Modeling quantity discounts under general price-sensitive demand functions: Optimal policies and relationships

Abstract

This paper presents models for determining optimal all-unit and incremental quantity discount policies and investigates the effect of quantity discounts on increasing demand and ensuring pareto-efficient transactions under general price-sensitive demand functions. The paper develops optimal quantity discount policies, investigates their interrelationships and their benefits to both the supplier and the buyer, and gains managerial insights for the scenarios of maximizing the supplier's profit and the joint profit. We develop simple and efficient solution approaches for determining the all-unit and the incremental optimal decision policies for general price-sensitive demand functions. We have three main findings. First, with price-sensitive demand there are two incentives in offering quantity discounts: increasing demand and ensuring pareto-efficient transactions. In most cases, increasing demand dominates in justifying the offering of quantity discounts. Second, using a single lot size associated with all efficient transactions as with the constant demand case does not hold with the price-sensitive demand case. Third, the optimal all-unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in benefiting both the supplier and the buyer.