A heterogeneous VRP which considers various capacities, fixed and variable costs was suggested in this study. The transportation cost for vehicle is composed of its fixed and variable costs incurred proportionately to the travel distance. The main objective is to minimize the total sum of transportation costs. A mathematical programming model was suggested for this purpose and it gives an optimal solution by using OPL-STUDIO (ILOG CPLEX). A genetic algorithm which considers improvement of an initial solution, new fitness function with weighted cost and distance rates, and flexible mutation rate for escaping local solution was also suggested. The suggested algorithm was compared with the results of a tabu search and sweeping method by Taillard and Lee, respectively. The suggested algorithm gives better solutions rather than existing algorithms.