orders in D. To ensure the freshness of food and customer satisfaction, it is assumed that food is picked up and delivered as soon as it is ready. That is, a delivery vehicle must arrive at the restaurant on or before when food is prepared. This service design is ideal for customers because it guarantees to serve all orders and deliver them at the desired time. On the other hand, it might bring inefficiencies for the service operator and environment. Consider two consecutive delivery trips D_A and D_B served by a single vehicle, and call the trip to connect them the ‘connection trip’ and the duration of the connection trip ‘connection time’ (t_AB (=t_B^p-t_A^d)). If this time is very long, it is possible to cause connection trips that occur at distant locations or times. An unreasonably large connection time leads to inefficiencies not only for the service provider in terms of cost, including fuel consumption and driver payment during the idle time but also for society in terms of emission and traffic congestion. We will look at the trade-off between VMT(VHT) and minimum fleet size by changing the upper bound connection time (t_max).

Performance measurement

   This study measures VMT, VHT, and minimum fleet size by changing t_max every 5 minutes between 5 and 40 minutes. We added a travel duration of 10 minutes and a travel distance of 1.5 miles for each service vehicle to take into account the out-of-service trips at the beginning and end of the service. The figure shows The minimum fleet size decreases rapidly until a 20-minute threshold, and then gradually decreases. In the case of VMT and VHT, they drop at the beginning and increase after 15 minutes and 10 minutes, respectively. It results from the travel time and distance imposed on out-of-service trips for a large number of vehicles in small t_max cases. It indicates that maintaining too many vehicles would harm both the service operation and society.

   The last figure is a four-panel plot comparing the estimated minimum fleet size for t_max of 10, 20, 30, and 40 minutes. In the first two graphs (t_max of 10 and 20 minutes), the minimum fleet size (blue line) follows the shape of the demand (orange line). It implies a situation the company flexibly deploys the drivers with ample driver supply and the very low marginal cost of the vehicle. However, this may be infeasible in the current online delivery infrastructure. When t_max increases to 40 minutes, the number of drivers tend to be maintained between the lunch peak and dinner peak. It leads to a gap between the order quantity and the fleet size, which producing larger VMT and VHT. However, this option brings a significant operational improvement in terms of the fleet size. Besides, if more drivers want longer operation hours as a full-time job, the latter can be a more reasonable solution.