We consider a new real-world application of vehicle routing planning in a finite time horizon. A company has a set of capacitated vehicles in some depots and must serve a set of clients. There is a frequency for each client stating how often this client must be visited. Time intervals between two consecutive visits must be the same but the visiting schedule is flexible. To get some competitive advantage, the company tries to increase its service quality. To this end, each client should be visited by one driver only. The goal is to minimize the total length of vehicles’ paths over the planning horizon under the frequency constraints and driver shift length constraints. We present an integer linear programming model for this new consistent capacitated vehicle routing problem. To find near-optimal solutions, we design the Variable Neighborhood Search metaheuristic with eleven neighborhood structures. The driver shift length and capacity constraints are penalized and included into the objective function. Empirical results for real test instances from Orenburg region in Russia with up to 900 clients and four weeks in the planning horizon are discussed.