Based Approximation for Series Inventory Systems
by Professor Sean Zhou
The author studies inventory management of an infinite-horizon, series system with multiple stages. Random demand with unknown distribution occurs at the most downstream stage. Each stage incurs inventory holding cost while the most downstream stage also incurs demand backlogging cost when it experiences inventory shortage. The objective is to minimize the expected total discounted cost over the planning horizon.
The sample average approximation (SAA) method is applied to obtain a heuristic policy (SAA policy) using the empirical distribution function constructed from a demand sample. An upper bound of sample size (viz., distribution-free bound) is derived that guarantees that the performance of the SAA policy be close to the optimal policy under known demand distribution with high probability. This result is obtained by first deriving a separable and tight cost upper bound of the whole system that depends on (given) echelon base-stock levels and then showing that the cost difference between the SAA and optimal policies can be measured by the distance between the empirical and the underlying demand distribution functions.
A lower bound of sample size is also provided that matches the upper bound. Furthermore, when the demand distribution is continuous and has an increasing failure rate (IFR), a tighter sample size upper bound (viz., distribution-dependent bound) is derived.
Both distribution-free and distribution-dependent bounds for the newsvendor problem, a special case of our series system, improve the previous results. In addition, it is shown that both bounds increase polynomially as the number of stages increases. The results to finite-horizon series systems are also extended. This is joint work with Kairen Zhang (Southeast University), Xiangyu Gao (CUHK), and Zhanyue Wang (Nankai University).
Sean Zhou is Professor and Chair of Department of Decisions, Operations and Technology, CUHK Business School, and Professor in Department of Systems Engineering and Engineering Management (by courtesy), at The Chinese University of Hong Kong (CUHK). He has held visiting positions at National University of Singapore and University of Toronto. He received his Ph.D. in Operations Research from North Carolina State University. His main research interests are inventory management, pricing, sustainable operations, data-driven supply chain optimization, and operations and marketing interface. He serves as Area Editor (Inventory and Supply Chain Optimization) of OR Letters, Senior Editor of POMS, and Associate Editor of various journals including Naval Research Logistics and Service Science.
