Shiming Deng, Professor, School of Management, Huazhong University of Science and Technology

Yu-hong Dai, Professor

Bootstrap-based Statistical Analysis for Multi-period Data-driven Inventory Models with Seasonal Demand

20:00-21:00 February 9 ( Thursday ) ，Tencent Meeting ID: 891-663-752

We study multi-period inventory control systems in which managers face seasonal demands with unknown distributions and make inventory decisions based on past demand data. It can be shown that a data-driven (S, s) policy converges to the true optimal policy under some regularity conditions. However, analyzing the statistical properties, such as the distribution and confidence interval/region of the estimated policy parameters and total costs, is much harder due to the following two challenges: 1) the sample costs evaluated under the estimated optimal policy are no longer independent of each other and thereby the standard CLT does not apply; and 2) the recursive nature of dynamic programming induces propagation of the estimation errors backward in time. We propose bootstrap-based methods to overcome the two challenges and prove their validity for analyzing the statistical properties of the data-driven solutions. Numerical experiments show that our methods provide better estimates of confidence intervals than existing methods, especially when sample size is small. Our methods can also be used to estimate the sample sizes for target confidence intervals. The sample sizes computed by our methods are much more accurate than those estimated using the best bound from existing literature.