Improved delivery policies for future drone-based delivery systems

Highlights

• Revenue and capacity decisions for drone delivery operations under demand uncertainty.

• Closed-form analytical solutions on when and how drone delivery should be offered.

• Practical insights on future drone-based delivery operations for e-commerce companies.

• Drone delivery fee and fleet size decisions through easy-to-implement policies.

Abstract

It is expected that commercial use of drones in the near future will involve delivery service operations by e-commerce companies. We consider relevant strategic and tactical decisions that these retailers will face in drone-based delivery operations, and derive policies on when to offer drone delivery, what delivery capacity to maintain, and what amount to charge for such deliveries. To this end, we develop a Markov decision process (MDP) framework, and introduce two heuristic procedures, through which near-optimal closed-form solutions can be obtained. The results are aimed at helping online retailers to determine in real time whether and to what extent to offer drone-based delivery for given product categories in different service zones. In addition, we study delivery fee structures and identify drone-based delivery pricing strategies under two widely used delivery pricing schemes. For capacity planning decisions, we describe an algorithm to identify the fleet size to utilize to fulfill uncertain demand in a given service region. We also identify structural characteristics on how these decisions and the expected profit are affected by changes in various problem parameters, which can generate generic insights on drone-based delivery operations for e-commerce companies. We find that retailers should prioritize more profitable items when allocating drone delivery capacity, and invest in adding more drones when per order opportunity costs are higher and promised delivery time thresholds are shorter. Retailers can potentially boost their net profits by increasing the effective promised delivery time threshold and/or decreasing the effective delivery delay costs and per order opportunity costs.

Introduction

Unmanned aerial vehicles (UAVs), also called drones, are expected to become a crucial part of everyday operations in many fields and industries. Several applications are already in place, such as in agricultural field analysis, crop spraying and monitoring, recreational video-taking, property and infrastructure inspections, and warehouse inventory checking (Anderson, 2017, Mazur, 2016). Such applications are expected to extend into various types of supply chain operations in the near future, specifically by playing an important role in delivery services for e-commerce companies. The Federal Aviation Administration (FAA) is in the process of developing rules and regulations for drones to fly at night and over populated areas, which should pave the way for drone-based commercial delivery services (Pasztor, 2019). As part of this process, UPS received the first authorization from the FAA to operate drones in a populated area, which is a big step towards commercial usage of drone deliveries (Black & Levin, 2019). Indications of this are also evident in moves by major online retailers and other delivery service operators. For example, Amazon has been investing significantly in its Prime Air program, which involves drone deliveries within a 30-minute time window to customers within a 15-mile radius from prospective areas where drone operations are possible. This program received approval from the FAA in 2020 (Palmer, 2020). Other leading players in this area include Google, which has been investing in a drone-delivery program named Project Wing (Kanellos, 2014), DHL through its Parcelcopter program (Bryan, 2014), Walmart (Reuters, 2020), and major e-commerce businesses Alibaba and JD.com in China which have been utilizing drones to fulfill demand in certain areas since 2016 (Harashima, 2017). Also, SF Express, the largest Chinese logistics firm, has received the first official permit to legally offer drone-based delivery services nationwide in China in March 2018 (Huang, 2018).

While specific details on drone-based delivery operations are not yet well-established, and are dependent on future government regulations, certain characteristics make this operational setting distinct when compared to traditional truck-based delivery operations. For example, drones to be used for e-commerce deliveries may deliver a small number of items per trip in a short distance, given payload weight limitations and battery capacity requirements. This is different from a regular truck-based delivery operation which involves much longer distances with a larger quantity of items. Drones can also travel at a constant high speed while trucks are vulnerable to road traffic conditions. Furthermore, drones can provide more customized delivery options, where orders can potentially be delivered to wherever the customer is located at a given time, e.g., at home, work, or on a boat. Given these types of distinctions, there exists a need for new operational approaches for the management of drone-based delivery systems to make these operations effective and efficient.

Our objective is to contribute to this emerging area by exploring several important research problems relevant to future delivery service operations using drones. More specifically, we focus on decisions involving revenue and capacity management in drone-based delivery service operations, and try to provide answers to the following research questions: Given random demand from different service zones for different product categories, when and at what rate should an online retailer accept drone-based delivery orders for each product category and service zone? Moreover, considering all relevant costs of operating a drone-based delivery operation, what are some optimal delivery fee policies? And finally, what is the optimal fleet size for a retailer, given the demand and cost structure in a service region? To answer these questions, we develop dynamic programming models to capture the specifics of the problem framework and identify policies that can help retailers make better decisions in drone-based delivery operations. We demonstrate the value of these policies through detailed numerical analyses, where we utilize representative data to improve drone delivery order acceptance policies, delivery fee structures, and system capacity decisions.

The remainder of this paper is organized as follows. In Section 2, we describe the relevant literature on drone-based deliveries and order acceptance decisions in various applications, while also highlighting the specific contributions and practical implications of our study. In Section 3, we describe the problem we investigate, and present the overall optimization model. In Section 4, we develop two practical heuristic solution approaches. In Section 5, we apply the results from the heuristics to study delivery fee structures and capacity management decisions for drone-based delivery. In Section 6, we perform numerical studies based on representative retail data and compare the performances of the two heuristics. In Section 7, we perform detailed numerical tests to investigate how the proposed policies vary with different parameter settings and to study some potential extensions, where we emphasize and provide practical implications for future drone-based operations for retailers. Finally, we summarize our findings and conclude the paper in Section 8.