A Novel Exact and Heuristic Solution for the Periodic Location-Routing Problem Applied to Waste Collection

In the development of Smart Cities, efficient waste collection networks are crucial, especially those that consider recycling. To plan for the future, routing and depot location techniques must handle heterogeneous cargo for proper waste separation. This paper introduces a Mixed-Integer Linear Programming (MILP) model and a three-level metaheuristic to address the Periodic Location Routing Problem (PLRP) for urban waste collection. The PLRP involves creating routes that ensure each customer is visited according to their waste demand frequency, aiming to minimize logistical costs such as transportation and depot opening. Unlike previous approaches, this approach characterizes each type of customer considering different needs for waste collection. A total of 25 customer types were created based on mixed waste demands and visit frequencies. The proposed algorithm uses Variable Neighborhood Search (VNS) and Local Search heuristics, comprising three neighborhood generation structures. Computational experiments demonstrate that the VNS algorithm delivers solutions seven times better than exact methods in a fraction of the time. For larger instances, VNS achieves feasible solutions where the MILP model fails within the same time frame.