A two-echelon divisible delivery and pick up location-routing problem model with time windows and multiple collection centers

The two-echelon location- routing problem (LRP-2E) is raised by the design of transportation networks with two types of trips: first-level trips and second-level trips. First-level trips consist of one main depot and a set of satellite depots, to be located, and second-level trips include customers assigned to these satellites. In this paper, we propose a new mixed integer linear programming model, which considers divisible delivery and pick up location routing problem in two echelons defines as a two-echelon divisible delivery and pick up problem with time windows and multiple collection centers. In addition, unlike the classical two-echelon location routing problem, in which vehicles return to the depot, we consider multiple collection centers, as much as distribution centers (depots), where vehicles deliver their loaded products at the end of the trip. We also propose a new hybrid particle swarm optimization algorithm which applies heuristic approaches to construct initial solutions and search for neighbors. The computational results on a large set of instances from Prodhon benchmark show that the proposed hybrid PSO algorithm provides better result compared to SA and GA algorithms.