Optimal Policies for a Multi-Echelon Inventory Problem with Service Time Target and Expediting

Problem definition: We study the optimal inventory ordering, expediting, and allocation decisions in a multiechelon supply chain over a finite horizon, in which customer orders are quoted with a fixed fulfillment time window, termed the service time target (STT). Academic/practical relevance: Service time target is commonly used as a marketing strategy to increase customer satisfaction and strengthen firms' competitive edge. However, how to efficiently manage a multistage supply chain to meet the target has received relatively scant attention in the literature. Our study fills this gap. Methodology: We use dynamic programming to characterize the optimal policy. Results: We show that an echelon base stock policy and a rationing policy are optimal for inventory ordering and inventory allocation/expediting, respectively. We also develop a polynomial-time algorithm to compute the optimal policy. To derive these results, we uncover a new functional property named the decomposable of degree 2 property, which is a nontrivial generalization of the celebrated Clark-Scarf decomposition. This property further allows us to derive induced penalty and compensation to coordinate a decentralized serial system with STT and expediting. Managerial implications: Our result provides an efficient decision tool for managing centralized and decentralized serial supply chains with STT and expediting. Our model can be used to quantify the tradeoff between marketing and operational decisions, such as the impact of a marginal reduction in STT on system cost and expedition frequency, as explored in our numerical studies.

Automated summary

This paper studies the optimal inventory ordering, expediting, and allocation decisions in a multiechelon supply chain with a fixed fulfillment time window. The results show that echelon base stock policy and rationing policy are optimal for inventory ordering and allocation/expediting, respectively. A polynomial-time algorithm is also developed to compute the optimal policy. The study fills a gap in the literature and provides an efficient decision tool for managing centralized and decentralized supply chains.