Modeling payment timing in multiechelon inventory systems with applications to supply chain coordination

Problem definition: How can one adapt multiechelon inventory models to capture the cash flows generated by various payment-timing contracts? What competitive inventory policy behavior arises under these various payment-timing arrangements? Academic/practical relevance: Technology advancements are increasing the variety of payment triggers between supply chain stages. However, traditional multiechelon inventory models, which were originally developed for vertically integrated systems, do not explicitly account for payments flowing up the supply chain nor issues of payment timing between stages. Methodology: We introduce an analytical modeling methodology to incorporate financial inventory costs generated by payment-timing arrangements between stages in multiechelon inventory models. We also combine these methods with established inventory theory to study competitive inventory policies in a two-echelon system. Results: Under a class of payment-timing contracts, we show how to express payment flows at each stage in terms of standard physical inventory metrics and the demand-arrival process. We also show how to calculate the average inventory costs for each stage under given inventory policies and payment-timing contracts. In the two-echelon base-stock model, we first show that the cost of decentralization under standard wholesale price contracts is significantly driven by too much inventory at the supplier; it is not exclusively driven by too little inventory at the retailer as in the selling-to-the-newsvendor literature. We show that wholesale price contracts with a type of popular consignment payment timing still leads to too little inventory at the retailer. However, we prove there exists a wholesale price contract with partial consignment timing that can achieve the centralized inventory levels at both the supplier and the retailer. Managerial implications: Researchers can leverage our methodology to incorporate the price transfers and timing aspects of contracts in multiechelon inventory models. Our insights also help managers better understand the impact of prices and payment timing on decentralized chain behavior and performance.

Duke Scholars

Author Jing-Sheng Song Fuqua School of Business