The work is aimed towards formulating a disaster-related emergency relief supply model of humanitarian relief goods and then solving with Genetic Algorithm and a more traditional approach of Linear Programming by considering collected data of a sample relief work. The model includes surpluses and shortages of goods as variables and vehicle space as a constraint. The constraints on demand, available minimum inventory, and maximum labor level, load capacity of the vehicle, distribution center (DC) space all of which affect a relief distribution system directly used in the model. The model determines and optimizes the amount of relief supplies to be stocked, loads to be transported in each trip, labor level required, and the number of surpluses and shortages goods so that the total cost is minimized. We compared results obtained by Genetic Algorithm and Linear Programming techniques. It is found that the Genetic Algorithm has better performance than the traditional Linear Programming. Finally, a comprehensive framework for restructuring the transportation and distribution system of humanitarian relief items is provided.