This paper proposes a discrete optimisation model and a heuristic algorithm to solve the landfill siting problem over large areas. Besides waste transport costs and plant construction and maintenance costs, usually considered in such problems, the objective function includes economic compensation for residents in the areas affected by the landfill, to combat the NIMBY (Not In My Back Yard) syndrome or, at least, reduce its adverse effects. The proposed methodology is applied to a real-scale case study, the region of Campania, Italy, where waste management is a thorny problem. Numerical results show that the proposed algorithm may be used to obtain a solution to the problem, albeit sub-optimal, with acceptable computing times, and the proposed model tends to locate landfills in sparsely populated sites.