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

Xiaobei Shen (), Yimin Yu () and Jing-Sheng Song ()
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Xiaobei Shen: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230052, China
Yimin Yu: Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon Tong, Hong Kong
Jing-Sheng Song: The Fuqua School of Business, Duke University, Durham, North Carolina 27708

Manufacturing & Service Operations Management, 2022, vol. 24, issue 4, 2310-2327

Abstract: 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.

Keywords: dynamic programming; inventory theory and control; service time target; inventory expediting; decomposition; coordination (search for similar items in EconPapers)
Date: 2022
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