Fleet Size and Mix Vehicle Routing Problem is considered in order to optimize the distribution of the tourists who have traveled between the airport and the hotels in the shortest distance by using the minimum cost. The initial solution space for the related methods are formed as a combination of Savings algorithm, Sweep algorithm and random permutation alignment. Then, two well-known solution methods named as Standard Genetic Algorithms and random search algorithms are used for changing the initial solutions. Computational power of the machine and heuristic algorithms are used instead of human experience and human intuition in order to solve the distribution problem of tourists coming to hotels in Alanya region from Antalya airport. For this case study, daily data of tourist distributions performed by an agency operating in Alanya region are considered. These distributions are then modeled as Vehicle Routing Problem to calculate the solutions for various applications. From the comparisons with the decision of a human expert, it is seen that the proposed methods produce better solutions with respect to human experience and insight. Random search method produces a solution more favorable in terms of time. As a conclusion, it is seen that, owing to the distribution plans offered by the obtained solutions, the agencies may reduce the costs by achieving savings up to 35%. [ABSTRACT FROM AUTHOR]