Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models
Name
SSRN-id2615134.pdf
Description
Accepted version
Size
447.06 KB
Format
Adobe PDF
Checksum (MD5)
3dc8c914af076bd3903088a194983095
Author(s)
Cheung, Wang Chi
Simchi-Levi, David
Date Issued
May 2019
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Cheung, Wang Chi and David Simchi-Levi. "Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models." Mathematics of Operations Research 44, 2 (May 2019): 668-692.
Version
Original manuscript
Abstract
We study the classical multi-period 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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MOOR.2018.0940
