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A capacitated multi-vehicle covering tour problem on a road network and its application to waste collection

In most Swiss municipalities, a curbside system consisting of heavy trucks stopping at almost each household is used for non-recoverable waste collection. Due to the many stops of the trucks, this strategy causes high fuel consumption, emissions and noise. These effects can be alleviated by reducing the number of stops performed by collection vehicles. One possibility consists of locating collection points throughout the municipality such that residents bring their waste to their most preferred location. The optimization problem consists of selecting a subset of candidate locations to place the points such that each household disposes the waste at the most preferred location. Provided that the underlying road network is available, we refer to this optimization problem as the capacitated multi-vehicle covering tour problem on a road network (Cm-CTP-R). We introduce two mixed-integer linear programming (MILP) formulations: a road-network-based formulation that exploits the sparsity of the network and a customer-based formulation typically used in vehicle routing problems (VRP). To solve large instances, we propose a two-phased heuristic approach that addresses the two subproblems the Cm-CTP-R is built on: a set covering problem to select the locations and a split-delivery VRP to determine the routes. Computational experiments on both small and real-life instances show that the road-network-based formulation is better suited. Furthermore, the proposed heuristic provides good solutions with optimality gaps below 0.5% and 3.5% for 75% of the small and real-life instances respectively and is able to find better solutions than the exact method for many real-life instances.