Dynamic Scheduling of a Battery-Operated Queue

Abstract

This paper considers a drone delivery system that delivers packages to multiple locations, using a model that captures three distinctive features of interest: first, a battery-operated drone that can fly a limited number of distance units on a fully charged battery; second, a set of demand locations with different flight distances and service-level requirements; third, an adjustable flight speed to trade off energy efficiency for faster deliveries. By leveraging drone speed, job sequencing and admission control, the system operator strives to achieve two managerial objectives: (i) to minimize the energy- and congested-related cost, (ii) and to maximize usage of battery energy over a discharge/charge cycle. E-commerce and shipping companies worldwide are testing and launching commercial drone delivery service to residences. According to a recent study, such service is expected to grow to $100 billion market by the end of next decade. Our work focuses on improving drone delivery operations, which can reduce costs and improve user satisfaction. Focusing on the first objective, we approximate system dynamics using diffusion processes and derive an optimal control policy for the approximate system. Interpreting that policy in the context of the physical system while taking into account the second objective, we devise an implementable set of speed control, job sequencing and admission strategies. The sequencing strategy, which selects a portfolio of jobs (termed as an activity) to be accomplished within a full battery cycle, results in a win-win scenario -- it allows both objectives to be optimized simultaneously. Using the activity-based prioritization method provides opportunities to improve the overall performance of the system. Additionally, to achieve the intended job prioritization, the system operator can rely on a small set of activities that is of equal size to the number of job classes.