Ongoing population growth in cities and increasing waste production has made the optimisation of urban waste management a critical task for local governments. Route planning in waste collection can be formulated as an extended version of the well-known vehicle routing problem, for which a wide range of solution methods already exist. Despite the fact that real-life applications are characterised by high uncertainty levels, most works on waste collection assume deterministic inputs. In order to partially close this literature gap, this paper first proposes a competitive metaheuristic algorithm based on a variable neighbourhood search framework for the deterministic waste collection problem. Then, this metaheuristic is extended to a simheuristic algorithm in order to deal with the stochastic problem version. This extension is achieved by integrating simulation into the metaheuristic framework, which also allows a closer risk analysis of the best-found stochastic solutions. Different computational experiments illustrate the potential of our methodology. [Received: 13 January 2016; Revised: 25 April 2016; Revised: 19 September 2016; Revised: 18 October 2016; Accepted: 25 October 2016]