Stochastic and robust truck-and-drone routing problems with deadlines: A Benders decomposition approach

Time-definite delivery service requires efficient and punctual delivery within specified deadlines. Enhancing the service level of delivery in last-mile logistics prompted the application of a truck-and-drone cooperative system. However, the inherent uncertainty in travel time contributes to frequent service delays. To address this challenge, our study addresses the stochastic and robust truck-and-drone routing problems with deadlines, aiming to minimize service delay risk under uncertainty. We leverage the sample average approximation (SAA) and robust optimization (RO) approaches to handle uncertainty in scenarios involving both big and small datasets. Benders decomposition (BD) algorithms are developed to solve the SAA and RO truck-and-drone routing problems efficiently. Numerical experiments showcase the algorithms’ effectiveness and reveal interesting insights. These findings suggest the importance of tailoring the approach to data availability for optimizing truck-and-drone delivery under uncertainty. Furthermore, the proposed model formulations and algorithms are generalized to address truck-and-drone routing problems under more complex scenarios, such as that with uncertainty of service time, or with nonlinear objective functions.