Facility location, route selection and load consolidation are integrated distribution planning problems. These three decisions are of long, medium and short terms respectively. In all these three decision areas, there could be economy or diseconomy of scale involved. Of particular interests are models with single and multiple price breaks. This paper studies a heuristic based on Linear Programming (LP) relaxation for solving this integrated distribution problem. The solution approach utilizes simple transportation problems which other known heuristics in literature have also employed. However, the solution approach ensures that a reduced number of transportation problems are solved. A numerical example is presented to ensure the comprehension of the workings of the solution method. Results obtained for the first set of computational problems show little or no statistical difference in means while the second set of problems had the modified u-v method final solution better than the other methods considered. Although computation studies on a small scale was done to compare the performance of the heuristic withthe solution provided by standard optimization environment of Java Eclipse and CPLEX , large problem sizes still proof necessary to compare the runtime and objective value of each solution method.