Transportation Type Models with Quantity Discounts

It is known to be real that the per unit transportation cost from a specific supply source to a given demand sink is dependent on the quantity shipped, so that there exist finite intervals for quantities where price breaks are offered to customers. Thus, such a quantity discount results in a nonconvex, piecewise linear functional. In this paper, an algorithm is provided to solve this problem. This algorithm, with minor modifications, is shown to encompass the incremental quantity discount and the fixed charge transportation problems as well. It is based upon a branch-and-bound solution procedure. The branches lead to ordinary transportation problems, the results of which are obtained by utilizing the cost operator for one branch and rim operator for another branch. Suitable illustrations and extensions are also provided.