The response time variability problem (RTVP) is a scheduling problem that has a wide range of real-world applications in mixed-model assembly lines, multi-threaded computer systems, machine maintenance, waste collection and others. The RTVP arises whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the points at which they receive the necessary resources is minimised. The RTVP has been demonstrated to be NP-hard and heuristic and metaheuristic techniques are needed to solve large, real-life instances. The best results, on average, in the literature for the RTVP were obtained with variable neighbourhood search hybidised with multi-start. Several algorithms based on simulated annealing are proposed to solve the RTVP. An extensive computational experiment is carried out and it is shown that the solution of the RTVP is clearly improved.