Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights

• 成果类型: Article
• 署名作者: Chen, Li; Song, Jing-Sheng; Zhang, Yue
• 署名单位: Cornell University; Duke University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1615
• 发表日期: 2017
• 页码: 1231-1249
• 关键词: state-dependent demands; base-stock policies; models; optimality; approximations; DECOMPOSITION

摘要

We study Inventory control of serial supply chains with continuous, Markov-modulated demand (MMD). Our goal is to simplify the computational complexity by resorting to certain approximation techniques, and, in doing so, to gain a deeper understanding of the problem. First, we perform a derivative analysis of the problem's optimality equations and develop general, analytical solution bounds for the optimal policy. This leads to simple-to-compute near-optimal heuristic solutions, which also reveal an intuitive relationship with the primitive model parameters. Second, we establish an MMD central limit theorem under long replenishment lead time through asymptotic analysis. We show that the relative errors between our heuristic and the optimal solutions converge to zero as the lead time becomes sufficiently long, with the rate of convergence being the square root of the lead time. Third, we show that, by leveraging the Laplace transform, the computational complexity of our heuristic is superior to the existing methods. Finally, we provide the first set of numerical study for serial systems under MMD. The numerical results demonstrate that our heuristic achieves near-optimal performance even under short lead times and outperforms alternative heuristics in the literature. In addition, we observe that, in an optimally run supply chain under MMD, the internal fill rate can be high and the demand variability propagating upstream can be dampened, both different from the system behaviors under stationary demand.