This study is inspired by a challenging logistic problem encountered in the cleaning service sector. The company wishes to solve the consistent vehicle routeing problem over a three-month planning horizon. The company has a heterogeneous vehicle fleet to guarantee multiple frequencies of visits to its customers. The objective is to minimise the number of vehicles used and the total distance travelled. This problem is a generalisation of the periodic vehicle routeing problem. We decompose the problem into two sub-problems, namely, the planning and routeing optimisation sub-problems. We construct a mathematical model for the former and a large neighbourhood search for the latter. We evaluate the performance of our approach using the results of the industrial partner and instances from the literature on problems that are closely related to our case study. Our approach is found to be effective and robust. Our results outperform the existing company's plan in terms of solution quality, and staff convenience, and speed. We also discovered new best solutions on some of the instances from the literature.