An innovative framework integrating MILP and a parallel optimal algorithm for UAV-Enabled last-Mile delivery

Urban last-mile delivery faces scalability, cost, and environmental challenges due to truck-based systems’ congestion and emissions. This study proposes a Customer-Centric UAV Last-Mile Delivery (CULMD) framework, eliminating truck dependency by optimising UAV routing, charging infrastructure, and sequencing for sustainable urban logistics. We introduce the Parallel Optimal Algorithm with MILP (POAM), a novel approach that decomposes the problem into two sub-problems: parallelised exact combinatorial optimisation for tour and parcel allocation, and MILP-based routing. POAM leverages multi-core CPU parallelisation to solve tour allocation across multiple regions and delivery windows concurrently, ensuring global optimality while reducing runtime by 21.5% compared to the Two-Stage Model (TSM) and 16-fold compared to the Integrated Model (IM). It outperforms metaheuristics like the Artificial Lemming Algorithm (ALA) and Hybrid Genetic Algorithm with Type-Aware Chromosomes (HGATAC+) by 12% and 11% in objective value, respectively. Sensitivity analyses show a 20% increase in regions cuts runtime by 68%, and a 20% increase in UAV load capacity reduces it by 22%. The CULMD framework, powered by POAM, advances sustainable logistics by minimising costs and environmental impacts, offering scalable solutions for urban delivery systems.