Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models

• 成果类型: Article
• 署名作者: Cheung, Wang Chi; Simchi-Levi, David
• 署名单位: Agency for Science Technology & Research (A*STAR); A*STAR - Institute of High Performance Computing (IHPC); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0940
• 发表日期: 2019
• 页码: 668-692
• 关键词: algorithms; complexity; bounds

摘要

We study the classical multiperiod capacitated stochastic inventory control problems in a data-driven setting. Instead of assuming full knowledge of the demand distributions, we assume that the demand distributions can only be accessed through drawing random samples. Such data-driven models are ubiquitous in practice, where the cumulative distribution functions of the underlying random demand are either unavailable or too complex to work with. We consider the sample average approximation (SAA) method for the problem and establish an upper bound on the number of samples needed for the SAA method to achieve a near-optimal expected cost, under any level of required accuracy and prespecified confidence probability. The sample bound is polynomial in the number of time periods as well as the confidence and accuracy parameters. Moreover, the bound is independent of the underlying demand distributions. However, the SAA requires solving the SAA problem, which is #P-hard. Thus, motivated by the SAA analysis, we propose a polynomial time approximation scheme that also uses polynomially many samples. Finally, we establish a lower bound on the number of samples required to solve this data-driven newsvendor problem to near-optimality.