A study of quantity discount pricing models with different ordering structures: Order coordination, order consolidation, and multi-tier ordering hierarchy

In this paper, we study quantity discount pricing models with different ordering structures in a system consisting of a single supplier and heterogeneous buyers. We start with the case where the ordering schedule of the buyers is not coordinated and determine the optimal parameters that minimize the joint (system) costs. Later, we consider the case where the discount policy is structured such that the buyers are encouraged to coordinate the timing of their orders. For the case of identical buyers, we show that order coordination always leads to a reduction in the system costs. However, with heterogeneous buyers, we derive the sufficiency conditions that determine when ‘order coordination’ would be preferable. A numerical example illustrating the benefit of ‘order coordination’ is also presented. Then, we consider the case when the buyers place a combined (single) order with the supplier (referred to as ‘order consolidation’). It is shown that if the supplier offers the same discounted price (the price offered when the buyers coordinate their orders), the buyers would prefer ‘order consolidation’ over ‘order coordination’. However, for the supplier, conditions derived indicate that the supplier would prefer that the buyers coordinate their orders. Finally, we consider the case of a multi-tier ordering hierarchy where only one of the buyers (for example, a major wholesaler) places an order from the supplier. The remaining buyers, in turn, place orders only from the major buyer. Optimal ordering decisions are again determined and comparisons made with the case of ‘order consolidation’.