Joint Ground and Aerial Package Delivery Services: A Stochastic Optimization Approach

Abstract

Unmanned aerial vehicles (UAVs), also known as drones, have emerged as a promising mode of fast, energyefficient, and cost-effective package delivery. A considerable number of works have studied different aspects of drone package delivery service by a supplier, one of which is delivery planning. However, existing works addressing the planning issues consider a simple case of perfect delivery without service interruption, e.g., due to accident which is common and realistic. Therefore, this paper introduces the joint ground and aerial delivery service optimization and planning (GADOP) framework. The framework explicitly incorporates uncertainty of drone package delivery, i.e., takeoff and breakdown conditions. The GADOP framework aims to minimize the total delivery cost given practical constraints, e.g., traveling distance limit. Specifically, we formulate the GADOP framework as a three-stage stochastic integer programming model. To deal with the high complexity issue of the problem, a decomposition method is adopted. Then, the performance of the GADOP framework is evaluated by using two data sets including Solomon benchmark suite and the real data from one of the Singapore logistics companies. The performance evaluation clearly shows that the GADOP framework can achieve significantly lower total payment than that of the baseline methods which do not take uncertainty into account.

Multi-Objective Optimization for Drone Delivery

“…The constraints in (11) and (12) ensure that the customers have the different serving order if they are served by the same drone. These constraints are similar to those in [3].…”

Study of the Problem of Optimal Maintenance of Unmanned Aerial Vehicles in Conditions of a Shortage of Vehicles

“…There is the task, the purpose of which is the express cargo delivery (in cases, case boxes) to N destinations. One of the tasks is to determine the optimal ratio between the amount of UAVs and the fuel (power) reserves used by the UAVs [1].…”

“…Let's try to develop an effective method of algorithms for solving the problem of optimal coverage of a special graph with restriction chains, chain length and total costs for the express car-Engineering go delivery [1]. The specificity of graph CZ reveals itself in the fact that the cost of the movement between the peaks is determined by the solution of the tasks of servicing the optimal routes in the auxiliary graph of transitions CZ [2].…”

“…In graph theories, the problem of constructing a chain with a maximum length can be formulated in the following way. Let ( ) 1 , , , G AO AX A AD be a bound oriented graph, where AO is the set of vertices of graph 1 , G such that 0 ; ∈ AO x AX -the set of vertices in graph 1 , G such that ; ∈ AO x AD -the set of the arcs of graph 1 , G which is necessarily a part of chain . ∈ AO BX The arcs ∈ ad AD of the graph have received the additive constraints ( ) 1 ,..., , = t V V V which correspond to the increments of the phase coordinates necessary for the transition from one vertex to another.…”

“…In this article, the main attention has been paid to the development of the method for solving the problem of determining the weight of the arcs of graph 1 G and the task of building a chain, which part is also the docking task.…”