The multi-fleet delivery problem combined with trucks, tricycles, and drones for last-mile logistics efficiency requirements under multiple budget constraints

In the increasingly competitive urban logistics delivery business field, enhancing last-mile logistics efficiency with constrained budgets is crucial for logistics companies. With the increasing adoption of emerging vehicles in last-mile logistics, neglecting the capacity of traditional vehicles may be uneconomical. This paper introduces the multi-fleet delivery problem combined with Trucks, Tricycles, and Drones (MFDP-TTD) for last-mile logistics efficiency requirements under multiple budget constraints, which represents a novel variant of the Two-Echelon Vehicle Routing Problem. Compared to the truck-drone mode, truck-tricycle mode, and the Two-Echelon Vehicle Routing Problem, by adding the collaboration of an emerging delivery vehicle (drones) and a traditional delivery vehicle (tricycle), the MFDP-TTD improves the speed of delivery of last-mile logistics more cost-efficiently. To tackle this intricate issue, this paper devises a Mixed Integer Linear Programming (MILP) model, taking into account fixed cost-related budgets and operating cost-related budgets. The model allows for the integration of diverse numbers of tricycles and drones across various fleets, with larger vehicles accommodating smaller ones to moving. In addition, some valid inequalities based on the properties of the problem are presented to accelerate the solution process. To solve this problem efficiently on a large scale, the paper proposes a multi-start improved adaptive large neighborhood search algorithm (MS-IALNS) that combines the advantages of an adaptive large neighborhood search algorithm and an ant colony algorithm. In addition, four fast feasibility-checking strategies designed based on valid inequalities are proposed. Extensive computational experiments demonstrate the validity of the MILP model and valid inequalities and the advantages of the MS-IALNS. Compared to the multi-fleet delivery problem with Trucks and Tricycles, the Two-Echelon Vehicle Routing Problem, the two-echelon city delivery mode with mobile satellites, and other potential multi-fleet collaborative delivery modes, the MFDP-TTD exhibits clear advantages in integrated time costs under same multiple budget constraints. In addition, a balanced mix of numbers of tricycles and drones within the fleet, an appropriate increase in the fixed cost-related budgets, and retrofitting of trucks and tricycles to accommodate smaller vehicles and to carry batteries for replacement are recommended.