Supply Chain Coordination Under Demand Uncertainty: Analysis of General Continuous Quantity Discounts

Abstract

Quantity discount (QD) contracts are commonplace in theory and practice with different complexities. There exist two classes of QD contracts: continuous versus discrete schemes. Under continuous QD schemes, a general differentiable wholesale-price function is considered as a decreasing function of ordering quantities while in discrete QD schemes there is a price list with decreasing wholesale-price levels such as all-unit QD or incremental QD contracts. In this paper, we aim to analyze the structure of general continuous quantity discounts to coordinate a two-tier supply chain with additive demand uncertainty. We demonstrate sufficient coordination conditions based on joint-optimization of ordering and pricing decisions. Considering prerequisites for achieving coordination, the specific case of linear QD contract is analyzed and some applicable non-linear continuous QD schemes are introduced. Moreover application of such non-linear schemes is discussed for implementation of QDs (continues and discrete schemes) in real cases.