Abstract
This article studies how to dimension and control at the system level a fleet of autonomous aerial vehicles delivering goods from depots to customers. Customer requests (jobs) arrive according to a space-time stochastic process. We compute a lower bound for the infrastructure expenditure required to achieve a certain expected delivery time. It is shown that job assignment policies can exhibit a tipping point behavior: One vehicle makes the difference between almost optimal delivery time and instability. This phenomenon calls for careful dimensioning of the system. We thus demonstrate the trade-off between financial costs and service quality. We propose a policy that assigns each incoming job to the vehicle that will do the job faster than other ones, seeking to minimize the overall workload in the system in the long term. This policy is scalable with the number of depots and vehicles, performs optimal in low load, and works well up to high loads. Simulations suggest that it stabilizes the system for any load if the number of vehicles per depot is sufficient.
Highlights
vehicle routing problems (VRPs) have a broad diversity of additional requirements and operational constraints affecting the construction of the optimal set of routes
For company-specific parameter values, a diagram like Fig. 6 translates the insights derived in the subsection above into the monetary domain. It relates a company’s expenditure I for depots and vehicles to average delivery time T. The purpose of such a plot is to provide decision making support for companies that set up an airborne delivery system equipped with small unmanned aerial vehicles (UAVs)
It was found that job assignment policies can experience a tipping point behavior: A stable system could immediately become unstable if one vehicle fails
Summary
We introduce an approach to dimension the system (How many vehicles and depots are needed for a certain area?) and propose and analyze policies for job assignment (How to assign customer requests to vehicles to minimize the expected delivery time?). FJWδ can stabilize the system for almost all arrival rates, as long as the number of vehicles per depot is sufficient This finding yields a connection between dimensioning and control of the system. The setup of the system (number of depots and vehicles) shapes its financial costs and, in conjunction with the job assignment policy, the service quality provided to the customers for which they are willing to pay. All results and discussions related to FJW policies are novel
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