Lot size decisions in a three-level supply chain with freight rate discounts

Previous research on the joint economic lot size (JELS) problem was focused on the decisions of lot sizes and batches delivered among players in the supply chain, assuming that transportation cost was independent of shipment amounts. Nevertheless, the transportation cost accounts for a major part of supply chain cost, especially when transportation companies offer freight rate discount schedules to the supply channel, shippers are able to claim over-declared shipment to lower their transportation costs. The impact of freight rate discount is significant and should not be overlooked. In this article, we address an integrated three-level JELS problem with freight rate discounts. Managerial insights of the model are illustrated in propositions and numerical examples are provided.