A learning and searching integration approach for same-day delivery problem with heterogeneous fleets considering uncertainty

Rising customer expectations for fast shipping, has significantly fuelled the widespread popularity of same-day delivery services. To optimise these services for dynamic and stochastic requests, employing heterogeneous fleets that include both vehicles and drones can effectively minimise the resources required for delivery. However, uncertainties in the real world, particularly in vehicle travel, adversely affect the service levels. This paper introduces a same-day delivery problem with heterogeneous fleets considering uncertain travel and service time (SDDPHF-UT). We utilise a route-based Markov decision process to formulate this problem, explicitly incorporating travel and service uncertainty into the state and action spaces. Next, we develop an adaptive optimisation approach integrating learning and searching (AILS) to solve the problem. This approach employs policy proximal optimisation and dynamic variable neighbourhood search, responsible for request assignments and vehicle route planning, respectively. These components are interdependent and collaborate to tackle the problem in a synchronised manner, enhancing adaptability to dynamic and stochastic scenarios. Computational results indicate that the AILS significantly outperforms baseline approaches, exhibiting robust generalisation across various data distributions and fleet sizes, and achieving an average service rate improvement of 7.23%. This underscores AILS' potential as a highly effective tool of optimising same-day delivery operations in the face of uncertainty.