The Network Transportation Problem with Volume Discount on Shipping Cost

It is assumed that the cost of goods per unit shipped from a given source to a given destination is fixed regardless of the amount shipped. But in actuality the cost is not always fixed. Volume discount however is sometimes allowed for large shipments. This project therefore seeks to develop a mathematical model using optimization techniques to bridge the gap between demand and supply by discounting so as to minimize total transportation cost. The problem that will be addressed in this study centers on the transportation problems experienced by freight companies. Volumes of goods to be shipped incur costs hence acquiring volume discounts could effectively lead to reduced shipping costs. However, there are transportation problems that hinder the materialization of improved total output through reduced costs of shipping. We shall provide algorithms and different solution procedures to the different cases that might arise. The main aim of this study is to design mathematical program that would improve the total output of freight companies especially since they deal with shipping of goods by volume. Whether maximum profit will be realized with discounts on large volumes or not means to determine the best transportation route that would lead to low transportation cost and the effective transportation of these goods. A test of this algorithm on the GALCO company limited (Kumasi, Ghana), recorded the following results as a feasible solution; x= ( x11 =15, x12 =0, x13=0, x21=5, x22=10, x23=8, x31=0, x32=0, x33=10). This will result in a total transportation cost of 1500x15 + 5000x5 + 10000x10 + 8000x8 + 10000x10= GHC 311, 500. This value as will be shown is far below the original value. These results are subject to readjustment and reassignment. Sometimes there may be different ways to model a particular problem but choosing the best approach minimizes the complicity of the problem and time to solve. Since any programming problem with constraint matrix structure the same as the transportation problem, can be regarded as a transportation type problem regardless of its physical meaning and because of its simple structure, modeling such problems as transportation problem requires much less effort to solve than modeling it differently.