Dynamic vehicle routing problem with drone resupply for same-day delivery

We study a same-day delivery problem where customer orders arrive dynamically throughout the day and the service operator must determine, in real-time, whether to accept the orders and how to adjust the ongoing distribution plan. We develop a route-based Markov Decision Process and an efficient online policy to dynamically route a truck that can receive newly arrived orders along its route via drones dispatched from a depot. Numerical experiments show that our online policy has an average fill rate decrease of at most 20% over the perfect-information counterpart. Further, this online policy has a fill rate increase of up to 8% over a naïve greedy policy. We also show that drone resupply increases fill rates by up to 21% compared to a conventional truck-only resupply system. Computational times to make each decision are in the hundredths of a second, thus allowing real-time feedback to customers regarding their eligibility for same-day delivery.