While transporting some material a circular way of the transportation is usually applied. Usually due to some capacity or time constraints or other reasons it is necessary to use more routes (i.e. more vehicles, or one vehicle must go out from its home place more times). This case is called the vehicle routing problem and there exist many types of this task because of the variety of reasons causing the necessity of use more than one route. Practically all the vehicle routing problems belong among the so-called NP-complete or NP-hard problems. This means that there exists no effective method which would succeed in finding a precise theoretical optimum for them. In such tasks, we can employ different approximation methods which provide us with solutions similar to a theoretical optimum and acceptable as an economic optimum. In practice, however, companies seldom pay enough attention to dealing with such problems, especially if transportation is not their principal work load and if it concerns a transportation task of a medium size. This article presents a case study of NOPEK Bakery in Vysoké Mýto. It demonstrates the effectiveness of the approximation method during the planning of the bakery products delivery to its customers. By the optimization of one of the so-called “fast deliveries“, we succeeded in the reduction of the number of vehicles needed for the delivery – about 18% – which turned out necessary. Similar savings of all “fast deliveries” in the company may lead to the reduction of tenure price (tenure fixture) by 17 mil. CZK. At the same time the profit will increase by 0.6 mil. CZK and profitability will go up by 2.5%. We also managed to ensure a balanced use of the vehicles. This made it possible for the bakery to deliver the goods to its customers in deadlines that they found more convenient.